Rational consumer choice ECO61 Microeconomic Analysis Udayan Roy Fall 2008

Rational consumer choice

ECO61 Microeconomic AnalysisUdayan Roy

Fall 2008

Consumer Choice

• We have seen how the consumer’s preferences are represented

• And how the consumer’s budget constraint is represented

• Now it’s time to bring preferences and constraints together to ask the consumer:

• What’s your choice? How do you decide what to buy?

Example

Consumer Maximization: What’s the best affordable choice?

• PZ = $1, PB = 2, M = 50

B,

Bu

rr ito

s p

er

sem

est

er

25

500

Z, Pizzas per semester

I1I2I3

d

fc

e

a

Consumer Maximization: Interior Solution

• Would Lisa be able to consume any bundle along I3 (i.e. bundle f)?– No! Lisa does not have

enough income to afford any bundle along I3

B,

Bu

rr ito

s p

er

sem

est

er

10

20

25

5030100


I1I2I3

d

fc

e

aA

B

Would Lisa be able to consume any bundle along I1? Yes; she could afford bundles d, c, and a.

Nevertheless, there are other affordable bundles that should be preferred and affordable. For instance bundle e

Bundle e is called a consumer’s optimum. If Lisa is consuming this

bundle, she has no incentive to change her behavior by substituting one good for another.

The budget constraint and the indifference curve have the same slope at the point e where they touch. Therefore, at point e:

Slope of indifference curve

Consumer Maximization: Interior SolutionB

, B

urr i

tos

pe

r se

me

ste

r

25

500


I2

e

B

ZZB P

PMRS

Slope of budget line

An algebraic example

MYPXP

YXU

YX

YX

constraintbudget thesubject to

max,

As was explained in chapter 2, the ≤ symbol can be replaced by the = symbol.

Ch. 2: Budget constraint algebra

XP

P

P

MY

P

XPMY

XPMYP

MYPXP

Y

X

Y

Y

X

XY

YX

Algebraic example (contd.)

• So, our choice problem becomes

• … which changes the choice problem to

2max X

P

MX

P

PX

P

P

P

MX

XY

X

Y

X

YX

2

22

2

22max X

P

MX

P

M

P

MX

P

MX

XXXXX

As these two terms cancel out, there’s no harm placing them here.


• But

• Therefore, our choice problem becomes

22

2

22

2222max

X

P

M

P

MX

P

MX

P

M

P

M

XXXXXX

XXX P

MXX

P

M

2 implies which

2min

2


• Then the budget constraint implies

YYY

XY

X

YY

X

Y

P

M

P

M

P

MY

P

M

P

P

P

MX

P

P

P

MY

22

2

Algebraic example (Done!)

• The choice problem

• has the solution:

MYPXP

YXU

YX

YX

constraintbudget thesubject to

max,

YX P

MY

P

MX

2 and

2

Consumer Maximization: Corner Solution

B,

Bu

rrito

s p

er

sem

est

er

Budget line

25

50


I1

I2

I3

e

MRSZB ≤ PZ/PB. The consumer would like to buy even less pizza, were the amount of pizza not already zero.

Food Stamps• Nearly 11% of U.S. households worry about

having enough money to buy food and 3.3% report that they suffer from inadequate food.

• Households that meet income, asset, and employment eligibility requirements receive coupons that can be used to purchase food from retail stores.

Food Stamps (cont).• The Food Stamps Program is one of the

nation’s largest social welfare programs with expenditures of $33.1 billion for nearly 29.1 million people in 2006.

• Would a switch to a comparable cash subsidy increase the well-being of food stamp recipients? – Would the recipients spend less on food and

more on other goods?

Food Stamps Versus Cash: Cash Wins

All

othe

r go

ods

per

mon

th

M M + 100

M + 100

0 100

Food per month

Budget line withfood stamps

Budget line under a cash grant

Originalbudget line

A

B

f

deM

C

I 1

I2I3

Food Stamps Versus Cash: Both Win

All

othe

r go

ods

per

mon

th

M M + 100

M + 100

0 100

Food per month

Budget line withfood stamps

Budget line under a cash grant

Originalbudget line

A

B

deM

C The best choice under both policies

Gifts: cash or kind?

• In the hit TV show Seinfeld, Elaine was once furious when Jerry gave her cash as a birthday gift– She was not objecting to the amount, which was

$182

• Does Jerry deserve such harsh treatment?

Figure 5.11: Effect of a Change in the Price of Soup on Consumption

5-20

The demand curve

Derivingan Individual’s Demand Curve

12.0

2.8

12.0

26.70

pb, $

per

uni

t

26.70

e1

E1

I1

Beer (b), Gallons per year

Win

e, (

W) ,

Gal

lons

per

year

(a) Indifference Curves and Budget Const raints

(b) Demand Cu rve

Initial optimal bundle of Beer and Wine

Initial ValuesPb = price of beer = $12PW = price of wine = $35M = Income = $419.

W = MPW

- Pb

PW

b


L1 (pb = $12)

Budget Line, L


4.3

12.0

2.8

12.0

6.0

26.70

pb, $

per

uni

t

L2 (pb = $6)

26.70 44.5

e2

e1

I1

I 2


Win

e, (

W) ,

Gal

lons

per

year

(a) Indifference Cu rves and Budget Const raints

(b) Demand Cu rveNew ValuesPb = price of beer = $6PW = price of wine = $35M = Income = $419.

W = MPW

- Pb

PW

b


L1 (p b = $12)

Budget Line, L

E1

Price of Beer goes down!

44.5

E2


4.3

5.2

12.0

2.8

12.0

6.0

4.0

26.70 44.5 58.9

pb, $

per

uni

t

L2 (pb = $6) L3 (pb = $4)

26.70 44.5 58.9

e

e1

I1

I 2

I3


D1, Demand for Beer

Price-consumption curve

Win

e, (

W) ,

Gal

lons

per

year

(a) Indifference Curves and Budget Const raints

(b) Demand Cu rveNew ValuesPb = price of beer = $4PW = price of wine = $35Y = Income = $419.

W = Y

PW

- Pb

PW

b


L1 (p b = $12)

Budget Line, L

E1

Price of Beer goes down again!

2

E2

e3

E3

Figure 5.17: Effect of a Change in Income on Consumption

5-25

Normal vs. Inferior Goods

• If a good is normal, an increase in income raises the amount that is consumed

• If a good is inferior, an increase in income decreases the amount that is consumed

• Consumption of many goods falls as income rises because people shift toward higher-quality products that fill similar needs– Examples: replace posters with art reproductions,

margarine with butter

5-26

Changes in income shift the demand curve: normal good case

Effects of a Price Change

• substitution effect - the change in the quantity of a good that a consumer demands when the good’s price changes, holding other prices and the consumer’s utility constant.

• income effect - the change in the quantity of a good a consumer demands because of a change in income, holding prices constant.

Substitution and Income Effects with Normal Goods

Initial Values

PD = price of DVDs = $20

PC = price of CDs = $15M = Income = $300.

C, Music CDs Units peryear12 20

L1

e1

I1

D, M

ovie

DV

Ds,

Uni

ts p

erye

ar

15

C D = MPD

- PD

Budget Line, L1

PC

C D = $300

$20-

$20$15


Initial Values



D =

M

PD-

PD

C

Budget Line, L

PC

C, Music CDs Units peryear6 12 20

L1

L2

e1e2

I1

I2

D, M

ovie

DV

Ds,

Uni

ts p

erye

ar

15D =

$300

$20-

$20C $15

PC goes up…

$30

Total effect = -6


• What if we compensated Laura so she could afford the same utility she had before the price of CDs increased?

– In other words, how much income she would need to afford indifference curve I1, with the new price of CDs ($30)

Initial Values



e*

L1

L2

e1e2

I1

I2

$20 $20

C

C

D = MPD

- PD

Budget Line, L2

PC

D = $300 - $30

Initial Values



C, Music CDs Units peryearIncome effect = -3 Substitution effect = -3

6 9 12 20

Total effect = -6

D, M

ovie

DV

Ds,

Uni

ts p

erye

ar

15

= Substitution Effect + Income Effect = -3 + (-3)

L*

Giffen GoodB

aske

tbal

l,T

icke

ts p

erye

ar

Movies, Tickets per year

L1

Total effect

L2

e1

e2

I1

I2

When the price of movie tickets decreases the budget constraint rotates out…

allowing the consumer to increase her utility.

Nevertheless, the total effect is negative. WHY?

Giffen GoodB

aske

tbal

l,T

icke

ts p

erye

ar

Movies, Tickets per year

L1

L*

Income effect

Substitution effect

L2

e1

e2

e*

I1

I2

Total effect

• Even though the substitution effect is positive….

– …the income effect is larger and negative (since this is an inferior good).

Labor-Leisure Choice

• Leisure - all time spent not working.• The number of hours worked per day, H,

equals 24 minus the hours of leisure or nonwork, N, in a day:

H = 24 − N.

– The price of leisure is forgone earnings.• The higher your wage, the more an hour of leisure

costs you.

Labor-Leisure Choice: Example• Jackie spends her total income, M, on good Y.

– The price of good Y is $1 per unit.

• Her utility, U, depends on how many goods and how much leisure she consumes:

U = U(Y, N).

• Jackie’s earned income equal:

wH.

• And her total income, M, is her earned income plus her unearned income, M*:

Y = wH + M*.

Demand for Leisure

Y, G

oods

per

da y Time constraint

H1 = 824 0N1 = 160 24

H,Work hours per day

N, Leisure hours per day

H1 = 8

N1 = 160H, Work hours per dayN, Leisure hours per day

I1

L1

(a) Indifference Curves and Constraints

w, W

age

per

hour

(b) Demand Curve

–w1 1

Y1

w1

e1

E1

Budget Line, L1

Y = w1H

Y = w1(24 − N).

Each extra hour of leisure she consumes costs her w1 goods.

Demand for Leisure

Y, G

oods

per

da y Time constraint

H2 = 12 H1 = 824 0

N2 = 12 N1 = 160 24

H,Work hours per day

N, Leisure hours per day

H2 = 12

N2 = 120H, Work hours per dayN, Leisure hours per day

Demand for leisure

I2

I1 1

–w2

L1

L2

(a) Indifference Curves and Constraints

w, W

age

per

hour

–w1 1

e2Y2

Y1

w1

w2

e1

E2

Budget Line, L1

Y = w1H

Y = w1(24 − N).

Budget Line, L2

Y = w2H

Y = w2(24 − N).

w2 > w1

(b) Demand Curve

E1

H1 = 8

N1 = 16

Supply Curve of Labor

Income and Substitution Effects of a Wage Change

Since income effect is positive, leisure is a normal good.

Y,

Go

od

s p

er

day Time constraint

H2H * H124 0

N2N * N10 24

Substitution effect

Income effect

Total effect

H, Work hours per day

N, Leisure hours per d ay

I2

I1

L2

L*

L1

e2

e1

e*

Labor Supply Curve That Slopes Upward and Then Bends Backward

Y, G

oods

per

day

(a) Labor-Leisure Choice

Time const raint

H2 H3H124 0


E1

E3

E2

L2

I2

I3

I1

L3

L1

e2

e1

e3

w, W

age

per

hour

(b) Supply Curve of Labor

Supply curve of labor

H2H3H1 240

, Work hours per day

At low wages, an increase in the wage causes the worker to work more….

H

but at high wages, an increase in the wage causes the worker to work less….

Why leisure is different• When the price of apples goes up,

– the substitution effect reduces the consumption of apples, and– Moreover, the consumer’s income decreases in terms of purchasing

power. This too reduces the consumption of apples, assuming apples are a normal good

• When the wage rate (w), which is also the price of leisure, goes up, the substitution effect works as in the apples example and reduces leisure

• But, the higher wage implies not a decrease but an increase in income. This increases leisure, assuming leisure is a normal good

• So, although an increase in the price of apples should reasonably be expected to reduce the consumption of apples, an increase in the price of leisure should not be expected to reduce the consumption of leisure

• That is, a backward bending labor supply should by no means be considered a freak phenomenon

Leisure and consumptionY

, G

oo

ds

pe

r d

ay Time constraint

H2H * H124 0

N2N * N10 24



• The price of leisure (N) is the wage (w) that is lost

• The budget constraint is wN + PYY = M = 24w + M*

• The slope is -w/PY(24w R+ M*) /PY

Consumption with non-labor income (M*/PY)

wR is the reservation wage: the minimum wage at which this individual will work

Leisure and consumptionY

, G

oo

ds

pe

r d

ay Time constraint

H2H * H124 0

N2N * N10 24



• As the wage rate increases, labor supply first increases and then decreases

• This is an instance of a backward-bending labor supply curve(24w R+ M*) /PY

Consumption with non-labor income (M*/PY)

Documents

Rational consumer choice ECO61 Microeconomic Analysis Udayan Roy Fall 2008