Topic #2: Budget Constraint Changes

Indifference maps may incorporate three types of changes: price changes, income changes, and changes in tastes and preferences. For example, suppose individuals may consume combinations of computers and typewriters and that recent empirical evidence shows that the consumption of computers has increased over the last 20 years. One explanation is that the price of computers has gone down (a price change):

Typewriters

T1

T2

U2

U1

BC1 BC2 C1 C2

Computers

Another explanation is that nominal incomes have increased (an income change):

Typewriters

U2

U1

BC1 BC2 C1 C2

Computers

Yet another explanation is that people are now less intimidated by computers (a change in tastes and preferences):

Typewriters

U1 (1980)

U2(2003)

C1 C2

Computers

Note that indifference curves can intersect in this instance because preferences can change over time.

Next, use the theory of consumer choice to derive a demand curve for consumption good X where consumption good X is measured on the horizontal axis and consumption good Y is measured on the vertical axis.

The first step is to raise the price of X from pXa to pXb to pXc. Each price increase will cause the budget constraint to pivot inward along the horizontal axis. The quantity of X consumed consequently decreases for each price increase. You may connect the utility-maximizing consumption bundles across the three different price levels to create a price-consumption line. (A price consumption line connects the utility maximizing consumption bundles for various prices.) Second, plot the price changes in the diagram below with corresponding changes in the quantity of X consumed. Connect the price-quantity coordinates to create the demand curve.

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Consumption Good Y

Yc

Yb

Ya

Ua Price-Consumption Line Ub

Uc

BCc BCb BCa

Xc Xb Xa Consumption Good X Price of Good X

pXc

pXb

pXa Demand curve for X

Xc Xb Xa Consumption Good X

In my example, when pX increases, the consumer buys less X but more Y (when the price of X increases, the utility maximizing quantity of Y increases from Ya to Yb to Yc). This indicates that X and Y are substitutes. An example of substitutes would be coke and pepsi: if the price of coke goes up, we’ll buy less coke and substitute toward pepsi. If X and Y had been complements, then when pX increases, the quantity of X and Y consumed would have fallen. An example of this would be milk and cereal: if the price of milk goes up, we’ll buy less milk and less cereal. The price-consumption line would then have sloped upward.

Now, derive the demand curve for complements such as milk and cereal. Connect the utility maximizing consumption bundles at various prices with a price-consumption line.

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Cereal

Ca Ua

BCa

Ma Milk Price of Milk

pMa

Ma Milk

Note that if the price-consumption line has a negative slope, then the consumption items are substitutes. However, if the price-consumption line has a positive slope, then the consumption items are complements.

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If the price of a related good changes, then the demand curve will shift. In particular, if the price of a substitute increases, then the demand curve will shift to the right and if the price of a complement increases, then the demand curve will shift to the left. To prove this, consider the demand for Sizzlin’ Steaks. If the price of a substitute, Western Steer Steaks changes, then the demand for Sizzlin’ Steaks will change. Let the price of Western Steer Steaks (pWS0) first increase to pWS1 and then decrease to pWS2.

BCc Uc

Western Steer Figure 1

pWS2<p WS0<p WS1

a BCb

Ua Ub

Sizzlin’ Steaks Price of Sizzlin’

Steaks Figure 2

pSS

Da Db

Dc SSc SSa SSb Sizzlin’ Steaks

The key thing to remember is that the price of Sizzlin’ Steaks has not changed, so the demand curve shifts.

Now, repeat this exercise with Sizzlin’ Steaks and A1 Sauce, where A1 Sauce and Sizzlin’ Steaks are complements.

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A1 Sauce

a

Ua

Sizzlin’ Steaks Price of Sizzlin’

Steaks

pSS

Da

SSa Sizzlin’ Steaks

Again, if the price-consumption line is negatively sloped, then the measured consumption items are substitutes, but if the price-consumption line is positively sloped, then the measured consumption items are complements.

Some have criticized microeconomics’ consumer theory, suggesting that it does not reflect real world behavior. One criticism is that indifference maps are two dimensional, which requires consumers to pick between only two consumption items. However, in the real world, consumers choose among thousands of consumption items. To incorporate more than two consumption items in the analysis, microeconomists model a consumption good of interest on the horizontal axis and “all other consumption goods” or “a composite consumption good” on the vertical axis.

Another criticism of microeconomics’ consumer theory is that consumers are not self-interested utility maximizers. Instead, consumers often do not maximize utility by giving money away in the form of charity. This is where Dr. Donald Frey, a macroeconomics professor at Wake Forest University, says microeconomic theory is flawed. Frey believes some individuals are not always motivated by self-interest and will give money to charity to help others though they personally derive no utility from their act of giving. These individuals may be motivated solely by helping others. Since microeconomics is based on the belief that individuals are rational, self-interested utility-maximizers, giving money away with no increase in utility in return is a contradiction, Frey explains.

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Dr. John Moorhouse, a microeconomics professor at Wake Forest University, has been known to say that modeling charitable giving in microeconomics requires no additional tools than the ones we have developed thus far in the course. He argues that because some individuals derive a certain personal satisfaction from giving away money, giving money to charities represents the purchase of a normal good from which utility can be gained. Thus, we might model a consumer’s preferences with respect to Mountain Dew and units of Charity just like we might for Mountain Dew and Mellow Yellow.

To respond to these two criticisms, model charitable giving on the horizontal axis and all other consumption items on the vertical axis in the next example.

Income changes will also shift the demand curve. Increases in income will shift the demand curve of a normal good to the right and increases in income will shift the demand curve of inferior goods to the left. To see this, we can draft an income-consumption line, which connects the utility maximizing consumption bundles for various income levels. To do this, increase income from Ia to Ib to Ic. Below, the budget constraint and indifference curves are adjusted appropriately.

All Other Goods

Income-Consumption Line

Uc

Ub

Ua

BCa BCb BCc

CGaCGb CGc Charitable Giving Price

p

Dc (Demand curve for Charitable Giving) Db

Da

CGa CGb CGc Charitable Giving

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Increases in income will shift the demand curve for charitable giving outward – to the right – if charitable giving is a normal good. If charitable giving is an inferior good, then increases in income shift the demand curve for charitable giving to the left.

Next, draft an income-consumption line where charitable giving is an inferior good:

All Other ConsumptionGoods

Ua

BCa

CGa Charitable Giving

Price of CharitableGiving

pCG

CGa Charitable Giving

Note that if the income-consumption line has a positive slope, then the measured consumption items are both normal goods, but if the income-consumption line has a negative slope, then one of the measured consumption items is an inferior good.

Charities often give homeless people in-kind gifts such as food instead of money. The reasoning reflects a pessimistic view of human nature: the homeless might take the money and spend it on alcohol rather than on food. In the figure below, a homeless person’s preferences are being modeled. The price of a unit of liqueur is $1, the price of a unit of food is $1, and the individual initially has $30.00 to spend. Assume that the individual will indeed spend any additional money he is given only on liqueur.

a) Suppose the charity gives the homeless person a gift of $20.00. Depict the pessimistic view of human nature where a gift of $20.00 spurs the homeless person to only increase his consumption of liqueur. Do this by drawing a new

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indifference curve showing the homeless person maximizing utility. Indicate the utility maximizing consumption bundle. The budget constraint with the in-kind gift of $20.00 is given by the dark dotted line.

b) When maximizing utility with the $20.00 gift, how many units of food will the homeless person consume?

c) Now suppose the charity gives the homeless person 20 free units of food in the form of an in-kind transfer. The budget constraint with the in-kind gift of 20 units of food is the light solid line. Given the preferences of the homeless person described above, what bundle will he consume? How many units of food and how many units of liqueur will the utility-maximizing consumption bundle contain?

Liqueur

30

15 U1

15 20 30 50 Food

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PROBLEM SET #2 Budget Constraint Changes

1. On an indifference map with good "X" measured on the horizontal axis and good "Y" measured on the vertical axis:

a) Construct the price consumption line for good X. Do this by raising the price of consumption good X from pXa to pXb to pXc where pXa < pXb < pXc.

b) Derive the demand curve for X from your indifference map.c) Are consumer goods "X" and "Y" complements or substitutes? How do you know?

2. Mellow Yellow and Mountain Dew are substitutes. At current prices in Figure 1, Bob’s utility maximizing consumption of both is represented by bundle “a” on budget constraint BCa where the price of Mellow Yellow is pa. Depicted in Figure 2 is Bob’s demand curve for Mountain Dew, labeled D. What happens to Bob’s demand curve for Mountain Dew when Mellow Yellow’s price changes?

a) First, increase the price of Mellow Yellow to pb. Label the new budget constraint BCb. Then, draw a new indifference curve for Bob representing his utility maximizing consumption bundle when the price of Mellow Yellow is pb. Finally, show how the described price change affects Bob’s demand curve for Mountain Dew in Figure 2.

b) Repeat exercise (a) for a decrease in the price of Mellow Yellow from pa to pc.

Mellow Yellow Figure 2

pc<pa<pb

a

U0, with price of pa

BCa

Mountain Dew Price of Mountain Dew Figure 2

D

MDa Mountain Dew

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3. Draft an income-consumption line for charitable giving with charitable giving measured on the horizontal axis and "other goods" measured on the vertical axis of your diagram. How does an increase in income affect the demand curve for charitable giving? Explain using a well-labeled graph of the demand curve for charitable giving.

4. At the turn of the century over 30% of American families employed domestic help. Today, in spite of the eight-fold increase in real family income, only 10 % of American families employ domestic help. Draft three indifference maps, which explain the decrease in the employment of servants by:

a) A change in tastes.b) An increase in income where domestic help is an inferior good.c) An increase in the price of domestic help.d) Which explanation do you find most persuasive? Why?

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Answer Key #2 Budget Constraint ChangesAnswer to question 1.

Consumption Good Y

Yc

Yb

Ya

Ua Price-Consumption Line Ub

Uc

BCc BCb BCa

Xc Xb Xa Consumption Good X Price of Good X

pXc

pXb

pXa Demand curve for X

Xc Xb Xa Consumption Good X

The first step is to raise the price of X from pXa to pXb to pXc. Each price increase will cause the budget constraint to pivot inward along the horizontal axis. The quantity of X consumed consequently decreases for each price increase. You may connect the utility-maximizing consumption bundles across the three different price levels to create your price-consumption line. Second, plot the price changes in the diagram below with corresponding changes in the quantity of X consumed. Connect the price-quantity coordinates to create the demand curve. In my example, when pX increases, the consumer buys less X but more Y (when the price of X increases, the utility maximizing quantity of Y increases from Ya to Yb to Yc). This indicates that X and Y are substitutes. If X and Y had been complements, then when pX increases, the quantity of X and Y consumed would have fallen. The price-consumption line would then have sloped upward.

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Answer to question 2.BCc Uc

Mellow Yellow Figure 1

Pc<Pa<Pb

a BCb

Ua, with price of Pa

Ub, with price of Pb Mountain Dew Price of Mountain Dew Figure 2

PMD

Da Db

Dc MDcMDa MDb Mountain Dew

The key thing to remember is that the price of Mountain Dew has not changed, so we are talking about “shifts” in the demand curve.

Answer to question 3.

The following graphs refer to charitable giving as a normal good, with a positively sloped income-consumption line. If you believe charitable giving to be an inferior good, then the income-consumption line will have a negative slope (sloping from North-West to South-East).

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Other Goods

Income-Consumption Line

Uc

Ub

Ua

BCa BCb BCc

CGa CGb CGc Charitable Giving Price

p

Dc (Demand curve for Charitable Giving) Db

Da

CGa CGb CGc Charitable Giving

Increases in income will shift the demand curve for charitable giving outward – to the right – if you assume charitable giving to be a normal good. If you believe charitable giving to be an inferior good, then increases in income shift the demand curve for charitable giving to the left.

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Answer to question 4.

a) Change in tastes. The indifference curves can cross without violating the assumption of transitivity because time has changed. Tastes can change over time.

Other Goods

U2 (1998)

U1 (1900)

Domestic Helpb) Domestic help is an inferior good. We see that when income increases

(reflected in a parallel shift outward of the budget constraint), less domestic help is employed.

Other Goods

U2

U1

BC1 BC2

Domestic Help

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c) The price of domestic help has increased. The real price of domestic help increased, which is reflected in the budget constraint pivoting inward and caused less domestic help to be employed.

Other Goods

U1

U2

BC2 BC1

Domestic Help

d) Any answer to part d is fine, as long as it reflects effort and is based on economic arguments.

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