Chapter The Theory of Consumer Choice 21. Budget Constraint: What the Consumer can Afford Budget...

Chapter

The Theory ofConsumer Choice

21

Budget Constraint: What the Consumer can Afford

• Budget constraint– Limit on the consumption bundles that a

consumer can afford• Trade-off between goods

• Slope of the budget constraint• Rate at which the consumer can trade one good

for the other• Change in the vertical distance• Divided by the change in the horizontal distance

– Relative price of the two goods2

Figure

The consumer’s budget constraint (table)

1

3

Number of Pizzas

Pints of Pepsi

Spending on Pizza

Spending on Pepsi

Total spending

1009080706050403020100

050

100150200150300350400450500

$1,000900800700600500400300200100

0

$0100200300400500600700800900

1,000

$1,0001,0001,0001,0001,0001,0001,0001,0001,0001,0001,000

The budget constraint shows the various bundles of goods that the consumer can buy for a given income. Here the consumer buys bundles of pizza and Pepsi. The table and graph show what the consumer can afford if his income is $1,000, the price of pizza is $10, and the price of Pepsi is $2.

Figure

The consumer’s budget constraint (graph)

1

4

The budget constraint shows the various bundles of goods that the consumer can buy for a given income. Here the consumer buys bundles of pizza and Pepsi. The table and graph show what the consumer can afford if his income is $1,000, the price of pizza is $10, and the price of Pepsi is $2.

Quantityof

Pepsi

Quantity of Pizza0

Consumer’sbudget constraint

50

500

100

250 C

B

A

Preferences: What the Consumer Wants

• Indifference curve– Shows consumption bundles that give the

consumer the same level of satisfaction– Combinations of goods on the same curve

• Same satisfaction

• Slope of indifference curve– Marginal rate of substitution

• Rate at which a consumer is willing to trade one good for another

– Not the same at all points5

Figure

The consumer’s preferences

2

6

The consumer’s preferences are represented with indifference curves, which show the combinations of pizza and Pepsi that make the consumer equally satisfied. Because the consumer prefers more of a good, points on a higher indifference curve (I2 here) are preferred to points on a lower indifference curve (I1). The marginal rate of substitution (MRS) shows the rate at which the consumer is willing to trade Pepsi for pizza. It measures the quantity of Pepsi the consumer must be given in exchange for 1 pizza.

QuantityOf Pepsi

Quantity of Pizza0

Indifferencecurve, I1

I2

C

B

A

D

1

MRS


• Four properties of indifference curves1.Higher indifference curves are preferred to

lower ones– Higher indifference curves – more goods

2.Indifference curves are downward sloping3.Indifference curves do not cross4.Indifference curves are bowed inward

7

Figure

The impossibility of intersecting indifference curves

3

8

A situation like this can never happen. According to these indifference curves, the consumer would be equally satisfied at points A, B, and C, even though point C has more of both goods than point A.

QuantityOf Pepsi

Quantity of Pizza0

C

B

A

Figure

Bowed indifference curves

4

9

Indifference curves are usually bowed inward. This shape implies that the marginal rate of substitution (MRS) depends on the quantity of the two goods the consumer is consuming. At point A, the consumer has little pizza and much Pepsi, so he requires a lot of extra Pepsi to induce him to give up one of the pizzas: The marginal rate of substitution is 6 pints of Pepsi per pizza. At point B, the consumer has much pizza and little Pepsi, so he requires only a little extra Pepsi to induce him to give up one of the pizzas: The marginal rate of substitution is 1 pint of Pepsi per pizza.

QuantityOf Pepsi

Quantity of Pizza0

Indifferencecurve

2 3 6 7

34

8

14

1

MRS=1

1

MRS=8

B

A


• Two extreme examples of indifference curves• Perfect substitutes

– Two goods with straight-line indifference curves

– Marginal rate of substitution – constant• E.g.: nickels and dimes bundles

• Perfect complements – Two goods with right-angle indifference curves

• E.g.: right shoe and left shoe bundle

10

Figure

Nickels

6

2

4

Perfect substitutes and perfect complements

5

11

When two goods are easily substitutable, such as nickels and dimes, the indifference curves are straight lines, as shown in panel (a). When two goods are strongly complementary, such as left shoes and right shoes, the indifference curves are right angles, as shown in panel (b).

(a) Perfect Substitutes

Dimes 0 1 32

I1I2 I3

Leftshoes

(b) Perfect Complements

Rightshoes

0 5 7

5

7 I2

I1

Optimization: What the Consumer Chooses

• The consumer’s optimal choices• Optimum

– Point where indifference curve and budget constraint touch

– Best combination of goods available to the consumer

– Slope of indifference curve• Equals slope of budget constraint

• Marginal rate of substitution = relative price

12

Figure

The consumer’s optimum

6

13

The consumer chooses the point on his budget constraint that lies on the highest indifference curve. At this point, called the optimum, the marginal rate of substitution equals the relative price of the two goods. Here the highest indifference curve the consumer can reach is I2. The consumer prefers point A, which lies on indifference curve I3, but the consumer cannot afford this bundle of pizza and Pepsi. By contrast, point B is affordable, but because it lies on a lower indifference curve, the consumer does not prefer it.

Quantityof

Pepsi

Quantity of Pizza0

Budget constraint

I2

I1

I3

AB

Optimum


• How changes in income affect the consumer’s choices

• Higher income– Consumer can afford more of both goods– Shifts the budget constraint outward– New optimum

14

Figure

An Increase in Income

7

15

When the consumer’s income rises, the budget constraint shifts out. If both goods are normal goods, the consumer responds to the increase in income by buying more of both of them. Here the consumer buys more pizza and more Pepsi.

Quantityof

Pepsi

Quantity of Pizza0

New budget constraint

I2

I1

New optimum

Initialbudgetconstraint

Initial optimum

1. An increase in income shifts thebudget constraint outward . . .

2. . . . raisingpizzaconsumption . . .

3. . . . andPepsiconsumption


• How changes in income affect the consumer’s choices

• Normal good– Good for which an increase in income raises

the quantity demanded• Inferior good

– Good for which an increase in income reduces the quantity demanded

16

Figure

An inferior good

8

17

A good is an inferior good if the consumer buys less of it when his income rises. Here Pepsi is an inferior good: When the consumer’s income increases and the budget constraint shifts outward, the consumer buys more pizza but less Pepsi.

Quantityof

Pepsi

Quantity of Pizza0


I2

I1

New optimum

Initial budgetconstraint

Initial optimum

1. When an increase in income shifts thebudget constraint outward . . .

2. . . . pizza consumption rises, making pizza a normal good. . .

3. . . . but Pepsiconsumption falls,making Pepsi aninferior good


• How changes in prices affect the consumer’s choices

• Price of one good falls– Rotates the budget constraint outward

• Steeper slope• Change in relative price

– Income effect– Substitution effect

18

Figure

A change in price

9

19

When the price of Pepsi falls, the consumer’s budget constraint shifts outward and changes slope. The consumer moves from the initial optimum to the new optimum, which changes his purchases of both pizza and Pepsi. In this case, the quantity of Pepsi consumed rises, and the quantity of pizza consumed falls.

Quantityof Pepsi

Quantity of Pizza0

I2

I1


1. A fall in the price of Pepsi rotatesthe budget constraint outward. . .

2. . . . reducing pizza consumption

3. . . . andraising Pepsiconsumption

New budgetconstraint

New optimum

Initial optimum

A

100

B500

D1,000


• Income effect– Change in consumption– When a price change moves the consumer

• To a higher or lower indifference curve

• Substitution effect– Change in consumption– When a price change moves the consumer

• Along a given indifference curve• To a point with a new marginal rate of

substitution20

Table

Income and substitution effects when the price of Pepsi falls

1

21

Good Income effect Substitution effect Total effect

Pepsi

Pizza

Consumer is richer, so he buys more Pepsi

Consumer is richer, so he buys more pizza

Pepsi is relativelycheaper, so consumerbuys more Pepsi

Pizza is relativelyMore expensive,so consumer buys less pizza.

Income and substitutioneffects act in samedirection, so consumerbuys more Pepsi

Income and substitutioneffects act in oppositedirections, so thetotal effect on pizzaconsumption isambiguous.

Figure

Income and substitution effects

10

22

The effect of a change in price can be broken down into an income effect and a substitution effect. The substitution effect—the movement along an indifference curve to a point with a different marginal rate of substitution—is shown here as the change from point A to point B along indifference curve I1. The income effect—the shift to a higher indifference curve—is shown here as the change from point B on indifference curve I1 to point C on indifference curve I2.

Quantityof Pepsi

Quantityof Pizza

0

I2

I1


New budgetconstraint

Initial optimumA

New optimumC

B

Substitution effect

Substitutioneffect

Income effect

Incomeeffect


• Deriving the demand curve– Quantity demanded of a good for any given

price– Initial optimum point

• Initial price of the good• Initial quantity of the good

– A change in price of the good (new price)• New optimum• New optimum quantity

23

Figure

Deriving the demand curve

11

24

Quantityof Pepsi

Panel (a) shows that when the price of Pepsi falls from $2 to $1, the consumer’s optimum moves from point A to point B, and the quantity of Pepsi consumed rises from 250 to 750 pints. Demand curve in panel (b) reflects this relationship between the price and the quantity demanded.

(a) The Consumer’s Optimum

Quantityof Pizza

0

Price ofPepsi

(b) The Demand Curve for Pepsi

Quantityof Pepsi

0 250 750

Demand

I2

I1

250

750



B

A1

$2

B

A

Three Applications

• Do all demand curves slope downward?• Law of demand

– When the price of a good rises, people buy less of it• Downward slope of the demand curve

• Giffen good– An increase in the price of the good raises the

quantity demanded• Income effect dominates the substitution effect• Demand curve – slopes upward

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Figure

A Giffen good

12

26

In this example, when the price of potatoes rises, the consumer’s optimum shifts from point C to point E. In this case, the consumer responds to a higher price of potatoes by buying less meat and more potatoes.

Quantity ofPotatoes

Quantity of Meat0

I1

Newbudgetconstraint

1. An increase in the price of potatoes rotates the budget constraint inward . . .

2. . . . whichincreasespotatoconsumptionif potatoesare a Giffengood.


A

D

B

Optimum with lowprice of potatoes

C

I2

Optimum with highprice of potatoes

E

• Potatoes - Giffen good during the Irish potato famine of the 19th century– Price of potatoes rose

• Large income effect• People – cut back on the luxury of meat• Buy more of the staple food of potatoes

• Chinese province of Hunan, rice– Poor households exhibited Giffen behavior

• Lower price of rice (with subsidy voucher)– Households - reduce their consumption of rice

• Higher price of rice (remove the subsidy)– Households – increase consumption of rice

The search for Giffen goods

27

Three Applications

• How do wages affect labor supply? • Trade-off between leisure and consumption• Bundle of goods: leisure and work

– Given wage– Budget constraint– Optimum

28

Figure

The work-leisure decision

13

29

This figure shows Sally’s budget constraint for deciding how much to work, her indifference curves for consumption and leisure, and her optimum.

Consumption

Hours of leisure0

I2

I1

I3

$5,000

100

Optimum

60

2,000

Three Applications

• How do wages affect labor supply? • Increase in wage

– Budget constraint shifts outward• Steeper• New optimum

– If enjoy less leisure• Work more• Upward-sloping labor supply curve• Substitution effect dominates

30

Three Applications

• How do wages affect labor supply? • Increase in wage

– Budget constraint shifts outward• Steeper• New optimum

– If enjoy more leisure• Work less• Backward-sloping labor supply curve• Income effect dominates

31

Figure

An increase in the wage (a)

14

32

Consumption

The two panels of this figure show how a person might respond to an increase in the wage. The graphs on the left show the consumer’s initial budget constraint, BC1, and new budget constraint, BC2, as well as the consumer’s optimal choices over consumption and leisure. The graphs on the right show the resulting labor-supply curve. Because hours worked equal total hours available minus hours of leisure, any change in leisure implies an opposite change in the quantity of labor supplied. In panel (a), when the wage rises, consumption rises and leisure falls, resulting in a labor-supply curve that slopes upward.

(a) For a person with these preferences . . .

Hours of Leisure0

Wage

. . . the labor supply curve slopes upward.

Hours of LaborSupplied

0

Labor supply

I2

I1

BC2

BC1A

B

1. When the wage rises . . .

2. . . . hours of leisure decrease . . . 3. . . . and hours of labor increase

Figure

An increase in the wage (b)

14

33

Consumption

The two panels of this figure show how a person might respond to an increase in the wage. The graphs on the left show the consumer’s initial budget constraint, BC1, and new budget constraint, BC2, as well as the consumer’s optimal choices over consumption and leisure. The graphs on the right show the resulting labor-supply curve. Because hours worked equal total hours available minus hours of leisure, any change in leisure implies an opposite change in the quantity of labor supplied. In panel (b), when the wage rises, both consumption and leisure rise, resulting in a labor-supply curve that slopes backward.

(b) For a person with these preferences . . .

Hours of Leisure0

Wage

. . . the labor supply curve slopes backward

Hours of LaborSupplied

0

Labor supplyI2

I1

BC2

BC1

1. When the wage rises . . .

2. . . . hours of leisure increase . . . 3. . . . and hours of labor decrease

• Labor- supply curve, over long periods– Slope backward

• A hundred years ago– People worked six days a week

• Today– Five-day workweeks– Length of the workweek has been falling– Wage of the typical worker (adjusted for inflation)

has been rising

Income effects on labor supply: historical trends, lottery winners,& Carnegie conjecture

34

• Explanation: Advances in technology– Higher worker productivity– Increase in demand for labor

• Higher equilibrium wages• Greater reward for working• Income effect dominates substitution effect• More leisure• Less work


35

• Winners of lotteries– Large increase in incomes– Large outward shifts in budget constraints

• Same slope• No substitution effect

– Income effect on labor supply• Substantial• People who win the lottery – tend to quit their jobs


36

• Andrew Carnegie, 19th century– “The parent who leaves his son enormous wealth

generally deadens the talents and energies of the son, and tempts him to lead a less useful and less worthy life than he otherwise would”

– Income effect on labor supply – substantial


37

Three Applications

• How do interest rates affect household saving? • Income decision

– Consume today or Save for future• Bundle of goods

– Consumption today and Consumption in the future

– Relative price = interest rates– Optimum: Budget constraint & Indifference

curves

38

Figure

The consumption-saving decision

15

39

This figure shows the budget constraint for a person deciding how much to consume in the two periods of his life, the indifference curves representing his preferences, and the optimum.

Consumptionwhen Old

Consumptionwhen Young

0

I2

I1

I3

$110,000

100,000

Optimum

$50,000

55,000

Three Applications

• How do interest rates affect household saving? • Increase in interest rates

– Budget constraint – shifts outward• Steeper

– Consumption in the future – rises– If consume less today

• Substitution effect dominates; Save more

– If consume more today• Income effect dominates; Save less

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Figure

An increase in the interest rate

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41

ConsumptionWhen

old

(a) Higher Interest Rate Raises Saving


0

I2

I1

BC2

BC1

1. A higher interest rate rotatesthe budget constraint outward . . .

ConsumptionWhen

old

In both panels, an increase in the interest rate shifts the budget constraint outward. In panel (a), consumption when young falls, and consumption when old rises. The result is an increase in saving when young. In panel (b), consumption in both periods rises. The result is a decrease in saving when young.

(b) Higher Interest Rate Lowers Saving


0

I2

I1

BC2

BC1

2. . . . resulting in lower consumption when young and, thus, higher saving.

1. A higher interest rate rotatesthe budget constraint outward . . .

2. . . . resulting in higher consumption when young and, thus, lower saving.

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