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Topic 6: Consumer Theory
6.1 The Budget Line
Learning objectives.
- Understand budget lines
- Explain price ratios
- Recreate budget lines after prices and income changes
The Budget Line
To understand how households make decisions, economists look at what consumers can afford. To do this, we must chart the consumer’s budget constraint. In a budget constraint, the quantity of one good is measured on the horizontal axis and the quantity of the other good is measured on the vertical axis. The budget constraint shows the various combinations of the two goods that the consumer can afford. Consider the situation of José, as shown in Figure 6.1a. José likes to collect T-shirts and movies.
In Figure 6.1a, the number of T-shirts José will buy is on the horizontal axis, while the number of movies he will buy José is on the vertical axis. If José had unlimited income or if goods were free, then he could consume without limit. But José, like all of us, faces a budget constraint . José has a total of $56 to spend. T-shirts cost $14 and movies cost $7.
Plotting the budget constraint is a fairly simple process. Each point on the budget line has to exhaust all $56 of José’s budget. The easiest way to find these points is to plot the intercepts and connect the dots. Each intercept represents a case where José spends all of his budget on either T-shirts or movies.
If José spends all his money on movies, which cost $7, José can buy $56/$7, or 8 of them. This means the y-intercept is the point (0,8). Here, José buys 0 T-shirts and 8 movies.
If José spends all his money on T-shirts, which cost $14, José can buy only 4 of them ($56/$14). This means the x-intercept is the point (4,0). Here, José buys 4 T-shirts and 0 movies.
By connecting these two extremes, you can find every combination that José can afford along his budget line . For example, at point R, José buys 2 T-shirts and 4 movies. This costs him:
T-Shirts @ $14 x 2 = $28
Movies @ $7 x 4 = $28
Total = $24 + $28 = $56
This point indeed exhausts José’s budget.
Budget Constraints
We now know that José must purchase at some point along the budget line, depending on his preferences. Note that any point within the budget line is feasible. José can spend less than $56, but this is not optimal as he can still buy more goods. Since T-shirts and movies are the only two goods, there is no ability in this model for José to save. This means that not spending his full budget is essentially wasted income. On the other hand, any point beyond the budget line is not feasible. If José only has $56, he cannot spend more than that. Notice that areas in the green zone are not necessarily more optimal than points along the budget line. The optimal point depends on José’s preferences, which we will explore when we discuss José’s indifference curve.
Though we can easily just connect the X and Y intercepts to find the budget line representing all possible combinations that expend José’s entire budget, it is important to discuss what the slope of this line represents. Remember, the slope is the rate of change. In economics, the slope of the graph is often quite important. In this situation, the slope is QY/QX. If we want to represent slope in terms of prices it is equal to Px/PY. This can seem unintuitive at first, as we are used to seeing slope as Y/X., but the reason this is not true for prices is because the y-axis represents quantity, not price. As we saw above, as price doubles, the quantity the consumer could previously purchase is halved.
If José is making $56:
When the price of movies is $7, he can buy 8 of them
When the price of movies is $14, he can buy 4 of them
Since price and quantity have this inverse relationship, we can use either Px/PY or QY/QX to find the slope. Since price is often the information given, it is important to remember that the slope can be calculated either way.
What Does Slope Mean?
The meaning of the budget line’s slope or price ratio is the same as the slope of a PPF. (The difference between these two curves is that the PPF shows all the different combinations given time a time/production constraint, whereas a budget line shows different combinations given budget constraint. Otherwise, the two graphs are basically the same). This means the slope of the curve is the relative price of the good on the x-axis in terms of the good on the y-axis. The price ratio of 2 means that José must give up 2 movies for every T-shirt. Likewise, the inverse slope of 1/2 means that José must give up 1/2 a T-shirt per movie.
When Income Changes
Because budget and prices are prone to change, José’s budget line can shift and pivot. For example, if José’s budget drops from $56 to $42, the budget line will shift inward, as he is unable to purchase the same number of goods as before.
To plot the new budget line, find the new intercepts:
Budget: $42
Price of movies: $7
Price of T-shirts: $14
Maximum number of movies (y-intercept): $42/$7 = 6
Maximum number of T-shirts (x-intercept): $42/$14 = 3
As a result of the shift, José’s budget line has shifted inward, leaving less consumption opportunities available.
When Price Changes
In addition to income changes, sometimes the prices of movies and T-shirts rises and falls. Suppose, from our original budget of $56, movies double in price from $7 to $14. Again, to plot the new graph, simply find the new intercepts:
Budget: $56
Price of movies: $14
Maximum number of movies (y-intercept): $56/$14 = 4
Maximum number of T-shirts (x-intercept): $56/$14 = 4
As a result of the pivot, José has fewer consumption opportunities available and the slope of the line changes. This has two effects:
The Size Effect : There are fewer opportunities for consumption (as a result of the price change, the purchasing power of José’s dollar has fallen).
The Slope Effect : The relative price of movies is now higher, while the relative price of T-shirts is now lower.
When Price and Income Change
The last type of change is when both price and income change. Suppose the price of movies increases from $7 to $12 and José’s budget increases to $63. To plot the new budget line, follow the same steps as before:
Budget: $63
Price of movies: $12
Maximum number of movies (y-intercept): $63/$12 = 5.25
Maximum number of T-shirts (x-intercept): $63/$14 = 4.50
These changes have interesting effects. José now has access to some new consumption opportunities, but many others are now unavailable. While the slope effect has clearly made the relative price of T-shirts lower, the size effect is uncertain. These effects are implicit in the income and substitution effects we will explore shortly.
Though we understand the different ways by which consumers can exhaust their income, we have not yet discussed how to determine which bundles of goods different consumers prefer. To finish our analysis, let’s take a look at Indifference Curves.
Exercises 6.1
1. In the diagram below, a consumer maximizes utility by choosing point A, given BL1.
Suppose that both good x is normal and good y is inferior, and the budget line shifts to BL2. Which of the following could be the new optimal consumption choice?
a) B. b) C. c) D. d) Either B or C or D.
2. Which of the following diagrams could represent the change in a consumer’s budget line if (i) the price of good y increases AND (ii) the consumer’s income decreases.
Principles of Microeconomics Copyright © 2017 by University of Victoria is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.
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Quickonomics
Budget Line
Definition of budget line.
A budget line, also known as a budget constraint, represents all the possible combinations of two goods or services that a consumer can purchase given their income level and the prices of those goods or services. It’s a graphical representation that shows the trade-off between two different goods, illustrating the limit to the consumer’s consumption choices based on their budget.
Imagine that Mary has a monthly budget of $100 to spend on two goods: books and movies. The price of a book is $20, and the price of a movie is $10. If Mary spends all her money on books, she can buy 5 books ($100/$20 per book) and no movies. Conversely, if she spends all her money on movies, she can buy 10 movies ($100/$10 per movie). The budget line would connect these two extremes, showing all the combinations of books and movies Mary can afford. For instance, she could also choose to buy 3 books (using $60) and 4 movies (using the remaining $40), among other combinations.
Why Budget Line Matters
The budget line is crucial for understanding consumer behavior and making decisions. It helps consumers visualize their options within their financial constraints, aiding in the allocation of their limited resources to maximize satisfaction. Economists use the concept of the budget line to analyze how changes in income and prices affect consumer choices. An outward shift in the budget line signifies an increase in purchasing power, either due to an increase in income or a decrease in the prices of goods or services. Conversely, an inward shift indicates a decrease in purchasing power.
Frequently Asked Questions (FAQ)
How does a change in income affect the budget line.
A change in income shifts the budget line without changing its slope. An increase in income shifts the budget line outward, meaning the consumer can now afford more combinations of the two goods. A decrease in income shifts the budget line inward, indicating fewer affordable combinations. The slope, which reflects the relative prices of the two goods, remains unchanged because a change in income does not affect the prices of the goods.
How do price changes affect the budget line?
Price changes alter the slope of the budget line. If the price of one good increases (while income and the price of the other good remain constant), the budget line rotates inward around the intercept of the unaffected good. This reflects that the consumer can now afford less of the good that has become more expensive. Conversely, if the price of a good decreases, the budget line rotates outward around the intercept of the unaffected good, showing that the consumer can now afford more of the cheaper good.
Can a budget line be linear?
Yes, the budget line is typically linear because it assumes constant prices of the two goods or services and a fixed income. The linearity of the budget line indicates a constant trade-off ratio between the two goods, known as the marginal rate of substitution, which remains unchanged as the consumer moves along the line choosing different combinations of the goods. However, in more complex scenarios with varying prices or additional constraints, the budget line might exhibit non-linear characteristics.
The budget line is a fundamental concept in consumer theory, providing insights into the choices consumers make given their budgetary constraints. It illustrates the fundamental economic problem of scarcity, highlighting that consumers must make choices about how to allocate their finite resources among various desires. Understanding the dynamics of the budget line helps in grasifying the effects of economic changes on consumer behavior and welfare.
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- Consumption Function
- Law of Diminishing Marginal Utility
- Equimarginal Principle
- Budget Line
- Consumer Behavior
- Shifts in Budget Line
- Indifference Curve
- Marginal Rate of Substitution
- Income vs Substitution Effect
- Price-Consumption Curve
- Income-Consumption Curve
- Consumer Surplus
- Engel Curve
- Externalities
Budget line (also known as budget constraint) is a schedule or a graph that shows a series of various combinations of two products that can be consumed at a given income and prices.
Budget line is to consumers what a production possibilities curve is to producers. It is a useful tool in understanding consumer behavior and choices. Budget line depicts the consumer choices between two products. Number of units of one product are displayed along horizontal axis while those of the other along vertical axes. Each possible combination of the two products is then plotted to obtain a budget constraint curve.
A budget line is a constraint in that it limits the total potential consumption of a consumer. Only such combination of two goods is attainable which falls within or on the budget line. Any combination of two goods which falls outside the budget line is unattainable.
Together with a consumer’s indifference curves , which shows different combinations of two products which give the consumer the same utility, we can arrive at a combination of two goods which is optimal for the consumer i.e. which gives the consumer maximum attainable satisfaction.
Budget Constraint Equation
Total spending on any combination of goods on the budget line is equal to consumer income. It can be expressed mathematically as follows:
$$ \text{Q} _ \text{A} \text{P} _ \text{A}+\text{Q} _ \text{B} \text{P} _ \text{B}=\text{I} $$
Where Q A and Q B are the units of good A and good B, P A and P B are their corresponding prices and I is total income of the consumer.
Let’s assume Product A is on y-axis and Product B is on x-axis. We can write the budget constraint in the standard format of the straight-line equation:
$$ \text{Q} _ \text{A}=\frac{\text{I}}{\text{P} _ \text{A}}-\frac{\text{P} _ \text{A}}{\text{P} _ \text{B}}\times \text{Q} _ \text{B} $$
It shows that the slope of the budget line equals the negative of the ratio of price of the good on x-axis on the price of the good on y-axis.
The budget line shifts when a consumer income changes: it shifts inwards when income decreases and shifts outwards when income increases. But when there is a change in price of only one good, the budget line rotates i.e. it shifts but not parallelly.
Assume you have received a $50 app store gift card from your friend. You are considering buying video games and songs for your smartphone. The price of a game is $5 and that of a song is $1. You can either spend the whole amount on games, in which case the games purchased would be 10 [=$50/5]. Or you can spend the whole amount on music, in which case the number of songs purchased would 50.
Let us say the number of songs are represented along horizontal axis X and those of games along vertical axis Y. We now have two points on budget line (0,10) and (50,0).
The above combinations will rarely be purchased by a typical consumer. You are mostly likely to buy both games and songs in some quantity above zero. Let’s say you buy 6 games. That would be $30 [=4×5]. The remaining amount can buy you 20 songs. We now have another point on the graph (20,6).
If we plot the above points and any other possible combinations you might choose, we obtain a straight budget line as shown below:
Attainable combination is any combination of two products which may be purchased using the given income. All points on or below the budget line are attainable, for example, 20 songs and 4 games.
Unttainable combination is any combination of two products which is impossible to purchase using the given income. All points above the budget line are un-attainable, for example, 30 songs and 6 games.
by Irfanullah Jan, ACCA and last modified on Feb 4, 2019
Related Topics
- Production Possibility Frontier
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Budget line: How to represent your budget trade offs graphically
1. understanding budget trade-offs, 2. the basics of budget line analysis, 3. identifying and quantifying trade-offs, 4. constructing the budget line graph, 5. interpreting the budget line graph, 6. analyzing changes in budget constraints, 7. exploring optimal budget allocations, 8. limitations and considerations in budget line analysis, 9. empowering financial decision-making with graphical representations.
One of the most important concepts in economics is the idea of trade-offs. trade-offs are the choices that we make when we have limited resources, such as money, time, or energy. Every decision we make involves giving up something else that we could have done or bought with those resources. For example, if you have $100 to spend, you can buy either a pair of shoes or a jacket, but not both. Or, if you have two hours of free time, you can watch a movie or read a book, but not both. In this section, we will explore how to represent your budget trade-offs graphically using a tool called the budget line. The budget line shows all the possible combinations of two goods or services that you can afford with your given income and prices. Here are some steps to construct and interpret a budget line:
1. Choose two goods or services that you want to compare. For example, suppose you want to compare how much pizza and soda you can buy with your weekly allowance of $20.
2. Find the prices of the two goods or services . For example, suppose a slice of pizza costs $2 and a can of soda costs $1.
3. Plot the two goods or services on a graph, with one on the x-axis and the other on the y-axis. For example, you can put pizza on the x-axis and soda on the y-axis.
4. Find the intercepts of the budget line. The intercepts are the points where the budget line crosses the axes. They show the maximum amount of each good or service that you can buy if you spend all your income on that good or service. To find the intercepts, divide your income by the price of each good or service . For example, if you spend all your $20 on pizza, you can buy 10 slices ($20 / $2 = 10). This is the x-intercept of the budget line. If you spend all your $20 on soda, you can buy 20 cans ($20 / $1 = 20). This is the y-intercept of the budget line.
5. Draw the budget line by connecting the two intercepts with a straight line. The budget line shows all the possible combinations of pizza and soda that you can buy with your $20. For example, you can buy 5 slices of pizza and 10 cans of soda, or 8 slices of pizza and 4 cans of soda, or any other point on the line.
6. Understand the slope of the budget line. The slope of the budget line shows the trade-off between the two goods or services. It tells you how much of one good or service you have to give up to get more of the other. To find the slope, use the formula: slope = - (price of good on x-axis) / (price of good on y-axis). For example, the slope of the budget line is - ($2 / $1) = -2. This means that for every slice of pizza that you buy, you have to give up 2 cans of soda. Or, for every can of soda that you buy, you have to give up 0.5 slices of pizza. The slope is negative because there is a trade-off between the two goods or services. The steeper the slope, the greater the trade-off.
The budget line is a useful tool to visualize your budget trade-offs graphically. It helps you to compare different combinations of goods or services that you can afford and to make optimal choices based on your preferences and constraints. You can also use the budget line to analyze how changes in income or prices affect your budget trade-offs and consumption choices. In the next section, we will look at some examples of how to do that. Stay tuned!
Startups, in some sense, have gotten so easy to start that we are confusing two things. And what we are confusing, often, is, 'How far can you get in your first day of travel?' with, 'How long it is going to take to get up to the top of the mountain?' Mitch Kapor
One of the most important concepts in economics is the budget line, which shows the possible combinations of two goods that a consumer can afford given their income and the prices of the goods. The budget line is also known as the budget constraint, because it represents the limit of the consumer's purchasing power. In this section, we will explore the basics of budget line analysis, such as how to draw a budget line, how to interpret its slope and intercepts, and how to use it to analyze the effects of changes in income and prices on the consumer's choices. We will also look at some applications of the budget line in different scenarios, such as when the consumer faces a lump-sum tax , a subsidy, or a rationing scheme.
To understand the budget line, we need to make some assumptions:
1. The consumer has a fixed income (Y) that they can spend on two goods, X and Y.
2. The prices of the two goods are given and constant (P_X and P_Y).
3. The consumer can buy any fraction of the goods, not just whole units.
4. The consumer spends all their income on the two goods, i.e., they do not save or borrow.
Given these assumptions, we can write the budget equation as:
$$P_X X + P_Y Y = Y$$
This equation shows that the total expenditure on the two goods must equal the income. We can rearrange this equation to solve for Y in terms of X:
$$Y = \frac{Y}{P_Y} - \frac{P_X}{P_Y} X$$
This equation shows that the budget line is a straight line with a negative slope and a positive intercept. The slope of the budget line is:
$$-\frac{P_X}{P_Y}$$
This slope shows the rate at which the consumer can trade one good for another, i.e., the opportunity cost of one good in terms of the other. The slope is negative because the consumer has to give up some amount of one good to get more of the other. The slope is also equal to the ratio of the prices of the two goods.
The intercept of the budget line on the Y-axis is:
$$\frac{Y}{P_Y}$$
This intercept shows the maximum amount of good Y that the consumer can afford if they spend all their income on it and none on good X. Similarly, the intercept of the budget line on the X-axis is:
$$\frac{Y}{P_X}$$
This intercept shows the maximum amount of good X that the consumer can afford if they spend all their income on it and none on good Y.
To draw a budget line, we need to know the income and the prices of the two goods. For example, suppose the consumer has an income of $100 and the prices of the two goods are $10 and $5, respectively. Then, the budget equation is:
$$10X + 5Y = 100$$
The slope of the budget line is:
$$-\frac{10}{5} = -2$$
The intercepts of the budget line are:
$$\frac{100}{5} = 20$$
$$\frac{100}{10} = 10$$
We can plot these points on a graph and connect them with a straight line to get the budget line , as shown below:
$ is the utility function, $X$ and $Y$ are the quantities of the two goods, and $k$ is a constant that represents the level of utility. The slope of the indifference curve is given by:
\frac{\Delta Y}{\Delta X} = -\frac{MU_x}{MU_y}
Where $MU_x$ and $MU_y$ are the marginal utilities of the two goods, which are the changes in utility from consuming one more unit of each good. The shape of the indifference curve depends on the properties of the utility function, such as whether the goods are substitutes or complements, whether the consumer has diminishing or increasing marginal utility, etc.
3. How to find the optimal budget allocation using the budget line and the indifference curves? The optimal budget allocation is the combination of goods that maximizes the utility of the consumer subject to the budget constraint. Graphically, it is the point where the budget line is tangent to the highest possible indifference curve. At this point, the slope of the budget line is equal to the slope of the indifference curve, which implies that the marginal rate of substitution (MRS) of the consumer is equal to the price ratio of the two goods. The MRS is the rate at which the consumer is willing to trade one good for another to maintain the same level of utility. The optimal budget allocation equation is given by:
MRS = \frac{MU_x}{MU_y} = \frac{P_x}{P_y}
Which shows the condition for utility maximization. To find the optimal quantities of the two goods, we can substitute this equation into the budget line equation and solve for $X$ and $Y$.
4. How do changes in income, prices, and preferences affect the optimal budget allocation? The optimal budget allocation is influenced by various factors, such as changes in income, prices, and preferences of the consumer. These factors can cause shifts or rotations in the budget line and/or the indifference curves, which can lead to different optimal points. Here are some examples of how these factors affect the optimal budget allocation:
- An increase in income causes a parallel shift of the budget line to the right, which means that the consumer can afford more of both goods. The optimal point moves to a higher indifference curve, which means that the consumer has a higher level of utility. The effect of income on the optimal quantities of the two goods depends on whether they are normal or inferior goods. Normal goods are goods that the consumer buys more of as their income increases, such as clothing, entertainment, etc. Inferior goods are goods that the consumer buys less of as their income increases, such as cheap food, public transportation , etc.
- An increase in the price of one good causes a rotation of the budget line around the intercept of the other good, which means that the consumer can afford less of the good whose price increased and more of the other good. The optimal point moves to a lower indifference curve, which means that the consumer has a lower level of utility. The effect of price on the optimal quantities of the two goods depends on whether they are substitutes or complements. Substitutes are goods that the consumer can use interchangeably, such as coffee and tea, pizza and burgers, etc. Complements are goods that the consumer uses together, such as coffee and cream, pizza and soda, etc.
- A change in preferences causes a shift or a rotation of the indifference curves, which means that the consumer has different levels of satisfaction from different bundles of goods. The optimal point moves to a different indifference curve, which may be higher or lower than the original one, depending on whether the consumer likes or dislikes the goods more or less. The effect of preferences on the optimal quantities of the two goods depends on the shape and the position of the indifference curves, which reflect the consumer's utility function.
These are some of the main topics that we have explored in this section of the blog. We have learned how to use the budget line and the indifference curves to represent our budget trade-offs graphically and to find our optimal budget allocation. We have also analyzed how different factors affect our optimal budget allocation and how to adjust our budgeting decisions accordingly. We hope that you have found this section informative and useful for your personal finance management . Thank you for reading!
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Budget line analysis is a useful tool to understand how consumers make choices under scarcity and how their preferences affect their demand for goods and services. However, there are some limitations and considerations that need to be taken into account when applying this method. In this section, we will discuss some of the main challenges and assumptions that underlie the budget line analysis and how they may affect the validity and applicability of the results. Some of the topics that we will cover are:
1. The linearity of the budget line. The budget line is drawn as a straight line that represents the trade-off between two goods, holding the prices and income constant. However, in reality, prices and income may vary depending on the quantity of goods purchased or the market conditions. For example, if a consumer buys a large amount of a good, they may benefit from a bulk discount or a lower marginal cost. Conversely, if a consumer buys a very small amount of a good, they may face a higher marginal cost or a minimum purchase requirement . These factors may make the budget line nonlinear or discontinuous, which would change the shape of the indifference curves and the optimal choice of the consumer.
2. The completeness and transitivity of preferences. The budget line analysis assumes that consumers have well-defined and consistent preferences over all possible bundles of goods. This means that consumers can rank any two bundles and that their rankings are transitive, i.e., if they prefer bundle A to bundle B and bundle B to bundle C, then they also prefer bundle A to bundle C. However, in reality, consumers may not have complete or transitive preferences, especially when they face complex or unfamiliar choices. For example, a consumer may not be able to compare two bundles that contain very different types of goods, such as a bundle of food and a bundle of entertainment. Or, a consumer may exhibit inconsistent or irrational preferences, such as preferring bundle A to bundle B, bundle B to bundle C, and bundle C to bundle A. These cases may violate the assumptions of the budget line analysis and make the indifference curves indeterminate or inconsistent.
3. The homogeneity and divisibility of goods. The budget line analysis assumes that the goods are homogeneous and divisible, i.e., that they have the same quality and that they can be purchased in any fraction. However, in reality, goods may differ in quality and may only be available in discrete units. For example, a consumer may prefer organic apples to conventional apples, but they may only be able to buy them in whole numbers. Or, a consumer may want to buy a car, but they may not be able to buy half a car or a quarter of a car. These factors may affect the budget line and the indifference curves, as the consumer may face different prices and quantities for different qualities and units of goods.
Limitations and Considerations in Budget Line Analysis - Budget line: How to represent your budget trade offs graphically
In this blog, we have learned how to use graphical representations to understand and analyze our budget constraints and preferences. We have seen how a budget line can show us the possible combinations of two goods that we can afford with a given income and prices. We have also learned how to use indifference curves to represent our preferences and utility levels. By combining these two concepts, we can find the optimal choice that maximizes our satisfaction subject to our budget constraint. In this concluding section, we will discuss how these graphical tools can empower our financial decision-making and help us achieve our goals. We will also explore some of the limitations and extensions of the budget line model.
1. Graphical representations can help us visualize and compare different scenarios and outcomes. For example, we can use budget lines and indifference curves to see how our optimal choice changes when our income, prices, or preferences change. We can also use them to compare different policies or interventions that affect our budget constraint, such as taxes, subsidies, or vouchers. By using graphs, we can easily see the trade-offs and opportunity costs involved in each decision and evaluate the effects on our utility and well-being.
2. Graphical representations can help us communicate and explain our decisions to others. For example, we can use budget lines and indifference curves to justify why we choose a certain bundle of goods over another, or why we prefer a certain policy over another. We can also use them to persuade others to adopt our point of view or to understand their perspectives. By using graphs, we can make our arguments more clear and convincing, and avoid misunderstandings or conflicts.
3. Graphical representations can help us discover new possibilities and opportunities. For example, we can use budget lines and indifference curves to find out if there are any bundles of goods that we have not considered before, or if there are any ways to improve our utility without increasing our spending. We can also use them to identify any gaps or inefficiencies in our budget constraint, such as unspent income or unused resources. By using graphs, we can expand our horizons and explore new options that might enhance our lives.
4. Graphical representations have some limitations and assumptions that we need to be aware of. For example, the budget line model assumes that we only consume two goods, that our preferences are complete, transitive, and convex, and that our income and prices are fixed and known. These assumptions may not always hold in reality, and they may affect the validity and applicability of the model. We also need to be careful about the scale and units of measurement that we use in our graphs, as they may affect the shape and slope of our budget lines and indifference curves. By being aware of these limitations and assumptions, we can avoid making errors or misinterpretations in our analysis and decision-making .
5. Graphical representations can be extended and modified to accommodate more realistic and complex situations. For example, we can use more than two goods in our budget line model, or we can use different types of preferences, such as non-convex, lexicographic, or interdependent preferences. We can also incorporate uncertainty and risk into our model, such as income or price fluctuations, or stochastic preferences. We can also use different types of budget constraints, such as nonlinear, kinked, or discontinuous budget constraints. By extending and modifying our graphical tools, we can capture more of the nuances and diversity of our financial decisions and behaviors.
About 10 million people start a business each year, and about one out of two will make it. The average entrepreneur is often on his or her third startup. Brad D. Smith
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3 Budget Constraints
The policy question hybrid car purchase tax credit—is it the government’s best choice to reduce fuel consumption and carbon emissions.
The US government policy of extending tax credits toward the purchase of electric and hybrid cars can have consequences beyond decreasing carbon emissions. For instance, a consumer that purchases a hybrid car could spend less money on gas and have more money to spend on other things. This has implications for both the individual consumer and the larger economy.
Even the richest people—from Bill Gates to Oprah Winfrey—can’t afford to own everything in the world. Each of us has a budget that limits the extent of our consumption. Economists call this limit a budget constraint . In our policy example, an individual’s choice between consuming gasoline and everything else is constrained by their current income. Any additional money spent on gasoline is money that is not available for other goods and services and vice versa. This is why the budget constraint is called a constraint.
The budget constraint is governed by income on the one hand—how much money a consumer has available to spend on consumption—and the prices of the goods the consumer purchases on the other.
Exploring the Policy Question
- What are some of the budget implications for a consumer who owns a hybrid car? What purchase decisions might this consumer make given their savings on gas, and how does this, in turn, affect the goals of the tax subsidy policy?
Learning Objectives
3.1 description of the budget constraint.
Learning Objective 3.1 : Define a budget constraint conceptually, mathematically, and graphically.
3.2 The Slope of the Budget Line
Learning Objective 3.2 : Interpret the slope of the budget line.
3.3 Changes in Prices and Income
Learning Objective 3.3 : Illustrate how changes in prices and income alter the budget constraint and budget line.
3.4 Coupons, Vouchers, and Taxes
Learning Objective 3.4 : Illustrate how coupons, vouchers, and taxes alter the budget constraint and budget line.
3.5 Policy Example Hybrid Car Purchase Tax Credit—Is It the Government’s Best Choice to Reduce Fuel Consumption and Carbon Emissions?
Learning Objective 3.5 : The Hybrid Car Tax Credit and Consumers’ Budgets
The budget constraint is the set of all the bundles a consumer can afford given that consumer’s income. We assume that the consumer has a budget—an amount of money available to spend on bundles. For now, we do not worry about where this money or income comes from; we just assume a consumer has a budget.
So what can a consumer afford? Answering this depends on the prices of the goods in question. Suppose you go to the campus store to purchase energy bars and vitamin water. If you have $5 to spend, energy bars cost fifty cents each, and vitamin water costs $1 a bottle, then you could buy ten bars and no vitamin water, no bars and five bottles of vitamin water, four bars and two vitamin waters, and so on.
This table shows the possible combinations of energy bars and vitamin water the student can buy for exactly $5:
It is also true that you could spend less than $5 and have money left over. So we have to consider all possible bundles—including consuming none at all.
Note that we are focusing on bundles of two goods so that we maintain tractability (as explained in chapter 1 ), but it is simple to think beyond two goods by defining one of the goods as “money spent on everything else.”
Mathematically, the total amount the consumer spends on two goods, [latex]A[/latex] and [latex]B[/latex], is
[latex]P_{A}A+P_{B}B[/latex] (3.1)
where [latex]P_{A}[/latex] is the price of good[latex]A[/latex] and [latex]P_{B}[/latex] is the price of good [latex]B[/latex]. If the money the consumer has to spend on the two goods, their income, is given as [latex]I[/latex], then the budget constraint is
[latex]P_{A}A+P_{B}B\leq I[/latex] (3.2)
Note the inequality: this equation states that the consumer cannot spend more than their income but can spend less. We can simplify this assumption by restricting the consumer from spending all of their income on the two goods. This will allow us to focus on the frontier of the budget constraint. As we shall see in chapter 4 , this assumption is consistent with the more-is-better assumption—if you can consume more (if your income allows it), you should because you will make yourself better off. With this assumption in place, we can write the budget constraint as
[latex]P_{A}A+P_{B}B=I[/latex] (3.3)
Graphically, we can represent this budget constraint as in figure 3.1 . We call this the budget line : the line that indicates the possible bundles the consumer can buy when spending all their income.
From the graph of the budget constraint in section 3.1 , we can see that the budget line slopes downward and has a constant slope along its entire length. This makes intuitive sense: if you buy more of one good, you are going to have to buy less of the other good. The rate at which you can trade one for the other is determined by the prices of the two goods, and they don’t change.
We can see these details in figure 3.2 .
We can find the slope of the budget line easily by rearranging equation 3.3 so that we isolate [latex]B[/latex] on one side. Note that in our graph, B is the good on the vertical axis, so we will rearrange our equation to look like a standard function, with B as the dependent variable:
[latex]B=\frac{I}{P_{B}}-\frac{P_{A}}{P_{B}}A[/latex] (3.4)
Now we have our budget line represented in point-slope form, where the first part, [latex]\frac{I}{P_{B}}[/latex], is the vertical intercept, and the second part, [latex]-\frac{P_{A}}{P_{B}}[/latex], is the slope coefficient on A.
Note that the slope of the budget line is simply the ratio of the prices, also known as the price ratio . This is the rate at which you can trade one good for the other in the marketplace. To see this, let’s return to the campus store with $5 to spend on energy bars and vitamin water.
Suppose you originally decided to buy five bottles of vitamin water and placed them in a basket. After some thought, you decided to trade one bottle for two energy bars. Now you have four bottles of vitamin water and two energy bars in the basket. If you want even more bars, the same trade-off is available: two more bars can be had if you give up one bottle of vitamin water and so on.
The slope of the budget line is also called the economic rate of substitution [latex](ERS)[/latex] .
The slope of the budget line also represents the opportunity cost of consuming more of good A because it describes how much of good B the consumer has to give up to consume one more unit of good A. The opportunity cost of something is the value of the next best alternative given up in order to get it. For example, if you decide to buy one more bottle of vitamin water, you have to give up two energy bars. Note that opportunity cost is not limited to the consumption of material goods. For example, the opportunity cost of an hour-long nap might be the hour of studying microeconomics that did not happen because of it.
From our mathematical description of the budget line, we can easily see how changes in prices and income affect the budget line and a consumer’s choice set—the set of all the bundles available to them at current prices and income. Let’s go back to equation 3.3 :
[latex]P_{A}A+P_{B}B=I[/latex]
We know from the previous figure that the vertical intercept for equation 3.3 is [latex]\frac{I}{P_{B}}[/latex] and the horizontal intercept is [latex]\frac{I}{P_{A}}[/latex].
Now consider an increase in the price of good [latex]A[/latex]. Notice that this increase does not affect the vertical intercept, only the horizontal intercept. As [latex]P_{A}[/latex] increases, [latex]\frac{I}{P_{A}}[/latex] decreases, moving closer to the origin. This change makes the budget line “steeper” or more negatively sloped, as we can see from the slope coefficient: [latex]-\frac{P_{A}}{P_{B}}[/latex]. As [latex]P_{A}[/latex] increases, this ratio increases in absolute value, so the slope becomes more negative or steeper. What this means intuitively is that the trade-off or opportunity cost has risen. Now the consumer has to give up more of good [latex]B[/latex] to consume one more unit of good [latex]A[/latex].
Next, consider a change in income. Suppose the consumer gets an additional amount of money to spend, so [latex]I[/latex] increases. [latex]I[/latex] affects both intercept terms positively, so as I increases, both [latex]\frac{I}{P_{B}}[/latex] and [latex]\frac{I}{P_{A}}[/latex] increase or move away from the origin. But [latex]I[/latex] does not affect the slope: [latex]-\frac{P_{A}}{P_{B}}[/latex]. Thus the shift in the budget line is a parallel shift outward—the consumer with the additional income can afford more of both (as displayed in figure 3.4 ).
Budget constraints can change due to changes in prices and income, but let’s now consider other common features of the real-world market that can affect the budget constraint. We start with coupons or other methods firms use to give discounts to consumers.
Consider a coupon or a sale that gives consumers a discount on the price of one item in our budget constraint problem. A coupon that entitles the bearer to a percentage off in price is essentially a reduction in price and has precisely the same effect. For example, a 20 percent off coupon on a good that normally costs $10 is the same as reducing the price to $8.
More complicated is a coupon that gives a percentage off the entire purchase. In this case, the percentage is taken from the price of both items A and B in our budget constraint problem. In this case, the price ratio, or the slope of the budget constraint, does not change.
For example, if the price of [latex]A[/latex] is regularly $10 and the price of [latex]B[/latex] is regularly $20, then with 20 percent off the entire purchase, the new prices are $8 and $16, respectively. Intuitively, we can see that this is equivalent to increasing the income and achieves the same result: by expanding the budget set, the consumer can now afford bundles with more of both goods.
Another common discount is on a maximum number of items. For example, you might see an advertisement for 20 percent off up to three units of good [latex]A[/latex]. This discount lowers the opportunity cost of [latex]A[/latex] in terms of [latex]B[/latex] for the first three units but reverts back to the original opportunity cost thereafter. Figure 3.5 illustrates this.
Taxes have the same effects as coupons but in the opposite direction. An ad valorem tax is a tax based on the value of a good, such as a percentage sales tax. In terms of the budget constraint, an ad valorem tax on a specific good is equivalent to an increase in price, as shown in figure 3.6 . A general sales tax on all goods has the effect of a parallel shift of the budget line inward. Note also that income taxes are, in this case, functionally equivalent to a general sales tax; they cause a parallel shift inward of the budget line.
Vouchers that entitle the bearer to a certain quantity of a good (either value or quantity) are slightly more complicated. Let’s return to your purchase of vitamin water and energy bars. Suppose you have a voucher for two free energy bars.
You have $5.
The price of one energy bar is $0.50.
The price of one bottle of vitamin water is $1.
How would we now draw your budget line?
One place to start is to consider the simple bundle that contains 2 energy bars and two bottles of vitamin water. Note that giving up one or two bars does not allow the student to consume any more vitamin water. The opportunity cost of these two bars is 0, and so the budget line in this part has a zero slope. After using the voucher, if the student wants more than two bars, the opportunity cost is the same as before—0.5 bottles of vitamin water for an energy bar—and so the budget line from this point on is the same as before. The new budget line with the voucher has a kink.
3.5 THE Policy Example Hybrid Car Purchase Tax Credit—Is It the Government’s Best Choice to Reduce Fuel Consumption and Carbon Emissions?
Learning Objective 3.5: The Hybrid Car Tax Credit and Consumers’ Budgets
For several chapters, we have considered the policy of a hybrid car tax credit. In chapter 1 , we thought about the various driving preferences of a typical consumer. In chapter 2 , we translated these preferences into a type of utility function and corresponding indifference curve . Now let’s think about the appropriate budget line for our policy example.
To start, let’s use the same two axes as we used for the indifference curve map as shown in figure 3.8 . In other words, let’s place “miles driven” on the horizontal axis and “$,” which is all the money spent on other consumption, on the vertical axis. For now, we won’t specify the precise level of income.
Now we can ask, “ What is the price of ‘other consumption’? ” Since we are talking about money left over after paying for miles driven, the price for other consumption is simply one. This is because we are talking about money itself, and the price of a dollar is a dollar. So the intercept on this axis is simply the value of [latex]I[/latex].
But what is the price of a mile driven? This question is more complicated and includes the cost of maintenance and depreciation. However, because we are focused on the effect of increasing the miles per gallon of gas, let’s concentrate on only the cost as it relates to the purchase of gasoline. In this case, the cost of driving a mile is the price of gasoline divided by the car’s miles per gallon (MPG). Since we are again interested not in an individual but in a group, we can use the average price of a gallon of regular gas divided by the average MPG of cars driven in the United States as a reasonable approximation of the cost of a mile driven in a non-hybrid car. Now we have the “price” of driving a mile; dividing income by this price gives us the intercept on the “miles driven” axis.
Now that we have a budget constraint for our electric and hybrid car subsidy policy example, we can see the effect of the policy on the constraint. Doubling the MPG from twenty to forty dramatically reduces the price of driving a mile. This reduction causes the “miles driven” intercept to move upward and the entire budget constraint to move outward. Note that now the typical consumer can afford to consume bundles with more of both miles driven and everything else—bundles that were unavailable to them prior to the policy.
Equation 3.4 summarizes the budget constraint for miles driven and other goods.
[latex]\text{Income} = (P_{Miles Driven})(\text{Miles Driven}) + \text{Dollars Spent on Other Consumption}[/latex]
- What can we say about the availability of bundles after the hybrid car tax credit is enacted compared to before? Do the bundles represent more consumption of only miles driven, or do they represent more of other goods as well?
- Another type of car that is high mileage (high MPG) is a diesel car. In the United States, however, the price of diesel gas is typically higher than the price of regular gas. How would only higher MPG shift the budget line in figure 3.8 ? How would only higher-priced gas shift the budget line in figure 3.8 ? How would these two factors together alter the budget line from figure 3.8 ?
- If the government subsidizes the purchase of hybrid cars through a rebate that adds to the income of consumers, what happens to the budget line in figure 3.8 ?
REVIEW: TOPICS AND RELATED LEARNING OUTCOMES
Learn: key topics.
A tax based on the value of a good, such as a percentage sales tax. In terms of the budget constraint, an ad valorem tax on a specific good is equivalent to an increase in price.
The limit of which a consumer has capital to purchase goods. The budget constraint is governed by income on the one hand—how much money a consumer has available to spend on consumption—and the prices of the goods the consumer purchases on the other.
The line that indicates the possible bundles the consumer can buy when spending all their income.
The slope of the budget line. The slope of the budget line also represents the opportunity cost of consuming more of good[latex]A[/latex]because it describes how much of good [latex]B[/latex] the consumer has to give up to consume one more unit of good [latex]A[/latex].
The value of the next best alternative given up in order to get it.
i.e., you have $3. Vitamin water is $1 and energy bars are $.50. You have already bought a bottle of vitamin water. If you decide to buy one more bottle of vitamin water, the opportunity cost is that you have to give up two energy bars.
Graphically produces a line that indicates the possible bundles the consumer can buy when spending all their income.
[latex]P_{A}A+P_{B}B[/latex]
The total amount a consumer spends on two goods, [latex]A[/latex] and [latex]B[/latex].
[latex]P_{A}A+P_{B}B\leq I[/latex]
An inequality that states that the consumer cannot spend more than their income but can spend less.
[latex]B=\frac{I}{P_{B}}-\frac{P_{A}}{P_{B}}A[/latex]
The budget line represented in point-slope form form, where the first part, [latex]\frac{I}{P_{B}}[/latex], is the vertical intercept, and the second part, [latex]-\frac{P_{A}}{P_{B}}[/latex], is the slope coefficient on A. The slope of this equation is the Economic Rate of Substitution [latex](ERS)[/latex] .
Media Attributions
- 32Artboard-1 © Patrick M. Emerson is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Figure 3.2.1 Intercepts and slope for the budget line © Patrick M. Emerson is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Figure 3.3.1 Changing the price of one good changes the slope of the budget line. Figure 3.3.1 Changing the price of one good changes the slope of the budget line. © Patrick M. Emerson is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Figure 3.3.2 A customer with more resources can spend more, and the line experiences an outward shift. © Patrick M. Emerson is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Figure 3.4.1 Effect of a 20 percent discount on the first Ā units of A © Patrick M. Emerson is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Figure 3.4.2 An ad valorem tax changes the slope and horizontal intercept of the budget line. © Patrick M. Emerson is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- 38Artboard-1 © Patrick M. Emerson is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
- Figure 3.5.1 A consumer’s budget constraint for the hybrid car policy © Patrick M. Emerson is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
The set of all the bundles a consumer can afford given the consumer's income.
See Section 1.1 .
Sometimes presented as more-is-better .
If bundle [latex]A[/latex] represents more of at least one good and no less of any other good than bundle [latex]B[/latex], then [latex]A[/latex] is preferred to [latex]B[/latex].
The line that indicates the possible bundles the consumer can buy when spending all of their income.
The slope of the budget line in the context of price ratios and opportunity costs.
How much of good B a consumer must give up to consume one more unit of good A; i.e., if two energy bars (good B) cost the same as one vitamin water (good A), a consumer has an opportunity cost of two energy bars, or two units, to consume one more vitamin water.
A tax based on the value of a good, such as a percentage sales tax.
[latex](y-y_1)=m(x-x_1)[/latex] where [latex]m[/latex] represents the slope and [latex](x_1, y_1)[/latex] any point along the line with given slope.
Intermediate Microeconomics Copyright © 2019 by Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.
How the Budget Line Changes
When prices and incomes change, the set of goods that a consumer can afford changes as well. How do these changes affect the budget set?
Let us first consider changes in income. It is easy to see from equation that an increase in income will increase the vertical intercept and not affect the slope of the line. Thus an increase in income will result in a parallel shift outward of the budget line. Similarly, a decrease in income will cause a parallel shift inward.
Increasing income. An increase in income causes a parallel shift outward of the budget line.
What about changes in prices? Let us first consider increasing price
While holding price 2 and income fixed. According to equation, increasing pi will not change the vertical intercept, but it will make the budget line steeper since P1/P2 will become larger.
Another way to see how the budget line changes is to use the trick described earlier for drawing the budget line. If you are spending all of your money on good 2, then increasing the price of good 1 doesn't change the maximum amount of good 2 you could buy—thus the vertical intercept of the budget line doesn't change. But if you are spending all of your money on good 1, and good 1 becomes more expensive, then your consumption of good 1 must decrease. Thus the horizontal intercept of the budget line must shift inward.
Increasing price. If good 1 becomes more expensive, the budget line becomes steeper.
What happens to the budget line when we change the prices of good 1 and good 2 at the same time? Suppose for example that we double the prices of both goods 1 and 2. In this case both the horizontal and vertical intercepts shift inward by a factor of one-half, and therefore the budget line shifts inward by one-half as well. Multiplying both prices by two is just like dividing income by 2.
We can also see this algebraically. Suppose our original budget line is
Pi% l P 2^2 = m.
Now suppose that both prices become t times as large. Multiplying both prices by t yields
Thus multiplying both prices by a constant amount t is just like dividing income by the same constant t. It follows that if we multiply both prices by t and we multiply income by then the budget line won't change at all.
We can also consider price and income changes together. What happens if both prices go up and income goes down? Think about what happens to the horizontal and vertical intercepts. If m decreases and pi and P2 both increase, then the intercepts m/p and m/p2 must both decrease. This means that the budget line will shift inward. What about the slope of the budget line? If price 2 increases more than price 1, so that —pi/p2 decreases (in absolute value), then the budget line will be flatter; if price 2 increases less than price 1, the budget line will be steeper.
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Readers' Questions
What happens if goods 2 increase and goods one stay constant?
If the price of goods 2 increases while the price of goods 1 remains constant, it could lead to several consequences: Substitution effect: Consumers may switch their preference from goods 2 to goods 1 since it is relatively cheaper, causing a decrease in the demand for goods 2. Decreased demand for goods 2: As the price of goods 2 increases, consumers may find it less affordable or less valuable, leading to a decrease in demand for goods This could result in lower sales and production for goods 2. Unknown impact on goods 1: The price of goods 1 staying constant does not necessarily imply any immediate impact on its demand or production. However, in the long run, increased demand for goods 1 may occur due to the substitution effect mentioned earlier. Market dynamics: Depending on the market structure, different factors may come into play. For instance, if goods 2 and goods 1 are substitutes and part of a competitive market, other firms producing goods 2 may increase their prices as well, resulting in an overall price increase for both goods. Overall, the impact of goods 2's price increase and goods 1's price remaining constant will depend on factors such as consumer preferences, market competition, and the availability of substitutes.
How the budget line changes in detail?
The budget line is a graphical representation of the different combinations of two goods that a consumer can afford given their budget constraint and the prices of the goods. As a result, the budget line can change in several ways. Here are some detail explanations of how the budget line can change: Changes in income: If a consumer's income increases, their budget line will shift outward or to the right. This means that they can now afford more of both goods. Conversely, a decrease in income will shift the budget line inward or to the left, indicating reduced affordability. Changes in price of one good: If the price of one good increases while the price of the other remains constant, the budget line will pivot inward at the vertical axis. This implies that the consumer now has reduced purchasing power for the good with the increased price but can still afford the same quantity of the other good. Changes in price of both goods: If the prices of both goods increase by the same proportion, the budget line will remain parallel but shift inward. This indicates that the consumer's purchasing power has decreased for both goods, and they can now afford fewer amounts of each good. Changes in preferences or tastes: If a consumer's preferences or tastes change, it can impact their willingness to purchase goods. This might result in a change in the shape of the budget line or alter the levels of consumption for each good. For example, if a consumer becomes more health-conscious, they may reduce their purchase of junk food, causing the budget line to tilt towards the other good. Changes in government policies: Government policies can also impact the budget line. For instance, if the government imposes taxes on a specific good, it effectively increases the price for consumers, which would lead to a shift or rotation of the budget line inward. These are some of the main factors that can cause changes in the budget line. It is important to note that a budget line represents the maximum combinations of goods a consumer can afford, given their budget constraint and market prices.
What does it mean for a budget lie to be steeper or shallower?
When referring to a budget line being "steeper" or "shallower", it typically relates to the slope or angle of the line on a budget graph. A steeper budget line means that for each unit of one good or service, a greater amount of the other good or service is sacrificed. In simple terms, it implies that the price or cost of one item is relatively higher compared to the other item. On the other hand, a shallower budget line suggests that for each unit of one good or service, a smaller amount of the other good or service is given up. This implies that the price or cost of one item is relatively lower compared to the other item. In essence, the steepness or shallowness of a budget line indicates the relative opportunity cost of consuming one item versus another.
What causes shift in budget line in economy to inc?
There are several factors that can cause a shift in the budget line in an economy to increase: Increase in income: When individuals or households earn higher incomes, their ability to spend more on goods and services increases. This leads to a shift in the budget line outward, allowing for higher levels of consumption. Decrease in prices: If the prices of goods and services decrease, individuals can purchase more of these items with their given income. This leads to an increase in the purchasing power of consumers, causing the budget line to shift outward. Increase in credit availability: When credit becomes more easily accessible, individuals can borrow more money to finance their purchases. This can lead to an increase in consumption and a shift in the budget line outward. Decrease in taxes: When taxes are reduced, individuals have more disposable income available to spend on goods and services. This increase in disposable income can cause a shift in the budget line to increase. Increase in government spending: If the government increases its spending on goods and services, it can stimulate economic activity. This increase in aggregate demand can lead to an increase in income and consumption, causing the budget line to shift outward. These factors, among others, can cause a shift in the budget line in an economy to increase, allowing for greater levels of consumption.
What causes budget line to reduce on y axis but in?
The reduction of the budget line on the y-axis can be caused by a decrease in income or a decrease in the price of the good or service measured on the y-axis. When there is a decrease in income, the individual has less money to allocate to different goods and services, resulting in a lower budget line. This means that they have fewer resources available to spend on the goods and services represented on the y-axis. Similarly, a decrease in the price of a good or service measured on the y-axis would also lead to a reduction in the budget line. When the price decreases, the individual can purchase more of that good or service with the given income, resulting in a lower budget line. They can now afford to allocate more resources towards the good or service measured on the y-axis. In both cases, the reduction in the budget line signifies a decrease in the individual's purchasing power for the specific good or service measured on the y-axis.
Which of the following shows the combinations of goods or services that a person can purchase?
The options given do not show the combinations of goods or services that a person can purchase. Please provide the list of options so that I can assist you further.
What happen to original budget line it income increase in 5o%?
If the income increases by 50%, the original budget line would shift upwards parallelly. This is because with a higher income, the individual now has more money to allocate towards various goods and services. As a result, they are able to afford more of each good. The new budget line will represent the increased purchasing power of the individual after their income has increased by 50%.
How to find slope of budget constraint?
To find the slope of a budget constraint, you need to know the prices of two goods and the amount of money available for spending. Here are the steps: Identify the two goods in question. Let's call them Good 1 and Good 2. Determine the prices of Good 1 and Good Let's call them P1 and P2, respectively. Calculate the total amount of money available for spending. Let's call it M. Write down the equation for the budget constraint. It can be expressed as P1x1 + P2x2 = M, where x1 and x2 represent the quantities of Good 1 and Good 2, respectively. Rearrange the budget constraint equation to solve for xIt will be x2 = (M/P2) - (P1/P2)x1. The slope of the budget constraint is the coefficient of x1, which in this case is -(P1/P2). So, the final step is to determine the ratio of P1 to P2 (P1/P 2) and then change the sign to find the slope of the budget constraint.
How do you determine if a budget line will become flatter or steeper?
The budget line will become flatter or steeper depending on the relative changes of income and prices of the goods. If income rises and the prices of the goods decrease, the budget line will become flatter with more available goods. On the other hand, if income decreases and the prices of the goods increase, then the budget line will become steeper, as fewer goods will be available at the same level of income.
When will the budget line becomes flatter os streeper?
The budget line will become flatter or steeper depending on the changes in the prices of the two goods. If the price of one good increases while the price of the other good stays the same, the budget line will become steeper. If the price of one good decreases while the price of the other good stays the same, the budget line will become flatter.
What makes a budget line shift outwards?
A budget line shifts outward when an increase in income occurs, an decrease in the price of a good occurs, or an increase in the quantity of goods purchased occurs.
Why does the budget line rotate inward when price of x increases?
When the price of X increases, it takes more of good Y to purchase the same quantity of good X. This causes the budget line to rotate inward because, for a given price of Y, a consumer has less money to spend on both X and Y. This shift in the budget line reflects that for the same budget, a consumer is able to purchase less of both X and Y.
What can change consumers budget line?
There are several factors that can affect a consumer's budget line. These include changes in income, taxes, inflation, debt, and prices. An increase in income allows consumers to purchase more goods and services, while a decrease in income would limit the goods and services a consumer can purchase. Changes in taxes, inflation, and debt can also affect a consumer's budget line. For example, inflation can cause prices to increase, while taxes can reduce the amount of money a consumer can spend on certain items. Finally, changes in prices of goods and services can also affect a consumer's budget line.
Does the change in income affect the slope of the budgetline explain?
Yes, the change in income will affect the slope of the budget line. The slope of the budget line indicates how much of each good a consumer can purchase with a given amount of money. As income increases, the budget line shifts outward, indicating that the consumer can now purchase more of both goods with the same amount of money. As the budget line shifts, the slope of the budget line also changes, as the consumer is now able to purchase a different combination of goods than they could before the income change.
What happens to a line when the yintercept is changed?
When the y-intercept is changed, the line will shift either up or down depending on the size and sign of the new y-intercept. The slope of the line remains unchanged.
Which event would cause the budget line to shift outward?
A rise in the cost of goods and services.
How to draw a budget line?
Start by drawing a graph on a sheet of paper. Label the x-axis as 'quantity of good' and the y-axis as 'price of good'. Draw a straight line from the origin up to a point on the y-axis. This line will serve as the budget line. Label the point on the y-axis where the budget line intersects with it as “Pmax” (maximum price). Label the point on the x-axis where the budget line intersects with it as “Qmax” (maximum quantity). Draw a second line that is parallel to the budget line. This line should pass through the origin and intersect with the y-axis at a lower price than the budget line. Label the lower price point as “Pmin” (minimum price). This serves as the lower limit of the budget line. Finally, label the point where the parallel line intersects with the x-axis as “Qmin” (minimum quantity). This serves as the upper limit of the budget line.
What happens budjet line if price of one comodity doubles?
If the price of one commodity doubles, the budget line will shift outwards along the price axis. The slope of the budget line remains the same, but the intercepts will change. The horizontal intercept will be twice the original amount and the vertical intercept will stay the same.
When do they say a budget line is stipper and flatter?
A budget line is said to be steeper when the slope of the line is larger and flatter when the slope of the line is smaller.
What happens to the slope of a budget line if a goods price increases?
The slope of a budget line decreases if the price of a good increases.
Is budget line will shift out ward parallel to the original if pruce of one good decreases?
Yes, if the price of one good decreases, then the budget line will shift outward parallel to the original. This is because the decrease in price increases the quantity of that good that can be purchased given the same level of income. This shift in the budget line will result in higher levels of consumption for both goods.
Does the change in income affect theslope of the budget line explain.?
Yes, the change in income will affect the slope of the budget line. This is because the budget line represents the relationship between the price of goods and the amount of income available to purchase them. If income increases, the slope of the budget line increases as well, since more income increases the available amount of goods that can be purchased. Conversely, if income decreases, the slope of the budget line decreases as well, since less income decreases the available amount of goods that can be purchased.
Why change in income doesnot affect the slope of the budget line?
Slope of the budget line is calculated by the change in the quantity of a good divided by the change in its price. Income plays no part in this equation, so it does not affect the slope of the budget line.
How does the change in income or prices changes budget line and slope of budget line?
A change in income or prices alters the budget line's slope and intercepts. When income increases, budget lines shift outwards from the origin, meaning that the slope of the budget line changes. A rise in prices results in an inward shift in the budget line, and the slope of the budget line also changes.
Does change in income affect slope of bugdet line?
Yes, a change in income will affect the slope of the budget line. When income increases, the budget line will become flatter, and when income decreases, the budget line will become more steep.
What happens to the budget line if the price of good 2 triples and good 1 doubles?
The budget line will shift outwards by the same proportion as the increase in price.
What happens to the original buget line if the budget falls by25?
The original budget line would need to be reduced by 25%.
Does the change incomes affect the slope of buget line explain?
Yes, the change in incomes will affect the slope of the budget line. A change in incomes will affect the ability of the consumer to purchase goods, which in turn affects the budget line and its slope. If incomes increase, then the budget line will become more steep, while if incomes decrease, then the budget line will become more flat.
WHAT HAPPENS TO THE BUDGET LINE IF PRICES OF BOTH GOODS INCREASES?
If prices of both goods increase, the budget line will shift upwards, as the combination of goods that can be purchased with a given budget will decrease.
What causes budget line to rotate inward?
A decrease in budget line rotation is caused by a decrease in the price of one of the two goods included in the budget line, an increase in the consumer's income, or a combination of the two.
When prices increase the budget line?
When prices increase, the budget line shifts outward, reflecting the greater cost of the same combination of goods and services.
When will the budget line shift downward?
The budget line will shift downward when the consumer's income increases and the amount they can spend on goods increases.
Does the change in income affect the slope of the buget line explain?
Yes, the change in income affects the slope of the buget line. As income increases or decreases, the budget line will shift up or down accordingly, and the slope of the line will also change accordingly. This is because, as income increases, the consumer can purchase more goods and services, leading to a steeper budget line, while as income decreases, the consumer can purchase fewer goods and services, resulting in a flatter budget line.
What is change in come affectthe slope budget line?
A change in income affects the slope of a budget line by shifting the entire line either outward or inward. If income increases, the line shifts outward, and if income decreases, the line shifts inward.
Why woud the bubget line become steeper?
The budget line becomes steeper when the relative price of one product changes with respect to another. As the relative price of one product increases, the budget line becomes steeper. This reflects the fact that people have less money to spend on other goods and must allocate more of their budget to the good that has become relatively more expensive.
Does the change in income affect the slop of the buget line?
Yes, the change in income affects the slope of the budget line because a change in income shifts the budget line to a new position.
When income decreases the budget line?
When income decreases, the budget line will shift downward and to the left, indicating that the consumer is able to purchase fewer goods and services with the same amount of money.
How does a budgets change?
A budget can change for a variety of reasons, such as changes in income, increases in expenses, or changes in the economic environment. A budget can also be adjusted to reflect changes in lifestyle or goals. For example, if a person decides to save more money, they may adjust their budget to reflect this change.
Does the change in income affect the slope of the budget line Wxplain.?
Yes, the change in income affects the slope of the budget line because it affects the amount of money available to purchase goods and services. As income increases, the amount of money available increases and the slope of the budget line will become more and more upward sloping. As income decreases, the amount of money available decreases and the slope of the budget line will become more and more downward sloping.
Does the change in income affect the slope of the budget line Explain.?
Yes, the change in income will affect the slope of the budget line. When income increases, the budget line will become less steep, meaning that more consumption of a given good is possible for any given price level. When income decreases, the budget line will become steeper, meaning that less consumption of a given good is possible for any given price level.
Does the change in income affect the slop of the budget line?
Yes, the change in income will affect the slope of the budget line. As income increases, the slope of the budget line increases. This indicates that a consumer has more money to spend, so the consumer will demand more goods and services. When income decreases, the budget line slope decreases, indicating that a consumer has less money to spend so the demand for goods and services decreases.
Does the change in income affect the slope of the budget line?
Yes, it does. When a person's income changes, the slope of their budget line will also change. A decrease in income will result in a steeper budget line, reflecting the fact that the same amount of goods can be purchased with less money. A rise in income will result in a flatter budget line, reflecting the fact that more goods can be purchased with the same amount of money.
What happens when both income and prices increase?
When both income and prices increase, the consumer has more purchasing power and the demand for goods and services increases. This causes an increase in production and business activity, leading to an economic growth and potentially higher wages.
What happens to budget line when one good becomes free?
The budget line will shift outward as the price of the good becomes free, meaning the consumer will be able to buy a larger quantity of both goods at the same price. This is due to the fact that the consumer has more money to spend on the other good since the price of one good has become zero.
What makes the budget line change?
The budget line can change due to changes in income, prices, availability of goods and services, or preferences. Changes in income, prices or availability of goods or services will cause a shift in the budget line. Changes in preferences, such as if a consumer prefers one good over another, can cause a rotation in the budget line.
How does the budget line change when good y has a higher price?
The budget line for good Y will shift upwards when the price of good Y increases. This is because the consumer now has less money available to spend on good Y and will therefore have to give up more units of good X in order to purchase the same amount of good Y.
What does it mean if the slope of the budget line changes indeterminately microeconomics?
In microeconomics, a change in the slope of the budget line means that the relative prices of goods have changed, influencing consumer purchasing decisions. When the slope of the budget line changes indeterminately, it means that the relative prices are changing in an unpredictable or uncertain manner. This could indicate a period of rapid inflation or deflation, or a market disruption due to a new government policy or external shock.
How will an increase in income affect the budget line?
An increase in income would result in an increase in the budget line, as the individual would have more money to allocate to their budget. This could mean either increasing the budget for certain items or adding in new budget items.
What happens to the slope of the budget line when both prices go down?
The slope of the budget line will decrease.
How increases income affect budget line in microeconomis?
An increase in income can lead to a rightward shift of a budget line in microeconomics. This occurs because an increase in income allows the individual to purchase more of a good or service. As the individual's budget increases, so does the amount of goods and services that can be purchased. This shift in the budget line to the right shows that there is an increase in the quantity of goods and services that can be purchased at each price point.
Does the price change make your budget line flatter or steeper explain your choice.?
The price change will make the budget line steeper. When the price of one good changes, the slope of the budget line (the ratio of the prices of the two goods) will change. If the price of one good increases, the slope of the budget line will become steeper, as it will require more of the other good to purchase the same quantity of the increased good.
What happens to the budget line when a good increase price?
The budget line will shift outward, reflecting the higher price of the good. This shift will also cause a proportionate decrease in the quantity demanded, as people will be able to purchase fewer units at the higher price.
How the budget line changes based on an increase in price?
If the price of a good increases, the budget line will shift downward and to the left, meaning that less of the good can be purchased for a given income.
What causes a budget line to move outward in microeconomics?
A budget line in microeconomics describes the combination of two different goods that a consumer can purchase with a given level of income. The budget line will move outward when the consumer's income increases, allowing them to purchase more goods and therefore move further along the budget line.
How does the budget line change slope position if we change income or the price of a good?
The budget line will shift if the income or the price of a good changes. If the income increases, the slope position of the budget line will become less steep (more shallow). This is because the consumer will have more money available to purchase goods or services. Conversely, if the price of a good increases, the slope position of the budget line will become steeper (more steep). This is because the consumer will have less money available to purchase goods or services.
What are factors affecting budget line?
Income: The amount of money a person or family has available to spend affects their budget line. Prices: Higher prices generally decrease the quantity of goods that a person can afford. Credit availability: Access to credit, either from a bank or other source, will affect the amount of goods a person can purchase. Interest rates: Higher rates lead to higher borrowing costs, which will reduce the amount of money available to spend. Inflation: Inflation erodes the purchasing power of money over time and can affect the budget line. Taxes: Taxes reduce the amount of money available to spend, which decreases the budget line. Government policies: Government policies such as subsidies and tariffs can affect the budget line.
What causeschange in budget line?
The primary causes of changes in budget lines are changes in economic conditions, changes in government policies and regulations, changes in revenue streams, changes in costs of goods and services, changes in expected demand for goods and services, changes in underlying assumptions about the future, and changes in attitudes of the public.
What happn budget line when there ischange in incone?
When there is a change in income, the budget line will shift. If income increases, the budget line will shift outwards, indicating that the consumer has the ability to purchase a larger quantity of goods. If income decreases, the budget line will shift inwards, indicating that the consumer has less ability to purchase goods.
How budget line can change?
A budget line can change in a variety of different ways. Some possible ways include changes in the prices of goods and services, changes in income levels, changes in tastes or preferences, changes in available resources, changes in taxes, and changes in government policies. In addition, a budget line can also change due to economic or political events, or unexpected changes in the macroeconomic environment.
What happens when price of good 1 and2 changes budget line?
If the price of good 1 or 2 changes, then the budget line will shift up or down. If the price of good 1 increases, then the budget line will shift downwards. If the price of good 2 increases, then the budget line will shift upwards. This shift in the budget line will cause a change in the mix of the goods that can be consumed with the same amount of money.
What factor can shift the budget line outward?
An increase in income or reduction in the price of a good will shift the budget line outward.
What happens to the budget line when price of both the goods and income becomes half?
The budget line will remain unchanged. The budget line represents the maximum amount of goods and services that can be purchased, given a certain amount of income and the prices of the goods and services. If the prices of both the goods and services and income are halved, the budget line will theoretically remain the same.
What causes the budget kjne to be steeper?
The budget kink is usually caused by changes in tax or transfer policy. A steeper budget kink occurs when governments raise taxes or reduce transfers to households. This causes a larger gap between the two curves, resulting in a steeper budget kink. Additionally, changes in the levels of public expenditure, prices and wages can also affect the shape of the budget kink.
What happens to the budget set if both the price nd income us double?
If both the price and the income are doubled, then the budget will also double.
Why does a budget line shift or tilt?
A budget line can shift or tilt due to changes in a consumer's income, prices of goods, or preferences. A budget line will shift if either the consumer's income or the price of two goods changes, while a budget line will tilt when the consumer's preferences for goods change.
What factors can shift the budget line outwards?
Increase in income (income effect). Decrease in the prices of goods (substitution effect). Increase in the overall level of prices (inflation). Increase in the availability of credit (credit effect). Increase in taxes (tax burden effect). Changes in government subsidies (subsidy effect). Changes in the relative prices of goods (price effect). Changes in the tastes and preferences of consumers (taste effect).
Why does budget line tilt?
Budget lines tilt because as the quantity of one item increases, the amount of money that can be spent on other items decreases. This is due to the constraint of the budget, which limits the amount of purchasing power available to the consumer. As the price of one item increases, the consumer must choose to buy less of the item or fewer of the other items. This is why the budget line must tilt downward in order for the consumer to maintain the same level of purchasing power.
What factor can shift the budget line outwards?
A change in income, a change in prices of goods, or a change in the individual's preferences for different goods are all factors that can shift the budget line outwards.
What shifts a budget line outward?
A budget line shifts outward when the price of one of the goods rises, while the price of the other good remains the same. This will cause the consumer to have to reallocate their spending to accommodate the higher cost of one good while maintaining the same quantity of both goods.
Is budget related to microeconomics?
Yes, budgeting is related to microeconomics because it is concerned with the decisions made by individual actors or households and how those decisions impact the allocation of resources. Microeconomics examines how the decisions of individuals and firms affect the allocation of resources and how resources are used. It also looks at how the government influences those decisions through taxation, subsidies, and other policies. Budgeting is part of microeconomics because it focuses on decisions about how much money is allocated to different areas and how those allocations impact economic decisions.
What happens when budget line increase?
When the budget line increases, it means the amount of money available to spend on goods and services increases, which can lead to higher levels of consumption. This can stimulate the economy by increasing demand for goods and services, which in turn creates more jobs and increases incomes. Increased incomes can also further stimulate the economy, allowing for further consumption, creating a positive feedback loop.
What causes a change in a budget?
A change in a budget can be caused by a variety of factors, including inflation, changes in government policies, new initiatives, unexpected expenditures, changes in tax laws, and fluctuations in interest rates. Other factors that can affect a budget include changes in economic conditions, increases in demand for goods or services, and changes in a company’s competitive landscape.
What causes a budget line to become steeper?
A budget line becomes steeper when a consumer's income increases but the prices of the goods remain the same. The increased income gives the consumer more purchasing power, allowing them to purchase more of the same goods. The higher quantity of goods purchased causes the budget line to become steeper.
What happens to the budget line when price and income changes?
When price and income change, the budget line will shift, either due to an increase in income or a decrease in prices. An increase in income will cause the budget line to shift outward, and a decrease in prices will cause the budget line to shift inward. The new budget line will reflect the new income level and prices of the goods and services being bought.
What happens to a budget line with the prices of both goods double?
If the prices of both goods double, the budget line will shift outward and to the right, because the same amount of money will now be able to purchase fewer goods.
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Nearpod version available
Graphing and Interpreting Linear Relationships in the Context of Budgeting
Students will be able to:
- Create a graph representing a budget line and calculate the trade-offs of moving along the line.
- Represent a budget line using an equation in two variables.
- Predict transformations of the budget line given changes in income, changes in price of a good, or both.
- Calculate an equation for a budget line.
- Explain the meaning of the budget line in terms of personal finance.
National Standards in Economics
State Standards
Common Core State Standards
In this personal finance lesson, students explore budget constraints by solving a contextual problem.
- Graphing & Interpreting Linear Relationships in the Context of Budgeting Presentation ppt File | pdf File
- Activity 1 , Pat and Sam Hangout, one copy per student
- Activity 2 , Trade-offs and Budget Constraints, one copy per pair of students
- Activity 1 Key and Activity 2 Key , one copy for the teacher
Budgets are an important part of personal finance and meeting financial goals. While a budget is a spending and saving plan, based on estimated income and expenses for an individual or an organization over a specific time period, budget constraints are limits. Goods are tangible objects and services are activities that people perform for us. Both satisfy economic wants. The prices of goods and services and the amount of personal income-(i.e., payments earned by households for selling or renting their productive resources which may include salaries, wages, interest and dividends)-limit spending and serve as constraints to budgets. This lesson considers a problem situation in which only two goods can be purchased with a given income. This simplified approach should enable students to extend the decision-making process to more complex (e.g., real-world) challenges virtually everyone faces. The budget line is represented using tables, graphs, and linear functions. Equations use constants and variables to represent relationships between quantities. Variables are symbols used to represent numbers. The impact of shifts in income and prices of goods can be analyzed by exploring transformations of the budget line that represent relationships between these quantities.
- Show Slide 1 and tell students they are going to explore the expenses involved in hanging out with friends.
- How much money might students your age have to spend? [ Answers will vary. ]
- How might students earn the money they have to spend? [ Answers will vary, but may include allowance or money received from jobs .]
- What are some things students your age buy regularly with the money you have earned? [ Answers will vary, but may include transportation, food, games, and other entertainment. ]
- Tell the students that they will investigate the expenses involved with “hanging out” in a problem situation designed to model the relationship between income and prices of goods.
- Show Slide 3. Write the following terms on the board: income, budget, budget constraint, and trade-off. Ask the students to share words that could be used to define each term. List the words the students use on the board.
- Write the definitions below on the board (or use Slide 4) and circle any of the words used by the students in the definitions. For example, if the students used the term “salaries,” circle the word in the definition of income.
- Income : Payments earned by households for selling or renting their productive resources. May include salaries, wages, interest, and dividends.
- Budget : A spending-and-saving plan, based on estimated income and expenses for an individual or an organization, over a specific time period.
- Budget constraint: All the combinations of goods and services that a consumer may purchase, given current prices, and still be within his or her given income.
- Tradeoff : Giving up some of one thing to gain some of something else.
- Distribute a copy of Activity 1 to each student. Show Slide 5 and ask volunteers to read the slide. Ask students if they ever hang out with someone. [ Answers will vary. ]
- Show Slide 6. Tell students that Pat rides the bus using the stops in green. Ask students to complete number 1 on Activity 1.
- Explain that Pat must use a token to ride to Sam’s bus stop, then get off the bus and go to Sam’s house. Next, Pat and Sam return to the bus stop. They then each use a token to ride together to Freddy’s to have fries. Pat and Sam then must each use a token to ride to Sam’s bus stop. Pat walks with Sam to Sam’s house and returns to the nearest bus stop and rides the bus back home. Ask a student to come up to the slide and trace the route Pat rides to pick up Sam and go to Freddy’s. Note that some students may not know what a token is. Explain that a bus token is a prepaid coin similar to a prepaid bus pass. Ask students if they have suggestions for how Pat might ride the bus using fewer bus tokens. [ Students will offer suggestions about how to ride the bus and use fewer bus tokens. Some students may say that Pat does not need to get off the bus, but that the two people can meet at Sam’s bus stop and Pat can just get on the bus. Explain that while they are first hanging out, the two want to ride together for the maximum amount of time. ]
- Ask students to complete number 2 on Activity 1.
- Show Slide 7. Ask students what else they would need to know to find out how much Pat needs to spend in order to hang out with Sam? [ Answers will vary. Students will likely say they need to know the price of a bus token and the price of the fries. ]
- Ask students to complete number 3 on Activity 1.
- Show Slide 8. Ask students, “Now that you have more information, what will Pat spend on the bus for both Pat and Sam? What will Pat spend on fries if each gets an order of fries?” [ Pat will spend 12 dollars on bus tokens and two dollars on fries. ]
- Ask the students to share how they found their answers. [ If six tokens are needed to hang out and each token is two dollars then you multiply six and two to get 12 dollars (i.e., Pat uses four tokens and Sam uses two). If an order of fries is one dollar and you want to buy two of them, you multiply two and one to get two dollars. ]
- Show Slide 9. Tell students that the values at the bottom of the table represent the quantities of fries that Pat can buy for a hang out. The values on the left side of the table represent the quantities of bus tokens that Pat can buy for a hang out. Ask students how they can find the total amount that Pat needs for a particular combination. Select a combination such as four fries and 12 tokens and ask what calculation they can do. [ One dollar times four plus two dollars times 12 for a total of 28. ]
- Ask students where the total expense of 28 should go in the table. [ Answers will vary. Go to the number 4 along the bottom row and identify the column associated with the expense for 4 fries. Identify the row with 12 bus tokens and see where the row intersects the column. This is the cell that represents the combination of 4 fries and 12 tokens. ]
- Instruct students to complete the table in number 4 on Activity 1. (Note: this is a good place to split this lesson if you want to do it in two days. You can assign the table completion for homework.)
- Show Slide 10. Ask students what patterns they notice and what they noticed that helped them fill in the table quickly. [ Answers will vary. Students may notice constant differences in rows (2) or columns (4). They may also notice diagonal differences are constant (6). ] Point out that this table represents the amount Pat would spend on different combinations of fries and tokens.
- Ask students to answer number 5 a-c on Activity 1. Review answers using the Activity 1 Answer Key.
- Which cells in the table show the number of fries and tokens you can buy for 32 dollars? Tell students to circle them. [ Student answers will vary, but they will identify all the cells in the table with 32 in the cell. ]
- Each of these cells shows us one combination of fries and tokens on which Pat could spend 32 dollars. How many different combinations are there? [Eight]
- How can you be sure there will not be other combinations as the number of fries and tokens increases? [ Answers will vary. Students may share that since both quantities are increasing, the total amount spent must also increase. ]
- Show Slide 11 to verify student answers. Tell students that now they will find an equation for all of the possible combinations.
- Show Slide 12. Put students into pairs. Give each pair a copy of Activity 2. Ask students to work with their partner and fill in the table in problem number 1 on Activity 2.
- Display Visual 1. When students complete this task, ask for volunteers to share their answers but be sure to write answers on Visual 1 in order so that patterns can be identified easily. Otherwise, show Slide 13 and ask what equation they could write if x is the number of fries Pat buys and y is the number of tokens and the total must be 32 dollars. [$ 1x+$2y=$32 ]
- Tell students they have now represented all of the possible combinations of fries and tokens Pat can buy with 32 dollars. Tell students this is an example of a budget constraint or all the combinations of goods and services that a consumer may purchase, given current prices, within his or her given income.
- Tell students they will now investigate how a graph can show all the possibilities if Pat wants to buy only bus tokens and fries with the 32 dollars. Point out to students that with an income of $32, Pat cannot buy all the fries and all the tokens that Pat may want. Pat must make a choice and when Pat determines how many fries and tokens to buy with 32 dollars, Pat makes a trade-off. Tell students that a trade-off is giving up some of one thing to gain some of something else. Ask students what trade-offs are made for the different combinations. For example, to go from 16 to 20 fries, Pat gains four fries, but what does Pat have to give up? [ Two tokens ] To gain six tokens, how many fries does Pat have to give up? [ 12. ]
- Show Slide 14. Tell students to work with their partner to complete numbers 2-4 and the table in number 5 on Activity 2. Give the students 10 minutes to finish this task. Review answers using the Activity 2 Answer Key.
- Tell students they are going to represent Pat’s budget and constraints on that budget with a graph. Ask for volunteers to suggest points you need to plot on the graph. Ask students to plot the points on the graph in number 5 on Activity 2.
- Tell students they can represent the limit of Pat’s budget with a line. Points below the line represent quantities of fries and tokens Pat can buy. Ask students to draw the budget line in number 6 on Activity 2.
- Display slide 15 and ask students to check their graph for accuracy.
- Ask students to complete numbers 7-12 on Activity 2. Give students 10 minutes to complete this work.
- As the students are completing the activity, circulate and ask them to share their ideas about the addends in the equation and the meaning of points above, on, and below the budget constraint line. [ Answers will vary, but students are expected to say that points above the line represent combinations that Pat’s budget will not allow and combinations below the line represent combinations Pat can afford. Addends (i.e., numbers added together) represent the total cost of fries and the total cost of bus tokens. Those points on the line represent combinations Pat can afford, but that will require Pat to spend all of the income. ]
- What is the equation of the line? [ Answers will vary, but students should be able to see that the equation of the line is the same as the equation from the table they created namely 1x+2y=32. ] Note that the goal is to build a link between the computations and the graph as a representation of Pat’s budget and its constraints for hang outs.
- What does 1x represent in the equation? [ Money spent on fries is represented by 1x. ]
- What does 2y represent in the equation? [ Money spent on bus tokens is represented by 2y. ]
- What does the point (6, 10) on your graph represent? [ The point represents six fries and 10 bus tokens for a total cost of 26 dollars. ]
- Can Pat purchase 10 fries and 10 bus tokens? How do you know? [ Yes, since the point (10, 10) is below the budget constraint line. ]
- Can Pat purchase 10 fries and 20 bus tokens? How do you know? [ No, since the point (10, 20) is above the budget constraint line. ]
- What do the points above the line represent? [ Answers will vary. They represent combinations that Pat cannot purchase with his income. ]
- Call the students back together and tell them that Pat just got some news. Show Slide 17. Ask students how this news will impact the budget constraint graph. Ask students to work with their partner to complete number 13 on Activity 2 and to create a new graph to represent the effect of the news. Give the students five minutes for this task.
- Call the students back together and ask what they found. [ Answers will vary. They may say the line decreases at a faster rate than the original budget constraint line. ]
- Show Slide 18 and ask students to explain the difference between the original line and the new line in terms of fries and bus tokens. [ Answers will vary, but students should say that the new price of fries means that fewer bus tokens can be purchased for a given quantity of fries, so all the y values for the points will be lower than they were before the increase in the price of fries. ]
- Ask students to complete number 14 on Activity 2.
- Show Slide 19 and ask the students how many times each month Pat can hang out with Sam if fries are two dollars and bus tokens are two dollars. [ Answers will vary, but students should find a maximum number of two times. Each bus round trip for both costs $12. Thus, with an income of $32, only two round trips can be purchased. ]
Review the key points of the lesson using the following questions:
- What is a budget? [ A spending and saving plan based on estimated income and expenses for an individual or an organization, over a specific time period. ]
- What is income? [ Payments earned by households for selling or renting their productive resources. This may include salaries, wages, interest, and dividends. ]
- When have you earned income? [ Answers will vary but students should recognize that they have earned income when they have been paid for work that they have done. ]
- What is a budget constraint? [ All the combinations of goods and services that a consumer may purchase, given current prices, within his or her given income. ]
- What is a trade-off? [ Giving up some of one thing to get some of something else. ]
- Given the budget constraint line has the equation 32 = 1 x + 2 y , x is the number of fries Pat can buy, and y is the number of tokens, what is the meaning of 32 in the equation? [ 32 is Pat’s total income. ]
- Given the budget constraint line has the equation 32 = 1 x + 2 y , x is the number of fries Pat can buy, and y is the number of tokens, what is the meaning of 2 in the equation? [ $2 is the price of a token. ]
- Given the budget constraint line has the equation 32 = 1 x + 2 y , x is the number of fries Pat can buy, and y is the number of tokens, what is the meaning of 1 x in the equation? [ $ 1 is the price of an order of fries and x is the number of order of fries. So 1x is the total amount Pat can spend on fries. ]
- Explain how to find the equation for a budget constraint line if you know that your total income is $20 and you can purchase soda and hotdogs. The price of each soda is $2.00 and the price of each hotdog is $4.00. [ First decide whether the number of sodas or hotdogs will be x. Second write your equation using the following approach: if the number of sodas is represented by x, then the number of hotdogs will be represented by y. The price of soda is $2 and 2x represents the amount spent on sodas. The price of a hotdog is $4 and 4y is the amount spent on hotdogs. So the total amount spent on hotdogs and soda is 2x + 4y = 20 .]
- Explain how to create the graph for the budget constraint line if you know that the total income is $20, the price of each soda is $2.00 and the price of each hotdog is $4.00. [ First find the number of sodas you could purchase if you bought no hotdogs. Second, find the number of hotdogs you could purchase if you bought no sodas. Third, putting the number of sodas on the x axis, plot the point (10, 0) representing 10 sodas and 0 hotdogs. All your money is spent on soda. Fourth, putting the number of hotdogs on the y-axis, plot the point (0, 5), representing zero sodas and five hotdogs. All your money is spent on hotdogs. Now draw the segment between the two points. This is the budget line that represents the limit for your income. ]
- How can we represent the relationship between income and prices of goods? [ This relationship can be represented by a line called the budget constraint line. ]
- 10 = 2 x + 1 y
- [10 = 1x + 2y]
- 10 = ½ x + y
- Bill has $10 dollars to spend on chips and soda. If the price of chips is $1 and the price of a soda is $2, which graph represents the relationship between Bill’s income and the quantity of chips ( x ) and soda ( y ) he can purchase with his money?
[Answer: a.]
- Create a graph of the budget constraint line if Pat’s income is 12 dollars, bus tokens are four dollars, and fries are two dollars.
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The budget line | set, slope and shift | microeconomics.
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So far, we have discussed different combinations of two goods that provide same level of satisfaction. But, which combination, will a consumer actually purchase, depends upon his income (‘consumer budget’) and prices of the two commodities.
Image Courtesy : images.flatworldknowledge.com/coopermicro/coopermicro-fig04_001.jpg
Consumer Budget states the real income or purchasing power of the consumer from which he can purchase certain quantitative bundles of two goods at given price. It means, a consumer can purchase only those combinations (bundles) of goods, which cost less than or equal to his income.
Budget line is a graphical representation of all possible combinations of two goods which can be purchased with given income and prices, such that the cost of each of these combinations is equal to the money income of the consumer. Alternately, Budget Line is locus of different combinations of the two goods which the consumer consumes and which cost exactly his income.
Let us understand the concept of Budget line with the help of an example: Suppose, a consumer has an income of Rs. 20. He wants to spend it on two commodities: X and Y and both are priced at Rs. 10 each. Now, the consumer has three options to spend his entire income: (i) Buy 2 units of X; (ii) Buy 2 units of Y; or (iii) Buy 1 unit of X and 1 unit of Y. It means, possible bundles can be: (2, 0); (0, 2) or (1, 1). When all these three bundles are represented graphically, we get a downward sloping straight line, known as ‘Budget Line’. It is also known as price line.
Budget Set :
Budget set is the set of all possible combinations of the two goods which a consumer can afford, given his income and prices in the market.
In addition to the three options, there are some more options available to the consumer within his income, even if entire income is not spent. Budget set includes all the bundles with the total income of Rs. 20, i.e. possible bundles or Consumer’s bundles are: (0, 0); (0, 1); (0, 2); (1, 0); (2, 0); (1,1). Consumer’s Bundle is a quantitative combination of two goods which can be purchased by a consumer from his given income.
Diagrammatic Explanation of Budget Line:
Suppose, a consumer has a budget of Rs. 20 to be spent on two commodities: apples (A) and bananas (B). If apple is priced at Rs. 4 each and banana at Rs. 2 each, then the consumer can determine the various combinations (bundles), which form the budget line. The possible options of spending income of Rs. 20 are given in Table 2.7:
Table 2.7: Schedule of Budget Line
In Fig. 2.8, number of apples is taken on the X-axis and bananas on the Y-axis. At one extreme (Point ‘E’), consumer can buy 5 apples by spending his entire income of Rs. 20 only on apples. The other extreme (Point ‘j’), shows that the entire income is spent only on bananas. Between E and J, there are other combinations like F, G, H and I. By joining all these points, we get a straight line ‘AB’ known as the Budget Line or Price line.
Every point on this budget line indicates those bundles of apples and bananas, which the consumer can purchase by spending his entire income of f 20 at the given prices of goods.
Important Points about Budget line (Refer Fig. 2.8):
1. Budget line AB slopes downwards as more of one good can be bought by decreasing some units of the other good.
2. Bundles which cost exactly equal to consumer’s money income (like combinations E to J) lie on the budget line.
3. Bundles which cost less than consumer’s money income (like combination D) shows under spending. They lie inside the budget line.
4. Bundles which cost more than consumer’s money income (like combination C) are not available to the consumer. They lie outside the budget line.
Algebraic Expression of Budget Line
The budget line can be expressed as an equation:
M = (P A x Q A ) + (P B x Q B )
M = Money income;
Q A = Quantity of apples (A);
Q B = Quantity of bananas (B);
P A = Price of each apple;
P B = Price of each banana.
All points on the budget line ‘AB’ indicate those bundles, which cost exactly equal to
Algebraic Expression for Budget Set: The consumer can buy any bundle (A, B), such that: M > (P A x Q A ) + (P B x Q B )
Slope of the Budget Line :
We know, the slope of a curve is calculated as a change in variable on the vertical or Y-axis divided by change in variable on the horizontal or X-axis. In the example of apples and bananas, slope of the budget line will be number of units of bananas, that the consumer is willing to sacrifice for an additional unit of apple.
Slope of Budget Line = Units of Bananas (B) willing to Sacrifice/ Units of Apples (A) willing to Gain = ∆B/∆A
As seen in Fig. 2.8, 2 bananas need to be sacrificed each time to gain 1 apple.
So, Slope of Budget Line = -2/1 = **2/1 = 2
Numerator will always have negative value as it shows number of units to be sacrificed. However, for analysis, absolute value is always considered.
This slope of budget line is equal to ‘Price Ratio’ of two goods.
What is Price Ratio?
Price Ratio is the price of the good on the horizontal or X-axis divided by the price of the good on the vertical or Y-axis. For instance, If good X is plotted on the horizontal axis and good Y on the vertical axis, then:
Price Ratio = Price of X (P X )/Price of Y(P Y ) = P X /P Y
Why slope of Budget Line is represented by Price Ratio?
A point on the budget line indicates a bundle which the consumer can purchase by spending his entire income. So, if the consumer wants to have one more unit of good 1 (say, Apples or A), then he will have to give up some amount of good 2 (say, Bananas or B)’The number of bananas needed to be given up to gain 1 apple depends on the prices of apples and bananas.
As per Table 2.7, Apple (A) is priced at Rs. 4 (P A ) and Bananas (B) at Rs. 2 (P B ). It means, to gain 1 apple, consumer will have to reduce his expenditure on bananas by Rs. 4, i.e. consumer will have to sacrifice 2 bananas to gain 1 apple. It means, consumer will have to give P A /P B units of Banana to gain one apple. P A /P B is nothing but the price ratio between Apples and Bananas. So, it is rightly said that Price Ratio indicates the slope of Budget Line.
Moreover, Price ratio remains constant throughout because P X and P Y on the basis of which AX and AY are calculated are constant throughout.
Shift in Budget Line :
Budget line is drawn with the assumptions of constant income of consumer and constant prices of the commodities. A new budget line would have to be drawn if either (a) Income of the consumer changes, or (b) Price of the commodity changes.
Let us understand this with the example of apples and bananas:
1. Effect of a Change in the Income of Consumer:
If there is any change in the income, assuming no change in prices of apples and bananas, then the budget line will shift. When income increases, the consumer will be able to buy more bundles of goods, which were previously not possible. It will shift the budget line to the right from ‘AB’ to ‘A 1 B 1 ‘, as seen in Fig. 2.9. The new budget line A 1 B 1 will be parallel to the original budget line ‘AB’.
Similarly, a decrease in income will lead to a leftward shift in the budget line to A 2 B 2 .
Why is the new Budget line parallel to original budget line?
The new budget line ‘A 1 B 4 ‘ or ‘A 2 B 2 ‘ is parallel to original budget line ‘AB’ because there is no change in the slope. We know, the slope of a curve is calculated as a change in one variable that occurs due to change in another variable. In case of budget line, slope = P X /P Y As change in income does not disturb the price ratio of the two commodities, the slope will not change and the budget line, after change in income will remain parallel to the original budget line.
2. Effect of change in the relative Prices (Apples and Bananas):
If there is any change in prices of the two commodities, assuming no change in the money income of consumer, then budget line will change. It will change the slope of budget line, as price ratio will change, with change in prices.
(i) Change in the price of commodity on X-axis (Apples):
When the price of apples falls, then new budget line is represented by a shift in budget line (see Fig. 2.10) to the right from ‘AB’ to ‘A 1 B’. The new budget line meets the Y-axis at the same point ‘B’, because the price of bananas has not changed. But it will touch the X-axis to the right of ‘A’ at point ‘A 1 , because the consumer can now purchase more apples, with the same income level.
Similarly, a rise in the price of apples will shift the budget line towards left from ‘AB’ to ‘A 2 B’.
(ii) Change in the price of commodity on Y-axis (Bananas):
With a fall in the price of bananas, the new budget line will shift to the right from ‘AB’ to AB 1 (see Fig. 2.11). The new budget line meets the X-axis at the same point ‘A’, due to no change in the price of apples. But it will touch the Y-axis to the right of ‘B’ at point ‘B 1 ‘, because the consumer can now purchase more bananas, with the same income level.
Similarly, a rise in the price of bananas will shift the budget line towards left from ‘AB’ to ‘AB 2 ‘.
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Budget Line
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Indifference curves and budget lines
An indifference curve is a line showing all the combinations of two goods which give a consumer equal utility. In other words, the consumer would be indifferent to these different combinations.
Example of choice of goods which give consumers the same utility
Table plotted as indifference curve
Diminishing marginal utility.
The indifference curve is convex because of diminishing marginal utility . When you have a certain number of bananas – that is all you want to eat in a week. Extra bananas give very little utility, so you would give up a lot of bananas to get something else.
Indifference curve map
We can also show different indifference curves.
All choices on I2 give the same utility. But, it will be a higher net utility than indifference curve I1.
I4 gives the highest net utility. Basically, I4 would require higher income than I1.
Budget line
A budget line shows the combination of goods that can be afforded with your current income.
If an apple costs £1 and a banana £2, the above budget line shows all the combinations of the goods which can be bought with £40. For example:
- 20 apples @ £1 and 10 bananas @£2
- 10 apples @£1 and 15 bananas @£2
Optimal choice of goods for consumer
- Given a budget line of B1, the consumer will maximise utility where the highest indifference curve is tangential to the budget line (20 apples, 10 bananas)
- Given current income – IC2 is unobtainable.
- IC3 is obtainable but gives less utility than the higher IC1
- The optimal choice of goods can also be shown with the Equi-marginal principle
Income-consumption curve
As income rises, you can afford to consume on higher indifference curves. This optimal choice will shift to the right. This we can plot consumption as income rises.
Impact of lower price
With a lower price of bananas (from £2 to £1.50), we can now afford more bananas with the same income. The budget line shifts to the right
With lower prices, we can now consume at a higher indifference curve of IC2, enabling more bananas and apples.
Income and substitution effect of a rise in price
When the price of a good rises. People buy less for two reasons
- Income effect. This looks at the effect of a price increase on disposable income. If the price of a good increases, then consumers will have relatively lower disposable income. For example, if the price of petrol rises, consumers may not be able to afford to drive as much, leading to lower demand.
- Substitution effect. This looks at the effect of a price increase compared to alternatives. If the price of petrol rises, then it is relatively cheaper to go by bus.
Income and substitution for a normal good
- A rise in price changes the budget line. You can now buy less of good Bananas. The budget curve shifts to B2
- Consumption falls from point A to point C (fall in Quantity of bananas from Q3 to Q1
To find different substitution and income effects.
- We draw a new budget line parallel to B2 but tangential to the first indifference curve.
- Being tangential to first indifference curve it enables the consumer to obtain the same utility as before (as if there was no change in income.)
- By focusing on B-3, we are examining the effect of price change – ignoring any income effect.
- The change from A to B (Q3 to Q2) is purely due to the substitution effect and relative price change.
Income effect
- However, income has fallen causing the consumer to choose from a lower indifference curve I2. The change due to income is, therefore, b to C (Q2 to Q1.)
- In this case of a normal good, the income and substitution effect reinforce each other – both leading to lower demand.
Effect of a rise in the price of an inferior good
- The substitution effect (using a parallel budget line of B-3) causes a big fall from a to b.
- However, the income effect leads to an increase in demand (Q1 to Q2)
- Overall demand falls, but the substitution effect is partly offset by the income effect.
- This is because when income falls, the decline in income causes us to buy more inferior goods because we can’t afford normal / luxury goods anymore.
Giffen goods
A Giffen good occurs when the income effect outweighs the substitution effect. This is quite rare, but it is theoretically possible for poor peasants who have a choice between expensive meat and cheap rice.
We start at Q2, the rise in the price of rice, reduces the budget line for rice to B2. But, the fall in income causes a large income effect that outweighs the substitution effect. Demand for rice rises to Q3 with a big fall in demand for meat.
- Allocative efficiency
- Consumer choice
- Budget constraints
Budget Line: Meaning, Formula, Shift in budget line
Meaning of budget line.
Budget line refers to straight line with downward slope indicating the distinct combinations of two commodities that can be afforded by customer at given market price and particular income allocation. In simple terms, it is a graphical representation of all feasible combinations of two commodities, purchasable with given income and cost such that each one of these combinations is equal to customer earnings. It is also known as budget constraint due to its nature of only exhibiting those product combinations falling within the purchasing power of customer at given market price. The budget line forms its basis on 2 essential components: a) Purchasing power of customers b). Market value of 2 products that are in consideration. Also, it is key to note that scope of budget line is in correlation with the cost of 2 commodities.
Therefore, the income level and market price of commodities are two robust constraints faced by consumer striving to attain maximum utility across indifference curve. Income serves as main constraint because of the fact that only a particular height can be reached in indifference curve at given level of income.
Equation of Budget line
The understanding of budget line equation is must in order to know this concept in more detailed manner. This equation is as represented below: –
M = Px × Qx + Py × Qy
Px =Price of product X
Py =Price of product Y
Qx =Quantity of product X
Qy =Quantity of product Y
M =Money income of consumer
The equation indicates that for buying commodity X and Y, customer cannot incur expenditure in excess of his or her income level (M).
Features of Budget line
A Budget line carries special features that distinguish it from other available tools of economics. Such features of budget line are as described below: –
- Negative Slope- The negative downward sloping line indicates inverse relationship in between the purchase of 2 products.
- Real Income Line- Real income line is dependent upon the individual’s income aspect and expenditure capacity. It is basically an indicator of income and spending size of customer.
- Straight Line- This line in budget line shows present market rate of exchange for each of the combination shown.
- Tangent to indifference curve- It is a point where indifference curve meets the budget line and is also known as consumer’s equilibrium.
Assumptions of Budget Line
The budget line concept, similar to most of the economic theories, is based on assumptions and not reality. For getting simple and precise results, the below mentioned points are taken into consideration by economists.
- Two commodities- It is assumed by economists that income is spend by customers on purchase of two commodities only.
- Market price- Customer is fully aware of each product’s market price.
- Customer’s income- The total monetary earnings of customer is constraint and designated for purchase of two products only.
- Similarity in income and expense- It is assumed that whatever income consumer earns, he spends whole of it.
Shift in Budget Line
Consistency of budget line is influenced by following factors: – Consumer income, price of two commodities and volume of two commodities purchased.
The quantity of product purchased is up to certain extend under the control of consumer, however its price and income of consumer varies with time. These change leads to shift in the budget line.
Shift due to price change: Price of product keeps on changing from time to time. Like suppose, if price and income of product A remains same and price of product B falls down then purchasing power for product B will automatically rise up. In the same manner, if Product B price increases and other factors remain constant then automatically its demand will fall down.
Shift due to income change: The change in income makes huge change thereby leading to variations in budget line. High income with customer means high purchasing power whereas low income means low purchasing potential, making budget line to shift.
Premises of Budget Line
The premises of budget line are as follows-
- Determination of commodities market price- Budget line presumes that customer is always updated about the market price of two products in consideration. The line will become infeasible if there are any alteration in prices.
- Number of commodities- Presence of only two commodities form the basis of establishment for budget line concept. It is presumed that there are necessarily only two commodities for fulfilling the demand of customer.
- Detail on consumer income- Budget line assumes that consumer’s income pertains to limited amount that is known accurately. In addition to this, only know number of products is utilized for allocation of resources.
Example of Budget line
A person has Rs. 100 to buy biscuits. He has following options available for allocating his amount in order to derive maximum utility from limited income.
The above-mentioned options are only one customer can choose to derive maximum utility out of his limited income amount i.e., Rs100. If he wants to purchase more of one commodity then he needs to sacrifice the other commodity.
Therefore, we can say, budget line is a component of budget set that includes all feasible combinations of 2 products and focuses on expenditure of total income. This works on principle of sacrificing one commodity for buying more units of other commodities within limited level of income and at particular market price.
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7.3 Indifference Curve Analysis: An Alternative Approach to Understanding Consumer Choice
Learning objectives.
- Explain utility maximization using the concepts of indifference curves and budget lines.
- Explain the notion of the marginal rate of substitution and how it relates to the utility-maximizing solution.
- Derive a demand curve from an indifference map.
Economists typically use a different set of tools than those presented in the chapter up to this point to analyze consumer choices. While somewhat more complex, the tools presented in this section give us a powerful framework for assessing consumer choices.
We will begin our analysis with an algebraic and graphical presentation of the budget constraint. We will then examine a new concept that allows us to draw a map of a consumer’s preferences. Then we can draw some conclusions about the choices a utility-maximizing consumer could be expected to make.
The Budget Line
As we have already seen, a consumer’s choices are limited by the budget available. Total spending for goods and services can fall short of the budget constraint but may not exceed it.
Algebraically, we can write the budget constraint for two goods X and Y as:
Equation 7.7
[latex]P_X Q_X + P_Y Q_Y \leq B[/latex]
where P X and P Y are the prices of goods X and Y and Q X and Q Y are the quantities of goods X and Y chosen. The total income available to spend on the two goods is B , the consumer’s budget. Equation 7.7 states that total expenditures on goods X and Y (the left-hand side of the equation) cannot exceed B .
Suppose a college student, Janet Bain, enjoys skiing and horseback riding. A day spent pursuing either activity costs $50. Suppose she has $250 available to spend on these two activities each semester. Ms. Bain’s budget constraint is illustrated in Figure 7.9 “The Budget Line” .
For a consumer who buys only two goods, the budget constraint can be shown with a budget line. A budget line shows graphically the combinations of two goods a consumer can buy with a given budget.
The budget line shows all the combinations of skiing and horseback riding Ms. Bain can purchase with her budget of $250. She could also spend less than $250, purchasing combinations that lie below and to the left of the budget line in Figure 7.9 “The Budget Line” . Combinations above and to the right of the budget line are beyond the reach of her budget.
Figure 7.9 The Budget Line
The budget line shows combinations of the skiing and horseback riding Janet Bain could consume if the price of each activity is $50 and she has $250 available for them each semester. The slope of this budget line is −1, the negative of the price of horseback riding divided by the price of skiing.
The vertical intercept of the budget line (point D) is given by the number of days of skiing per month that Ms. Bain could enjoy, if she devoted all of her budget to skiing and none to horseback riding. She has $250, and the price of a day of skiing is $50. If she spent the entire amount on skiing, she could ski 5 days per semester. She would be meeting her budget constraint, since:
$50 x 0 + $50 x 5 = $250
The horizontal intercept of the budget line (point E) is the number of days she could spend horseback riding if she devoted her $250 entirely to that sport. She could purchase 5 days of either skiing or horseback riding per semester. Again, this is within her budget constraint, since:
$50 x 5 + $50 x 0 = $250
Because the budget line is linear, we can compute its slope between any two points. Between points D and E the vertical change is −5 days of skiing; the horizontal change is 5 days of horseback riding. The slope is thus −5/5=−1 . More generally, we find the slope of the budget line by finding the vertical and horizontal intercepts and then computing the slope between those two points. The vertical intercept of the budget line is found by dividing Ms. Bain’s budget, B , by the price of skiing, the good on the vertical axis ( P S ). The horizontal intercept is found by dividing B by the price of horseback riding, the good on the horizontal axis ( P H ). The slope is thus:
Equation 7.8
[latex]Slope = - \frac{B/P_S}{B/P_H}[/latex]
Simplifying this equation, we obtain
Equation 7.9
[latex]Slope = - \frac{B}{P_S} \times \frac{P_H}{B} = - \frac{P_H}{P_S}[/latex]
After canceling, Equation 7.9 shows that the slope of a budget line is the negative of the price of the good on the horizontal axis divided by the price of the good on the vertical axis.
It is easy to go awry on the issue of the slope of the budget line: It is the negative of the price of the good on the horizontal axis divided by the price of the good on the vertical axis. But does not slope equal the change in the vertical axis divided by the change in the horizontal axis? The answer, of course, is that the definition of slope has not changed. Notice that Equation 7.8 gives the vertical change divided by the horizontal change between two points. We then manipulated Equation 7.8 a bit to get to Equation 7.9 and found that slope also equaled the negative of the price of the good on the horizontal axis divided by the price of the good on the vertical axis. Price is not the variable that is shown on the two axes. The axes show the quantities of the two goods.
Indifference Curves
Suppose Ms. Bain spends 2 days skiing and 3 days horseback riding per semester. She will derive some level of total utility from that combination of the two activities. There are other combinations of the two activities that would yield the same level of total utility. Combinations of two goods that yield equal levels of utility are shown on an indifference curve . Because all points along an indifference curve generate the same level of utility, economists say that a consumer is indifferent between them.
Figure 7.10 “An Indifference Curve” shows an indifference curve for combinations of skiing and horseback riding that yield the same level of total utility. Point X marks Ms. Bain’s initial combination of 2 days skiing and 3 days horseback riding per semester. The indifference curve shows that she could obtain the same level of utility by moving to point W, skiing for 7 days and going horseback riding for 1 day. She could also get the same level of utility at point Y, skiing just 1 day and spending 5 days horseback riding. Ms. Bain is indifferent among combinations W, X, and Y. We assume that the two goods are divisible, so she is indifferent between any two points along an indifference curve.
Figure 7.10 An Indifference Curve
The indifference curve A shown here gives combinations of skiing and horseback riding that produce the same level of utility. Janet Bain is thus indifferent to which point on the curve she selects. Any point below and to the left of the indifference curve would produce a lower level of utility; any point above and to the right of the indifference curve would produce a higher level of utility.
Now look at point T in Figure 7.10 “An Indifference Curve” . It has the same amount of skiing as point X, but fewer days are spent horseback riding. Ms. Bain would thus prefer point X to point T. Similarly, she prefers X to U. What about a choice between the combinations at point W and point T? Because combinations X and W are equally satisfactory, and because Ms. Bain prefers X to T, she must prefer W to T. In general, any combination of two goods that lies below and to the left of an indifference curve for those goods yields less utility than any combination on the indifference curve. Such combinations are inferior to combinations on the indifference curve.
Point Z, with 3 days of skiing and 4 days of horseback riding, provides more of both activities than point X; Z therefore yields a higher level of utility. It is also superior to point W. In general, any combination that lies above and to the right of an indifference curve is preferred to any point on the indifference curve.
We can draw an indifference curve through any combination of two goods. Figure 7.11 “Indifference Curves” shows indifference curves drawn through each of the points we have discussed. Indifference curve A from Figure 7.10 “An Indifference Curve” is inferior to indifference curve B . Ms. Bain prefers all the combinations on indifference curve B to those on curve A , and she regards each of the combinations on indifference curve C as inferior to those on curves A and B .
Although only three indifference curves are shown in Figure 7.11 “Indifference Curves” , in principle an infinite number could be drawn. The collection of indifference curves for a consumer constitutes a kind of map illustrating a consumer’s preferences. Different consumers will have different maps. We have good reason to expect the indifference curves for all consumers to have the same basic shape as those shown here: They slope downward, and they become less steep as we travel down and to the right along them.
Figure 7.11 Indifference Curves
Each indifference curve suggests combinations among which the consumer is indifferent. Curves that are higher and to the right are preferred to those that are lower and to the left. Here, indifference curve B is preferred to curve A , which is preferred to curve C .
The slope of an indifference curve shows the rate at which two goods can be exchanged without affecting the consumer’s utility. Figure 7.12 “The Marginal Rate of Substitution” shows indifference curve C from Figure 7.11 “Indifference Curves” . Suppose Ms. Bain is at point S, consuming 4 days of skiing and 1 day of horseback riding per semester. Suppose she spends another day horseback riding. This additional day of horseback riding does not affect her utility if she gives up 2 days of skiing, moving to point T. She is thus willing to give up 2 days of skiing for a second day of horseback riding. The curve shows, however, that she would be willing to give up at most 1 day of skiing to obtain a third day of horseback riding (shown by point U).
Figure 7.12 The Marginal Rate of Substitution
The marginal rate of substitution is equal to the absolute value of the slope of an indifference curve. It is the maximum amount of one good a consumer is willing to give up to obtain an additional unit of another. Here, it is the number of days of skiing Janet Bain would be willing to give up to obtain an additional day of horseback riding. Notice that the marginal rate of substitution ( MRS ) declines as she consumes more and more days of horseback riding.
The maximum amount of one good a consumer would be willing to give up in order to obtain an additional unit of another is called the marginal rate of substitution (MRS) , which is equal to the absolute value of the slope of the indifference curve between two points. Figure 7.12 “The Marginal Rate of Substitution” shows that as Ms. Bain devotes more and more time to horseback riding, the rate at which she is willing to give up days of skiing for additional days of horseback riding—her marginal rate of substitution—diminishes.
The Utility-Maximizing Solution
We assume that each consumer seeks the highest indifference curve possible. The budget line gives the combinations of two goods that the consumer can purchase with a given budget. Utility maximization is therefore a matter of selecting a combination of two goods that satisfies two conditions:
- The point at which utility is maximized must be within the attainable region defined by the budget line.
- The point at which utility is maximized must be on the highest indifference curve consistent with condition 1.
Figure 7.13 “The Utility-Maximizing Solution” combines Janet Bain’s budget line from Figure 7.9 “The Budget Line” with her indifference curves from Figure 7.11 “Indifference Curves” . Our two conditions for utility maximization are satisfied at point X, where she skis 2 days per semester and spends 3 days horseback riding.
Figure 7.13 The Utility-Maximizing Solution
Combining Janet Bain’s budget line and indifference curves from Figure 7.9 “The Budget Line” and Figure 7.11 “Indifference Curves” , we find a point that (1) satisfies the budget constraint and (2) is on the highest indifference curve possible. That occurs for Ms. Bain at point X.
The highest indifference curve possible for a given budget line is tangent to the line; the indifference curve and budget line have the same slope at that point. The absolute value of the slope of the indifference curve shows the MRS between two goods. The absolute value of the slope of the budget line gives the price ratio between the two goods; it is the rate at which one good exchanges for another in the market. At the point of utility maximization, then, the rate at which the consumer is willing to exchange one good for another equals the rate at which the goods can be exchanged in the market. For any two goods X and Y, with good X on the horizontal axis and good Y on the vertical axis,
Equation 7.10
[latex]MRS_{X.Y} = \frac{P_X}{P_Y}[/latex]
Utility Maximization and the Marginal Decision Rule
How does the achievement of The Utility Maximizing Solution in Figure 7.13 “The Utility-Maximizing Solution” correspond to the marginal decision rule? That rule says that additional units of an activity should be pursued, if the marginal benefit of the activity exceeds the marginal cost. The observation of that rule would lead a consumer to the highest indifference curve possible for a given budget.
Suppose Ms. Bain has chosen a combination of skiing and horseback riding at point S in Figure 7.14 “Applying the Marginal Decision Rule” . She is now on indifference curve C . She is also on her budget line; she is spending all of the budget, $250, available for the purchase of the two goods.
Figure 7.14 Applying the Marginal Decision Rule
Suppose Ms. Bain is initially at point S. She is spending all of her budget, but she is not maximizing utility. Because her marginal rate of substitution exceeds the rate at which the market asks her to give up skiing for horseback riding, she can increase her satisfaction by moving to point D. Now she is on a higher indifference curve, E . She will continue exchanging skiing for horseback riding until she reaches point X, at which she is on curve A , the highest indifference curve possible.
An exchange of two days of skiing for one day of horseback riding would leave her at point T, and she would be as well off as she is at point S. Her marginal rate of substitution between points S and T is 2; her indifference curve is steeper than the budget line at point S. The fact that her indifference curve is steeper than her budget line tells us that the rate at which she is willing to exchange the two goods differs from the rate the market asks. She would be willing to give up as many as 2 days of skiing to gain an extra day of horseback riding; the market demands that she give up only one. The marginal decision rule says that if an additional unit of an activity yields greater benefit than its cost, it should be pursued. If the benefit to Ms. Bain of one more day of horseback riding equals the benefit of 2 days of skiing, yet she can get it by giving up only 1 day of skiing, then the benefit of that extra day of horseback riding is clearly greater than the cost.
Because the market asks that she give up less than she is willing to give up for an additional day of horseback riding, she will make the exchange. Beginning at point S, she will exchange a day of skiing for a day of horseback riding. That moves her along her budget line to point D. Recall that we can draw an indifference curve through any point; she is now on indifference curve E . It is above and to the right of indifference curve C , so Ms. Bain is clearly better off. And that should come as no surprise. When she was at point S, she was willing to give up 2 days of skiing to get an extra day of horseback riding. The market asked her to give up only one; she got her extra day of riding at a bargain! Her move along her budget line from point S to point D suggests a very important principle. If a consumer’s indifference curve intersects the budget line, then it will always be possible for the consumer to make exchanges along the budget line that move to a higher indifference curve. Ms. Bain’s new indifference curve at point D also intersects her budget line; she’s still willing to give up more skiing than the market asks for additional riding. She will make another exchange and move along her budget line to point X, at which she attains the highest indifference curve possible with her budget. Point X is on indifference curve A , which is tangent to the budget line.
Having reached point X, Ms. Bain clearly would not give up still more days of skiing for additional days of riding. Beyond point X, her indifference curve is flatter than the budget line—her marginal rate of substitution is less than the absolute value of the slope of the budget line. That means that the rate at which she would be willing to exchange skiing for horseback riding is less than the market asks. She cannot make herself better off than she is at point X by further rearranging her consumption. Point X, where the rate at which she is willing to exchange one good for another equals the rate the market asks, gives her the maximum utility possible.
Utility Maximization and Demand
Figure 7.14 “Applying the Marginal Decision Rule” showed Janet Bain’s utility-maximizing solution for skiing and horseback riding. She achieved it by selecting a point at which an indifference curve was tangent to her budget line. A change in the price of one of the goods, however, will shift her budget line. By observing what happens to the quantity of the good demanded, we can derive Ms. Bain’s demand curve.
Panel (a) of Figure 7.15 “Utility Maximization and Demand” shows the original solution at point X, where Ms. Bain has $250 to spend and the price of a day of either skiing or horseback riding is $50. Now suppose the price of horseback riding falls by half, to $25. That changes the horizontal intercept of the budget line; if she spends all of her money on horseback riding, she can now ride 10 days per semester. Another way to think about the new budget line is to remember that its slope is equal to the negative of the price of the good on the horizontal axis divided by the price of the good on the vertical axis. When the price of horseback riding (the good on the horizontal axis) goes down, the budget line becomes flatter. Ms. Bain picks a new utility-maximizing solution at point Z.
Figure 7.15 Utility Maximization and Demand
By observing a consumer’s response to a change in price, we can derive the consumer’s demand curve for a good. Panel (a) shows that at a price for horseback riding of $50 per day, Janet Bain chooses to spend 3 days horseback riding per semester. Panel (b) shows that a reduction in the price to $25 increases her quantity demanded to 4 days per semester. Points X and Z, at which Ms. Bain maximizes utility at horseback riding prices of $50 and $25, respectively, become points X′ and Z′ on her demand curve, d, for horseback riding in Panel (b).
The solution at Z involves an increase in the number of days Ms. Bain spends horseback riding. Notice that only the price of horseback riding has changed; all other features of the utility-maximizing solution remain the same. Ms. Bain’s budget and the price of skiing are unchanged; this is reflected in the fact that the vertical intercept of the budget line remains fixed. Ms. Bain’s preferences are unchanged; they are reflected by her indifference curves. Because all other factors in the solution are unchanged, we can determine two points on Ms. Bain’s demand curve for horseback riding from her indifference curve diagram. At a price of $50, she maximized utility at point X, spending 3 days horseback riding per semester. When the price falls to $25, she maximizes utility at point Z, riding 4 days per semester. Those points are plotted as points X′ and Z′ on her demand curve for horseback riding in Panel (b) of Figure 7.15 “Utility Maximization and Demand” .
Key Takeaways
- A budget line shows combinations of two goods a consumer is able to consume, given a budget constraint.
- An indifference curve shows combinations of two goods that yield equal satisfaction.
- To maximize utility, a consumer chooses a combination of two goods at which an indifference curve is tangent to the budget line.
- At the utility-maximizing solution, the consumer’s marginal rate of substitution (the absolute value of the slope of the indifference curve) is equal to the price ratio of the two goods.
- We can derive a demand curve from an indifference map by observing the quantity of the good consumed at different prices.
- Suppose a consumer has a budget for fast-food items of $20 per week and spends this money on two goods, hamburgers and pizzas. Suppose hamburgers cost $5 each and pizzas cost $10. Put the quantity of hamburgers purchased per week on the horizontal axis and the quantity of pizzas purchased per week on the vertical axis. Draw the budget line. What is its slope?
Suppose the consumer in part (a) is indifferent among the combinations of hamburgers and pizzas shown. In the grid you used to draw the budget lines, draw an indifference curve passing through the combinations shown, and label the corresponding points A, B , and C . Label this curve I.
- The budget line is tangent to indifference curve I at B . Explain the meaning of this tangency.
Case in Point: Preferences Prevail in P.O.W. Camps
Figure 7.16
Wikimedia Commons – CC BY-SA 3.0.
Economist R. A. Radford spent time in prisoner of war (P.O.W.) camps in Italy and Germany during World War II. He put this unpleasant experience to good use by testing a number of economic theories there. Relevant to this chapter, he consistently observed utility-maximizing behavior.
In the P.O.W. camps where he stayed, prisoners received rations, provided by their captors and the Red Cross, including tinned milk, tinned beef, jam, butter, biscuits, chocolate, tea, coffee, cigarettes, and other items. While all prisoners received approximately equal official rations (though some did manage to receive private care packages as well), their marginal rates of substitution between goods in the ration packages varied. To increase utility, prisoners began to engage in trade.
Prices of goods tended to be quoted in terms of cigarettes. Some camps had better organized markets than others but, in general, even though prisoners of each nationality were housed separately, so long as they could wander from bungalow to bungalow, the “cigarette” prices of goods were equal across bungalows. Trade allowed the prisoners to maximize their utility.
Consider coffee and tea. Panel (a) shows the indifference curves and budget line for typical British prisoners and Panel (b) shows the indifference curves and budget line for typical French prisoners. Suppose the price of an ounce of tea is 2 cigarettes and the price of an ounce of coffee is 1 cigarette. The slopes of the budget lines in each panel are identical; all prisoners faced the same prices. The price ratio is 1/2.
Suppose the ration packages given to all prisoners contained the same amounts of both coffee and tea. But notice that for typical British prisoners, given indifference curves which reflect their general preference for tea, the MRS at the initial allocation (point A) is less than the price ratio. For French prisoners, the MRS is greater than the price ratio (point B). By trading, both British and French prisoners can move to higher indifference curves. For the British prisoners, the utility-maximizing solution is at point E, with more tea and little coffee. For the French prisoners the utility-maximizing solution is at point E′, with more coffee and less tea. In equilibrium, both British and French prisoners consumed tea and coffee so that their MRS ’s equal 1/2, the price ratio in the market.
Figure 7.17
Source: R. A. Radford, “The Economic Organisation of a P.O.W. Camp,” Economica 12 (November 1945): 189–201; and Jack Hirshleifer, Price Theory and Applications (Englewood Cliffs, NJ: Prentice Hall, 1976): 85–86.
Answers to Try It! Problems
- The budget line is shown in Panel (a). Its slope is −$5/$10 = −0.5.
- Panel (b) shows indifference curve I . The points A, B, and C on I have been labeled.
The tangency point at B shows the combinations of hamburgers and pizza that maximize the consumer’s utility, given the budget constraint. At the point of tangency, the marginal rate of substitution ( MRS ) between the two goods is equal to the ratio of prices of the two goods. This means that the rate at which the consumer is willing to exchange one good for another equals the rate at which the goods can be exchanged in the market.
Figure 7.18
1 Limiting the situation to two goods allows us to show the problem graphically. By stating the problem of utility maximization with equations, we could extend the analysis to any number of goods and services.
Principles of Economics Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.
Shift and Rotation of the Budget Line (With Diagram)
In this article we will discuss about the shift and rotation of the budget line, explained with the help of a suitable diagram.
In the indifference curve theory, it is assumed that the consumer purchases and consumes only two goods (here X and Y). If the prices of goods X and Y, and the money income of the consumer is given, then the equation of the budget line of the consumer would be
M̅ = p x .x + p y .y [eqn.(6.15)]
The slope of the budget line (6.15) is –p x /p y = negative, and x-and y-intercept of the line are M/p x and M/p y , respectively.
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Now suppose, initially the values of M, p x and p y are such that the budget line of the consumer has been obtained to be a line like L 1 M 1 in Fig. 6.7.
If now the money income (M) of the consumer rises, p x and p y remaining unchanged, then, the slope (-p x /p y ) of his budget line remaining constant, the intercepts of the line (M/p x and M/p y ) would increase.
As a result, the budget line would have a rightward parallel shift from L 1 M 1 to a new position like L 2 M 2 . Conversely, if the money income of the consumer decreases, prices remaining constant, the budget line would have a parallel shift to the left. This rightward or leftward parallel shift of the budget line is known as “shift” of the budget line.
On the other hand, if the money income of the consumer remaining constant, the price of one of the goods changes, then it is known as the “rotation of the budget line”. For example, suppose, initially, the consumer’s budget line is L 1 M 1 in Fig. 6.7.
Now if the money income (M) of the consumer and the price of good Y remaining unchanged, the price of good X diminishes, then the y- intercept of the budget line (M̅/p y ) remains constant at OL 1 , but the x-intercept (M̅/p x ) increases from OM 1 to, say, OM 3 .
As a result, now the budget line of the consumer would be L 1 M 3 . Here the budget line while changing its position from L 1 M 1 to L 1 M 3 , rotates anticlockwise about the point L 1 . This is known as the “rotation” of the budget line.
Similarly, if M and p x remaining constant, p y falls, then also a rotation of the budget line from the initial L 1 M 1 position to a position like L 3 M 1 . Now the x-intercept of the budget line remaining constant, the y-intercept increases and the rotation of the budget line would be clockwise about the point M 1 .
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The budget line can define as a,
graphical representation of all possible combinations of two commodities that can be purchased with given income and prices, with the cost of each combination equal to the consumer’s money income.
You must have knowledge of the concept of the budget line to understand the theory of consumer equilibrium . When the budget line touches the indifference curve , that point gives the maximum utility. The touchpoint point is the customer equilibrium point.
What is the budget line formula?
Px X Qx + Py X Qy = M
- PX – Price of commodity X
- PY – Price of commodity Y
- QX – Quantity of commodity X
- QY – Quantity of commodity Y
- M – Consumer income
The above equation indicates that a consumer’s expenditure on X and Y products cannot exceed his or her income (M).
The budget line can use to represent this income constraint.
Properties of budget line
- Budget line is a straight line.
- Budget line has a negative slope.
- The slope of the budget line is negative of the price ratio.
- Budget line is tangent to indifference curve .
Assumptions of a budget line
- It is expected that the consumer would spend all of his money on only two goods.
- The consumer’s income is limited and known, even if it is entirely dedicated to the purchase of only two items.
- The consumer is aware of the market pricing of both commodities.
- We suppose the customer spends all of his or her money.
Budget line questions and answers
Let’s discuss budget line questions and answers.
Why is budget line a straight line?
The slope of this line equals the ratio of these commodities’ prices. The slope of the budget line is also constant since the prices of the two goods are constant. As a result, the budget line is a simple straight line.
Why is the budget line downward sloping?
Budget line is a downward sloping line because the consumer must consume less of something else to consume more of one good.
Most of the Good-X can be purchased when Good-Y is purchased in small quantities.
What is the slope of budget line equal to?
The slope of the line is equal to the ‘Price Ratio’ of two goods. The price ratio expresses the relation between the prices of two items, X and Y, that are inversely related to one another. It’s constant throughout a budget line.
Price Ratio = Px/Py
What happens to budget line if income increases?
When a consumer’s income rises, he or she may purchase more of both commodities, showing a budget line shift to the right. (outward) When income falls, however, the consumer’s consumption capacity falls, and the budget line shifts inwards.
What is the difference between the Budget set and the Budget line?
Budget line is a line that shows the different combinations of two goods that a consumer can attain given his income and market price of the goods. Budget set is a set of goods that the customer can purchase.
Difference between indifference curve and budget line
An indifference curve is a curve that shows the different combinations of two goods that yield the same level of satisfaction, whereas a budget line is a combination of two goods that is possible for consumption at a fixed level of income.
What do you mean by budget constraints?
The budget constraint refers to all potential combinations of commodities that one can purchase in terms of the price of the products, when all revenue is spent.
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- Key Differences
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Difference Between Budget Line and Budget Set
You might have come across the term ‘budget’ at least once in your life. To know what quantities of two commodities will be purchased by a consumer, what we need to know is – ‘How much money the consumer is willing to incur on those commodity and at what price the commodities are available in the market?’ This information will help us to plot a budget line.
What is Budget Constraint?
A budget constraint indicates that a consumer can pick any combinations of the two goods, provided that the cost is less than or equal to the income of the consumer.
In this post, we will talk about the differences between Budget Line and Budget Set.
Content: Budget Line Vs Budget Set
Comparison chart, shifts in budget line, definition of budget line.
Budget Line refers to all the possible bundles of two goods, that a consumer can buy at a given income and price of the goods, when he spends his entire income , to purchase the two goods.
Alternatively, it is called a consumption possibility line or price line . The bundles indicate the maximum quantities of the commodity that can be purchased with the given income. It can be expressed as under:
P X Q X + P Y Q Y = M
- If X = 0, then Y = M/P Y
- If Y = 0, then X = M/P X
OA = If the consumer incurs all his income on good Y, he can buy M/P Y or OA units of Y. OB = If the consumer incurs all his income on good X, he can buy M/P X or OB units of X. AB = Budget Line
Assumptions of Budget Line
- Income of the Consumer is provided and remains constant.
- Price of the commodities are provided and remains constant.
When you have an idea of the prices and income of a consumer, you can easily draw a consumer’s budget line by determining the combination of the two commodities that a consumer can ‘just afford’ and create a straight line that passes through both the points.
Properties of Budget Line
- Downward Sloping : If a consumer wants more of a particular good, then he/she would have less of the other, indicating an inverse relationship. So the slope is negative due to which it is downward sloping.
- Straight-line : As the price of the commodity is irrespective of the quantity of units purchased, i.e. there will be no discount on volume. So, if a consumer wants one more unit of a commodity, he has to pay the extra amount for that, which is possible by foregoing a certain amount of the other good. Hence, the constant rate of sacrifice makes budget line a straight one.
- Full Utilization : Budget Line reflects that the consumer spends all his income, on the purchase of the two goods, which means that there is full utilization of the income.
Definition of Budget Set
Budget Set implies the set of all the possible combinations of two goods that the consumer can afford or buy, which his/her income, at the existing market prices. Basically, it contains all those combinations in the positive quadrant, fall under or on the budget line. It can be expressed as:
P X Q X + P Y Q Y ≤ M
P X = Price of good x Q X = Quantity of good x P Y = Price of good y Q Y = Quantity of good y M = Income
OA = If the consumer incurs all his income on good Y, he can buy M/P Y or OA units of Y. OB = If the consumer incurs all his income on good X, he can buy M/P X or OB units of X. ΔAOB = Budget Set
Here every bundle of bracketed value represents a budget set, which represents the set of two goods which consumer can buy, with his given income, at the prevailing prices in the market. Of the given combinations, (0, 2), (2, 0) and (1, 1) cost equal to ₹ 100, while the other costs less than ₹ 100. However, any combination other than those given above, for instance (2, 3), (3, 4), etc. will cost more than ₹. 100, at the given prices, which is simply unachievable.
What will happen if the prices of the goods and income of the consumer doubles?
If the prices of the goods and income of the consumer doubles then there will be no change in the Budget Set, because the double price will be offset by double income and the effect will be same.
Key Differences Between Budget Line and Budget Set
The difference between budget line and budget set can be drawn clearly on the following grounds:
- The budget line represents all those consumption possibilities of two commodities with the help of a graph, which the consumer can buy spending his entire fixed income on the two commodities, at their prevailing prices. On the other hand, a consumer can afford any combination of the two goods, that lies on or inside the price line, and so that area is termed as a budget set.
- The budget line indicates the maximum amount which a consumer can spend on purchasing the goods. As against, Budget Set represents all the combinations of the two goods that lie on or below the budget line.
- The price of the sets of the goods that form the budget line is equal to the income of the consumer. Conversely, in case of a budget set, the sets of the goods that fall on or under the budget line, indicates that the total price of the two goods is less than or equal to the income of the consumer.
- The budget line is the borderline of the budget set. This means that the points lying inside the budget line represent what consumer can afford, whereas points lying outside the budget line indicates what consumer cannot afford. In contrast, the different combinations of two goods that help in drawing the budget line are the budget set.
We all know that, whatever purchases are made by the consumers, are based on two main factors – Consumer’s income and Prices of goods . So, these two factors decide the consumption limits of the consumer. Hence, if there is a change in any one of these determinants, it may result in the change of the budget line. Come let us understand the effect of change in these two factors:
Change in Income
Change in Prices of Goods
- If the price of good X and Y falls by an equal proportion, and in the same direction, then the price line will shift right. This will happen because the consumer will be able to buy more units of the two commodities with the same budget.
- If the price of good X and Y rises by an equal proportion, and in the same direction, then the price line will shift left. This is because, the consumer will have to forego some units of both the commodities, as the budget is fixed.
The table represented below highlights the bundles of shoes (₹ 100) and clothes (₹ 200) a consumer can buy, spending his income, i.e. ₹ 1000.
Basically, Budget Line shows the price ratio between two goods, i.e. X and Y or the rate at which one commodity can be exchanged for the other, where the prices of the two goods are given. Budget line depends on the consumer’s income and price of the commodities.
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Differences between Budget Line and Budget Set
Budget line.
A Budget Line is a graphical representation of all possible combinations of two goods that a consumer can purchase within a given amount. The purchasing power of a consumer and the market value of these two products determine the ratio in which one buys these two commodities. This budget line is a straight line with a negative slope depicting the reverse correlation between the two commodities. It can shift one way or the other depending on one of these two things:
- Change in the income of the consumer.
- Change in price of one or both goods.
Budget Set is a bundle of the combination of two commodities that the Budget Line represents. It lies below the Budget Line, and it helps determine the possible quantities of each item that a consumer can buy given their income and the market value of those two goods.
The main differences between Budget Line and Budget Set are as follows:
The differences between Budget Line and Budget Set help us understand the constraints under which a consumer has to operate while planning their expenditure, to ensure maximum possible satisfaction of their needs.
Frequently Asked Questions on Budget Line and Budget Set
What are the main assumptions behind the concept of budget line and budget set.
You can draw the Budget Line and Budget Set after considering the following assumptions:
- The consumers will spend their entire income on two commodities.
- They know the market price of the two products.
- Their total income is spent for purchasing these two products and there is no room for other expenses.
What is a shift in the Budget Line and when does it happen?
The Budget Line can shift in a particular direction in certain circumstances. The two circumstances that can influence this line are a change in the consumer’s income and a change in the price of one/both goods. Let us analyse both of these factors in greater detail below:
- Increase in income – Suppose there is an increase in the consumer’s income, but the prices of goods remain unchanged. It will increase their capacity to buy more goods and the consumer has the option to purchase a greater quantity of the same commodity. This increase in a consumer’s income will shift the Budget Line in a rightward direction.
- Decrease in income – Suppose there is a decrease in a consumer’s income, but the prices of goods remain unchanged. It will decrease their capacity to buy more goods, and they will also have to contend with buying a lesser quantity of the same commodity. This decrease in a consumer’s income will shift the Budget Line in a leftward direction.
- Change in price of one commodity – If the price of one product changes but everything else stays the same, it will also impact the Budget Line. If the price of one product falls, the consumer will have the option to purchase more units of that product. And if the market price of that same product goes up, the consumer will have to contend with buying fewer units of that product.
- Change in price of both commodities – If the market price of both products decreases simultaneously, the consumer will be able to purchase more units for both items and the Budget Line will shift towards the right. But if the prices of both products increase together, the consumer will have to purchase less of both commodities and the Budget Line will shift leftwards. If the price of one commodity rises but the other one falls, the buyer can purchase more of the first product but will have to reduce the quantity of the second product. This scenario will further affect the Budget Line.
- Deriving a Demand Curve from Indifference Curve and Budget Constraints
- Consumer Equilibrium
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- CBSE Class 11 Microeconomics Notes
Chapter 1: Introduction
- Introduction to Microeconomics
- Microeconomics and Macroeconomics: Meaning, Scope, Difference and Interdependence
- Difference Between Expansion of Supply and Increase in Supply
- Interdependence between Microeconomics and Macroeconomics
- Economic Problem & Its Causes
- Central Problems of an Economy
Chapter 2: Consumer's Equilibrium
- Theory of Consumer Behaviour
- Utility Analysis : Total Utility and Marginal Utility
- Law of Diminishing Marginal Utility (DMU) : Meaning, Assumptions & Example
- Consumer's Equilibrium in case of Single and Two Commodity
- Indifference Curve : Meaning, Assumptions & Properties
- Budget Line: Meaning, Properties, and Example
Difference between Budget Line and Budget Set
- Shift in Budget Line
- Consumer’s Equilibrium by Indifference Curve Analysis
Chapter 3: Demand
- Theory and Determinants of Demand
- Individual and Market Demand
- Difference between Individual Demand and Market Demand
- What is Demand Function and Demand Schedule?
- Law of Demand
- Movement along Demand Curve and Shift in Demand Curve
- Difference between Expansion in Demand and Increase in Demand
- Difference between Contraction in Demand and Decrease in Demand
- Substitute Goods and Complementary Goods
- Difference between Substitute Goods and Complementary Goods
- Normal Goods and Inferior Goods
- Difference between Normal Goods and Inferior Goods
- Types of Demand
- Substitution and Income Effect
- Difference between Substitution Effect and Income Effect
- Difference between Normal Goods, Inferior Goods, and Giffen Goods
Chapter 4: Elasticity of Demand
- Price Elasticity of Demand: Meaning, Types, Calculation and Factors Affecting Price Elasticity
- Methods of Measuring Price Elasticity of Demand: Percentage and Geometric Method
- Relationship between Price Elasticity of Demand and Total Expenditure
Chapter 5: Production Function: Returns to a Factor
- Production Function: Meaning, Features, and Types
- What is TP, AP and MP? Explain with examples.
- Law of Variable Proportion: Meaning, Assumptions, Phases and Reasons for Variable Proportions
- Relationship between TP, MP, and AP
- Law of Returns to Scale: Meaning and Stages
- Difference between Returns to Factor and Returns to Scale
Chapter 6: Concepts of Cost and Revenue
- What is Cost Function?
- Difference between Explicit Cost and Implicit Cost
- Types of Cost
- What is Total Cost ? | Formula, Example and Graph
- What is Average Cost ? | Formula, Example and Graph
- What is Marginal Cost ? | Formula, Example and Graph
- Interrelation between Costs
- Concepts of Revenue| Total Revenue, Average Revenue and Marginal Revenue
- Break-even Analysis: Importance, Uses, Components and Calculation
- What is Break-even Point and Shut-down Point?
Chapter 8: Theory of Supply
- Theory of Supply: Characteristics and Determinants of Individual and Market Supply
- Difference between Stock and Supply
- Law of Supply: Meaning, Assumptions, Reason and Exceptions
- Types of Elasticity of Supply
Chapter 9: Forms of Market
- Market : Characteristics & Classification
- Perfect Competition Market: Meaning, Features and Revenue Curves
- Monopoly Market: Features, Revenue Curves and Causes of Emergence
- Monopolistic Competition: Characteristics & Demand Curve
- Oligopoly Market : Types and Features
- Difference between Perfect Competition and Monopoly
- Difference between Perfect Competition and Monopolistic Competition
- Difference between Monopoly and Monopolistic Competition
- Distinction between the four Forms of Market(Perfect Competition, Monopoly, Monopolistic Competition and Oligopoly)
- Long-Run Equilibrium under Perfect, Monopolistic, and Monopoly Market
Chapter 10: Market Equilibrium under Perfect Competition
- Determination of Market Equilibrium under Perfect Competition
- Effects of Changes in Demand and Supply on Market Equilibrium
- Price Ceiling and Price Floor or Minimum Support Price (MSP): Simple Applications of Supply and Demand
- Difference between Price Ceiling and Price Floor
- Important Formulas in Microeconomics | Class 11
What is Budget Line?
A graphical representation of all possible combinations of two goods which a consumer can purchase with the given prices and income in a way that the cost of each of these combinations is equal to the consumer’s money income is known as a budget line. a budget line is also known as Price Line. For example, a consumer’s income is ₹10 and he wants to spend the money on two commodities, say X and Y and both of these goods are priced at ₹5 each. Now the consumer has three options for spending his income. The first option is to buy two units of commodity X. Second option is to buy two units of commodity Y. or the third option is to buy one unit of commodity X and one unit of commodity Y. This means that the possible bundles, in this case, can be (2, 0); (0, 2); and (1, 1). Now, when all of these three bundles are represented on a graph, a downward-sloping straight line is formed which is known as a budget line.
What is Budget Set?
The set of all possible combinations of the two commodities a consumer can afford to buy with his given income and price in the market is known as a budget set. In the above example, besides the three options; viz., (2, 0); (0, 2); and (1, 1), there are some other options which are available for the customer within his total income of ₹10, even if he does not spend his entire income. A budget set in this case will include all the bundles which have a total income of ₹10. The possible Consumer’s Bundles are (0, 0); (0, 1); (0, 2); (1, 0); (2, 0); and (1, 1). Hence, a consumer’s bundle is a quantitative combination of two goods which a consumer can purchase from his given income.
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Budget line is a graphical representation of all possible combinations of two goods which can be purchased with given income and prices, such that the cost of each of these combinations is equal to the money income of the consumer. Let us understand the concept of Budget line with the help of an example: Suppose, a consumer has an income of $20.
To plot the new budget line, find the new intercepts: Budget: $42. Price of movies: $7. Price of T-shirts: $14. Maximum number of movies (y-intercept): $42/$7 = 6. Maximum number of T-shirts (x-intercept): $42/$14 = 3. Figure 6.1c. As a result of the shift, José's budget line has shifted inward, leaving less consumption opportunities available.
Budget Line Budget Set; It is a graphical representation of a downward-sloping straight line. A budget set is an area under the price line represented on a graph. This line shows the maximum quantity of a commodity a consumer can buy for a certain quantity of the other good.
A budget line, also known as a budget constraint, represents all the possible combinations of two goods or services that a consumer can purchase given their income level and the prices of those goods or services. It's a graphical representation that shows the trade-off between two different goods, illustrating the limit to the consumer's ...
Budget line (also known as budget constraint) is a schedule or a graph that shows a series of various combinations of two products that can be consumed at a given income and prices.. Budget line is to consumers what a production possibilities curve is to producers. It is a useful tool in understanding consumer behavior and choices. Budget line depicts the consumer choices between two products.
The budget line can be written algebraically as follows: P x X + P y Y = M … (8.1) ADVERTISEMENTS: Where P x and P y denote prices of goods X and Y respectively and M stands for money income. The above budget-line equation (8.1) implies that, given the money income of the consumer and prices of the two goods, every combination lying on the ...
A budget line is a graphical representation of the possible combinations of two goods or services that a consumer can afford with a given income and prices. It shows the trade-off between spending on one good versus another. To draw a budget line, we need to know the income of the consumer, the prices of the two goods, and the axes on which we ...
Figure 3.1 The budget line—graph of budget constraint (equation 3.3) 3.2 The Slope of the Budget Line. Learning Objective 3.2: Interpret the slope of the budget line. From the graph of the budget constraint in section 3.1, we can see that the budget line slopes downward and has a constant slope along its entire length. This makes intuitive ...
The budget line is a graphical representation of the different combinations of two goods that a consumer can afford given their budget constraint and the prices of the goods. As a result, the budget line can change in several ways. Here are some detail explanations of how the budget line can change:
Objective. Students will be able to: Create a graph representing a budget line and calculate the trade-offs of moving along the line. Represent a budget line using an equation in two variables. Predict transformations of the budget line given changes in income, changes in price of a good, or both. Calculate an equation for a budget line.
Budget line is a graphical representation of all possible combinations of two goods which can be purchased with given income and prices, such that the cost of each of these combinations is equal to the money income of the consumer. Alternately, Budget Line is locus of different combinations of the two goods which the consumer consumes and which ...
We can explain a price or budget line with the help of a table. Suppose the monetary income of a consumer is Rs.40 which he wants to spend on two goods X and Y. The price of good X is Rs.2 per unit and that of good Y Re.1 per unit. Given his income and prices of two goods, the alternative consumption or expenditure possibilities of a consumer ...
Budget line. A budget line shows the combination of goods that can be afforded with your current income. If an apple costs £1 and a banana £2, the above budget line shows all the combinations of the goods which can be bought with £40. For example: 20 apples @ £1 and 10 bananas @£2; 10 apples @£1 and 15 bananas @£2
In simple terms, it is a graphical representation of all feasible combinations of two commodities, purchasable with given income and cost such that each one of these combinations is equal to customer earnings. ... Shift in Budget Line. Consistency of budget line is influenced by following factors: - Consumer income, price of two commodities ...
where P X and P Y are the prices of goods X and Y and Q X and Q Y are the quantities of goods X and Y chosen. The total income available to spend on the two goods is B, the consumer's budget.Equation 7.7 states that total expenditures on goods X and Y (the left-hand side of the equation) cannot exceed B.. Suppose a college student, Janet Bain, enjoys skiing and horseback riding.
This rightward or leftward parallel shift of the budget line is known as "shift" of the budget line. On the other hand, if the money income of the consumer remaining constant, the price of one of the goods changes, then it is known as the "rotation of the budget line". For example, suppose, initially, the consumer's budget line is L 1 ...
2563. The budget line can define as a, graphical representation of all possible combinations of two commodities that can be purchased with given income and prices, with the cost of each combination equal to the consumer's money income. You must have knowledge of the concept of the budget line to understand the theory of consumer equilibrium.
The term budget line refers to a graphical representation of all the potential combinations of two commodities that can be bought within a certain income and price, and all of these combinations provide the same satisfaction level. It comes with the condition that the cost of each combination must be less than or equal to the consumer's money ...
The budget line is a graphical representation of all those combinations of two goods which can be bought with a given budget, at existing prices of the two goods, by fully spending the income. Budget set entails all the combinations of the two commodities that a consumer can purchase with his limited income, at prevailing market prices. ...
The main differences between Budget Line and Budget Set are as follows: A Budget Line is a graphical representation of all possible combinations of two goods that a consumer can purchase within a fixed budget, i.e. their income and existing market prices. A Budget Set includes all combinations of two commodities that a consumer can buy within a ...
The term budget line refers to a graphical representation of all the potential combinations of two commodities that can be bought within a certain income and price, and all of these combinations provide the same satisfaction level. It comes with the condition that the cost of each combination must be less than or equal to the consumer's money ...
Budget Lines are a graphical representation of the combinations of goods that can be purchased with a certain amount of income and given the price of two goods. ... inside the person's opportunity set Good A (50A, 2581 125A, SA Budget Line Income $100, P-51. P.-S2 Good Suppose the budget line on the graph is for an income of $500, the PA=$5 and ...
A graphical representation of all possible combinations of two goods which a consumer can purchase with the given prices and income in a way that the cost of each of these combinations is equal to the consumer's money income is known as a budget line. a budget line is also known as Price Line.