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Budget Constraint

Wouldn't it be nice to be able to afford to buy a bunch of items at a store when you can't decide which one to choose? Of course! Unfortunately, each and every individual is faced with a budget constraint. Budget constraints limit our choices as a consumer and affect our overall utility. However, all hope is not lost, as economists can show you how you can still maximize utility given a limited budget. If you are ready to start learning how then keep scrolling!

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# Budget Constraint

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Nie wieder prokastinieren mit unseren Lernerinnerungen. Wouldn't it be nice to be able to afford to buy a bunch of items at a store when you can't decide which one to choose? Of course! Unfortunately, each and every individual is faced with a budget constraint. Budget constraints limit our choices as a consumer and affect our overall utility. However, all hope is not lost, as economists can show you how you can still maximize utility given a limited budget. If you are ready to start learning how then keep scrolling!

## Budget Constraint Definition

Let's jump straight into the definition of the budget constraint! When economists refer to a budget constraint, they mean the constraints imposed on consumer choices by their limited budgets. Take a look at an example below.

If you have only $100 to spend in a store to buy a coat, and you like two coats, one for$80 and one for $90, then you can only buy one. You have to choose between the two coats as the combined price of the two coats is greater than$100.

A budget constraint is a constraint imposed on Consumer Choice by their limited budget.

All consumers have a limit on how much they earn and, therefore, the limited budgets that they allocate to different goods. Ultimately, limited incomes are the primary cause of budget constraints. The effects of the budget constraint are evident in the fact that consumers can't just buy everything they want and are induced into making choices, according to their preferences, between the alternatives.

## Difference between Budget Set and Budget Constraint

There is a difference between budget set and budget constraint.

Let's contrast the two terms below so that it becomes clearer!The budget constraint represents all the possible combinations of two or more goods that a consumer can purchase, given current prices and their budget. Note that the budget constraint line will show all the combinations of goods you can buy given that you spend all the budget you allocate for these particular goods.It is easier to think about it in two goods scenario. Imagine you can buy only apples or bananas and have only $2. The price of an apple is 1$, and the cost of a banana is $2. If you only have$2, then all the possible combinations of goods that represent your budget constraint are as follows:

 Market Basket Apples Bananas Choice A 2 apples 0 bananas Choice B 0 apples 1 banana

Table 1 - Budget constraint exampleThese two choices are illustrated in Figure 1 below. Fig. 1 - Budget constraint example

Figure 1 shows a budget constraint line for a scenario depicted in Table 1. Because you cannot buy half an apple or half a banana, the only practically feasible points are A and B. At point A, you buy 2 apples and 0 bananas; at point B, you buy 1 banana and 0 apples.

A budget constraint line shows all the combinations of goods a consumer can purchase given that they spend all their budget that was allocated for these particular goods.

In theory, all the points along the budget constraint represent the possible combinations of apples and bananas you could buy. One such point - point C, where you buy 1 apple and half a banana to spend your $2 is shown in Figure 1 above. However, this consumption combination is unlikely to be achieved in practice. Because of the ratio of the two prices and the limited income, you are induced into choosing to trade off 2 apples for 1 banana. This trade-off is constant and results in a linear budget constraint with a constant slope. • Properties of the budget constraint line: • The slope of the budget line reflects the trade-off between the two goods represented by the ratio of the prices of these two goods. • A budget constraint is linear with a slope equal to the negative ratio of the prices of the two goods. Let's now look at how a budget set differs from the budget constraint. A budget set is more like a consumption opportunity set that a consumer faces, given their limited budget. Let's clarify by looking at Figure 2 below. Fig. 2 - Budget set example Figure 2 above shows a budget set represented by the green area within the budget constraint. All the points within that area, including the ones that lie on the budget constraint, are theoretically possible consumption bundles as they are the ones you can afford to purchase. This set of possible consumption bundles is what the budget set is. For the consumption bundles practicality in this example, the goods would need to be purchasable in quantities smaller than one. A budget set is a set of all possible consumption bundles given specific prices and a particular budget constraint. ## Budget Constraint Line What is the budget constraint line? The budget constraint line is a graphical representation of the budget constraint. Consumers who choose a consumption bundle that lies on their budget constraints utilize all of their income.Let's consider a hypothetical scenario in which a consumer must allocate all their income between the necessities of food and clothing. Let's denote the food price as $$P_1$$ and the quantity chosen as $$Q_1$$. Let the clothing price be $$P_2$$, and the quantity of clothing be $$Q_2$$. Consumer income is fixed and denoted by $$I$$.What would the budget constraint line formula be? ### Budget constraint formula The formula for the budget constraint line would be:$$P_1 \times Q_1 + P_2 \times Q_2 = I$$Let's plot this equation to see the budget constraint line graph! Fig. 3 - Budget constraint line Figure 3 above shows a general budget constraint line graph that works for any two goods with any prices and any given income. The general slope of the budget constraint is equal to the ratio of the two product prices $$-\frac{P_1}{P_2}$$. The budget constraint line intersects the vertical axis at point $$\frac{I}{P_2}$$; the horizontal axis intersection point is $$\frac{I}{P_1}$$. Think about it: when the budget constraint intersects the vertical axis, you are spending all your income on good 2, and that is exactly the coordinate of that point! Conversely, when the budget constraint intersects the horizontal axis, you are spending all your income on good 1, and so the intersection point in units of that good is your income divided by the price of that good! Want to explore more?Check out our article:- Budget Constraint Graph. ## Budget Constraint Example Let's go over an example of a budget constraint!Imagine Anna, who has a weekly income of$100. She can spend this income on either food or clothing. The price of food is $1 per unit, and the price of clothing is 2$ per unit.As the budget constraint line represents a few of the consumption combinations that would take up her entire income, we can construct the following table.

 Market Basket Food (units) Clothing (units) Total Expenditure ($) A 0 50$100 B 40 30 $100 C 80 10$100 D 100 0 $100 Table 2 - Consumption combinations example Table 2 above shows the possible market baskets A, B, C, and D that Anna can choose to spend her income on. If she buys basket D, she spends all her income on food. Conversely, if she purchases basket A, she spends all her income on clothing and has nothing left to buy food, as clothing per unit costs$2. Market baskets B and C are possible intermediate consumption baskets between the two extremes.

Note that there are more consumption baskets that exist along the budget constraint for all the possible combinations of food and clothing. We chose 4 market baskets for illustrative purposes.

Let's plot Anna's budget constraint! Fig. 4 - Budget constraint example

Figure 4 above shows Anna's weekly budget constraint for food and clothing. Points A, B, C, and D represent the consumption bundles from Table 2.

What would the equation of Anna's budget constraint line be?

Let's denote the food price as $$P_1$$ and the quantity that Anna chooses to buy weekly as $$Q_1$$. Let the clothing price be $$P_2$$, and the quantity of clothing that Anna chooses $$Q_2$$. Anna's weekly income is fixed and denoted by $$I$$.

The general formula for the budget constraint:$$P_1 \times Q_1 + P_2 \times Q_2 = I$$

Anna's budget constraint:

$$\1 \times Q_1 + \2 \times Q_2 = \100$$

Simplifying:

$$Q_1 + 2 \times Q_2 = 100$$

What would the slope of Anna's budget constraint be?

We know the slope of the line is the ratio of the prices of the two goods:

$$Slope=-\frac{P_1}{P_2}=-\frac{1}{2}$$.

We can also check the slope by re-arranging the equation in terms of $$Q_2$$:

$$Q_1 + 2 \times Q_2 = 100$$

$$2 \times Q_2= 100 - Q_1$$

$$Q_2= \frac{1}{2} \times(100 - Q_1)$$

$$Q_2= 50-\frac{1}{2} Q_1$$

The coefficient in front of $$Q_1$$ is equal to $$-\frac{1}{2}$$ which is the same as the slope of the budget line!

We bet we got you hooked on these topics!

Why not check out:

- Income and substitution effects;

- Revealed preferences.

## Budget Constraint - Key takeaways

• A budget constraint is a constraint imposed on consumer choice by their limited budget.
• A budget constraint line shows all the combinations of goods a consumer can purchase given that they spend all their budget that was allocated for these particular goods.
• A budget set is a set of possible consumption bundles given specific prices and a particular budget constraint.
• The general formula for the budget constraint:$$P_1 \times Q_1 + P_2 \times Q_2 = I$$
• The slope of the budget line is the ratio of the prices of the two goods:

$$Slope=-\frac{P_1}{P_2}=-\frac{1}{2}$$.

The general formula for the budget constraint is:

P1 * Q1 + P2 * Q2 = I

Ultimately, limited incomes are the primary cause of budget constraints.

The effects of the budget constraint are evident in the fact that consumers can't just buy everything they want and are induced into making choices, according to their preferences, between the alternatives.

A budget constraint is linear with a slope equal to the negative ratio of the prices of the two goods.

The slope of the budget line reflects the trade-off between the two goods represented by the ratio of the prices of these two goods.

## Budget Constraint Quiz - Teste dein Wissen

Question

What is the marginal rate of substitution?

The marginal rate of substitution is the maximum amount of a certain good an individual is willing to exchange for receiving an additional unit of another good.

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Question

One of the critical assumptions of the marginal rate of substitution hypothesis is that trade-offs made between two items that an individual substitutes for one another does ________ their utility.

not affect

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Question

What's the indifference curve?

An indifference curve is a kind of graph that is used to illustrate the many combinations of two distinct goods that provide consumers with the same level of utility and pleasure.

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Question

What's the relationship between the MRS and the indifference curve?

The marginal rate of substitution is the slope of the indifference curve.

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Question

Why is the indifference curve not a straight line?

That's because the marginal rate of substitution is not equal at all points of the indifference curve.

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Question

When an individual moves from consuming 10 units of coffee and 1 unit of pepsi, to consuming 5 units of coffee and 2 units of pepsi, the MRS equals ______ .

5

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Question

When an individual moves from consuming 5 units of coffee and 2 unit of pepsi, to consuming 3 units of coffee and 3 units of pepsi, the MRS equals ______ .

2

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Question

Diminishing marginal utility means that the MRS throughout the indifference curve declines.

True

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Question

The diminishing marginal rate of substitution is why the indifference curve is ______

Convex

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Question

What is the formula for MRS?

$$MRS = -\frac{\Delta\hbox{Good 1}}{\Delta\hbox{Good 2}}$$

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Question

Why is the MRS important?

The importance of the marginal rate of substitution comes from its ability to reveal and measure whether a consumer would exchange one product or service for another one.

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Question

Why is it the minus sign added to the MRS formula?

To make the MRS a positive number as the change in good 1 is always negative.

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Question

As the consumption of one good in terms of another increase, the magnitude of the slope of the indifference curve _______

Decreases

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Question

What does the term “utility” represent in economics?

Utility is an abstract value that an agent gets from a preference. It may also be defined as satisfaction gained from a selection.

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Question

How can we define a utility function?

Utility functions are a special type of function that connects or maps the amount of utility gained from preferences or bundles of goods.

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Question

What is the marginal utility?

Marginal utility is the change in the total utility with respect to the increase or decrease in consumption by one unit.

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Question

What is the Perfect Complement?

A bundle of goods is perfect complements if the goods in the bundle are consumed together with the same proportion.

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Question

What is the Perfect Substitutes?

A bundle of goods contains perfect substitutes if and only if the goods in the bundle can be used for each other’s places precisely the same way.

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Question

What is the relationship between indifference curves and utility functions?

If the results of a utility function are the same between different bundle combinations, we can say that the consumer is indecisive between these two bundles. Thus, if we draw a curve between these points, we will get an indifference curve.

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Question

Let’s define a utility function, $$u$$, as follows.
$$u(x) = x^2 + x | x\in R^{+}$$

What is the additional utility gained from one unit of x?

if $$u(x) = x^2 + x$$, then we can find additional utility gained from an additional consumption of x as follows.
$$\dfrac{\partial u(x)}{\partial x} = 2x + 1$$

Show question

Question

Let’s define a utility function, as follows.

$$u(x,y) = x^2 + y^2 + xy | x,y \in R^{+}$$

What is the additional utility gained from one unit of y?

If $$u(x,y) = x^2 + y^2 + xy$$ then we can calculate the additional utility gained from y as follows.

$$\dfrac{\partial u(x,y)}{\partial y} = 2y + x$$

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Question

Following function is a linear utility function.
$$u(x) = ax + x^2 | x ,a \in R^{+}$$

FALSE

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Question

Following function is a linear utility function.

$$u(x) = mx + c | x,m,c \in R^{+}$$

TRUE

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Question

The following function can be given as the general structure of the Cobb-Douglas utility functions.

$$u(x,y) = x^a y^b | a,b \in R, a+b = 1$$

TRUE

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Question

Let’s assume that we have the budget, $$w$$, which is equal to 20. There exist a commodity, $$x$$, with a price, $$P_x = 4$$. What is the maximum amount of utility we can get according to the utility function, $$u(x) = x^2 - x | x \in R^{+}$$ ?

We are trying to maximize our utility with respect to our budget. Thus, If the price of $$x$$ is equal to 4, we can get 5 $$x$$. Therefore, our maximum utility is $$u(5) = 25 -5 = 20$$

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Question

Which one of the following is not a common type of utility function?

Indifference Curves

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Question

A bundle of goods is perfect complements if the goods in the bundle are consumed together with the same proportion.

TRUE

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Question

If the consumption of two goods is relational in such a way that an increase in one’s consumption decreases the other good, these goods are substitutes for each other.

TRUE

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Question

How can we define the substitution effect?

The substitution effect occurs due to a decrease in the price of one good while the other good’s price remains the same. This changes the marginal rate of substitution and the slope of the budget line. The exact difference between new tangent point where new  budget line meets the indifference curve and the old tangent point where old budget line meets the indifference curve is the substitution effect.

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Question

How can we define the income effect?

The income effect is the change in consumption of goods due to increased real income. The income effect causes indifference curves to move up or down. If the price of the good decreases, our real income increases, and the indifference curve will move upwards and vice versa.

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Question

We are defining the effect of decreasing or increasing prices over consumption amount as the total effect of income and substitution.

True

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Question

How do you find the substitution effect from a graph?

The substitution effect occurs due to a decrease in the price of one good while the other good’s price remains the same. This changes the marginal rate of substitution and the slope of the budget line.

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Question

$$\text{Total Effect} (\Delta Q) = \text{Substitution Effect} + \text{Income Effect}$$

True

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Question

Do income and substitution effect work together?

They are separate effects. Nonetheless, combined together, they compose the total effect of decreased prices over consumption.

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Question

What is the relationship between income and substitution effect and the law of demand?

They are the driving force behind the downward slope of the total demand curve. They explain why lower prices will cause more consumption.

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Question

What can be said about the importance of income and substitution effect?

The income and substitution effect takes an important place in consumer choice theory and it may help us to explain the complex behavior of consumers in a more simple manner.

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Question

Let’s assume that due to decreased prices of one good, you wanted to consume that good instead of the other good. This can be called substitution effect.

True

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Question

Let’s assume that due to decreased prices of one good, you wanted to consume that good instead of the other good. This can be called the income effect.

False

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Question

Let’s assume that price of a good decreased and your real income has increased. So you decided to consume more of that good. This change happened due to the income effect.

True

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Question

Let’s assume that price of a good decreased and your real income has increased. So you decided to consume more of that good. This change happened due to the substitution effect.

False

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Question

We can find the income effect if we sum the substitution effect and the total effect.

False

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Question

What is a substitute?

A substitute good is a good that serves the same purpose as another good for consumers.

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Question

What is a complement?

A complementary good is a good that adds value to another good when they are consumed together.

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What are independent goods?

Independent goods are two good whose price changes do not influence the consumption of each other.

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Question

The main difference between a substitute and a complement is that substitute goods are consumed with each other, whereas complements are consumed in place of each other.

False

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Question

For substitute goods, a price reduction in one good ____ the demand for the other good.

Increases

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Question

____ refers to how a price change in one good causes a change in the quantity demanded of the another good.

Cross-price elasticity of demand

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Question

If the cross-price elasticity of demand of the two goods is positive, then the goods are ____.

Substitutes

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Question

If the cross-price elasticity of demand of the two goods is negative, then the goods are ____.

Complements

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Question

The formula for cross-price elasticity of demand is:

$$Cross\ Price\ Elasticity\ of\ Demand=\frac{\%\Delta Q_D\ Good A}{\%\Delta P\ Good\ A}$$

False

Show question

## Test your knowledge with multiple choice flashcards

One of the critical assumptions of the marginal rate of substitution hypothesis is that trade-offs made between two items that an individual substitutes for one another does ________ their utility.

When an individual moves from consuming 10 units of coffee and 1 unit of pepsi, to consuming 5 units of coffee and 2 units of pepsi, the MRS equals ______ .

When an individual moves from consuming 5 units of coffee and 2 unit of pepsi, to consuming 3 units of coffee and 3 units of pepsi, the MRS equals ______ .

Flashcards in Budget Constraint93

Start learning

What is the marginal rate of substitution?

The marginal rate of substitution is the maximum amount of a certain good an individual is willing to exchange for receiving an additional unit of another good.

One of the critical assumptions of the marginal rate of substitution hypothesis is that trade-offs made between two items that an individual substitutes for one another does ________ their utility.

not affect

What's the indifference curve?

An indifference curve is a kind of graph that is used to illustrate the many combinations of two distinct goods that provide consumers with the same level of utility and pleasure.

What's the relationship between the MRS and the indifference curve?

The marginal rate of substitution is the slope of the indifference curve.

Why is the indifference curve not a straight line?

That's because the marginal rate of substitution is not equal at all points of the indifference curve.

When an individual moves from consuming 10 units of coffee and 1 unit of pepsi, to consuming 5 units of coffee and 2 units of pepsi, the MRS equals ______ .

5

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