bài giảng kinh tế vi mô tiếng anh ch4 consumer choice

Assumption 1: Completeness• consumer can rank any two bundles of goods • only one of following is true: consumer • prefers Bundle x to Bundle y • prefers Bundle y to Bundle x • is indiff

Chapter 4

Consumer Choice

Key issues

1 properties of preferences

2 utility

3 budget constraint

4 consumer's constrained choice

Tastes

• individual tastes (preferences) determine

pleasure people derive from goods

• economists usually

• take tastes as given

• do not judge taste

Individual decision making

• consumers face constraints on their choices

• consumers maximize their pleasure from consumption subject to constraints

• we want to predict behavior not judge i

Consumer’s problem

• consumer allocates money over goods: buys

a bundle or market basket of goods

• 2 possible theories of consumer behavior

• maximizing behavior

• random behavior (next chapter)

Assumptions about consumer

preferences

1 completeness

2 transitivity

3 more is better

Assumption 1: Completeness

• consumer can rank any two bundles of

goods

• only one of following is true: consumer

• prefers Bundle x to Bundle y

• prefers Bundle y to Bundle x

• is indifferent between them

Assumption 2: Transitivity

(rationality)

• consumer's preference over bundles is consistent:

• if consumer prefers

• Bundle z to Bundle y and

• Bundle y to Bundle x

• then consumer prefers Bundle z to Bundle x

Economist’s transitivity

experiment

• Weinstein (1968)

• no subject knew the purpose of the experiment

• each given choices between 10 goods of equal

value, offered in all possible combinations of pairs

• $3 in cash

• 8-cup Wearever aluminum coffee percolator

• free pass to next 4 Saturday matinees at subject's

favorite motion picture theater

Results

• transitive responses

• 93.5% adults ( ≥ 18 years old)

• 79.2% children aged 9 to 12

• result may explain why political and economic restrictions are placed on youths

Psychologists' transitivity

experiment

• Bradbury and Ross (1990)

• share of people who made intransitive choice

involving 3 colors:

• nearly 50% of 4 or 5 year olds

• 15% of 11-13 year olds

• 5% for adults

• novelty (a preference for a new color) is

responsible for most of the intransitive responses

• novelty effect is especially strong in children

Assumption 3: More is better

• more of a good is better than less of it

• good: commodity for which more is preferred

to less at least at some levels of consumption

• bad: something for which less is preferred to more, such as pollution

• consumers are not satiated

Which assumptions are critical

for our model?

• completeness and transitivity assumptions

are crucial

• more-is-better assumption is included only

to simplify the analysis

Why do economists make the more-is-better assumption?

• it appears to be true about most people

• with free disposal, you can't be worse off with extra goods

• consumers only buy goods where this condition is met (we'll show later)

Preference maps

• we summarize information about a Lisa’s

preferences using a graph

• we can rank some bundles using

more-is-better assumption

Figure 4.1a Bundles of Pizzas and Burritos Lisa Might Consume

B, Burritos

per semester (a) Ranking Regions

30 25 15

Z, Pizzas per semester

25

20

15

10

0

d

a b e

c

f A

B

Indifference curve

• we ask Lisa to identify all the bundles that

give her the same amount of pleasure as

consuming bundle e

• her answer: Curve I in Figure 4.1b,

“Indifference Curve”

Figure 4.1b Bundles of Pizzas and Burritos Lisa Might Consume

B, Burritos

per semester (b) Indifference Curve

30 25 15

Z, Pizzas per semester

25

20

15

10

0

d

a

e c

f

Indifference or preference map

• complete set of indifference curves that

summarize a consumer's tastes

• Figure 4.1c shows parallel curves, but they

need not be parallel

B, Burritos

per semester (c) Preference Map

30 25 15

Z, Pizzas per semester

25

20

15

10

0

d

I0

I1

I2

e

c

f

Indifference curve properties

1 bundles on indifference curves farther

from the origin are preferred to those on

indifference curves closer to the origin

2 there is an indifference curve through

every possible bundle

3 indifference curves cannot cross

4 indifference curves are “thin”

5 indifference curves slope down

Property 1: Better off on farther

indifference curves

• bundles on indifference curves farther from the origin are preferred to those on

indifference curves closer to the origin

• by more is better assumption

Figure 4.1c Bundles of Pizzas and Burritos Lisa Might Consume

B, Burritos

per semester

(c) Preference Map

30 25 15

Z, Pizzas per semester

25

20

15

10

0

d

I0

I1

I2

e

c

f

Property 2: Indifference curve through every possible bundle

• by completeness: consumer can compare any bundle to another

• compared to a given bundle, some bundles are

• preferred,

• enjoyed equally

• inferior

• connecting bundles that give the same pleasure produces an indifference curve that includes the given bundle

Property 3: Indifference curves

cannot cross

• assume the opposite: two indifference

curves cross at Bundle e in Figure 4.2a

• look for a contradiction

B, Burritos

per semester (a) Crossing

Z, Pizzas per semester

I1

I0

a b e

Property 4: Indifference curves

are "thin"

• assume the opposite: suppose an

indifference curve were thick (Figure 4.2c)

• look for a contradiction

Figure 4.2c Impossible Indifference Curves

B, Burritos

per semester

a b

(c) Thick

Z, Pizzas per semester

I

Property 5: Indifference curves

slope down

• assume the opposite: indifference curve I

slopes up in Figure 4.2b

• look for a contradiction

Figure 4.2b Impossible Indifference Curves

B, Burritos

per semester (b) Upward Sloping

Z, Pizzas per semester

I

a b

Willingness to substitute

• downward-sloping indifference curve ⇒

consumer is willing to substitute one good

for the other

• marginal rate of substitution (MRS) of

burritos (rise) for pizza (run), is slope of

indifference curve:

B MRS

Z

∆

=

∆

MRS varies along the indifference curve

• indifference curve bow away from the origin (convex)

• indicates diminish marginal rates of

substitution (MRS)

Figure 4.3a Marginal Rate of Substitution

B, Burritos

per semester

(a) Indifference Curve Convex to the Origin

5

3 8

1 –1 1

1 2

0 –2 – 3

Z, Pizzas per semester

a

b

c d I

Concave indifference curve

• if indifference curve bows toward the origin (concave)

• then (implausibly) increasing MRS

Figure 4.3b Marginal Rate of Substitution

B, Burritos

per semester

(b) Indifference Curve Concave to the Origin

5 7

1 1

2

0

–2

–3

Z, Pizzas per semester

a

b

c I

Perfect substitutes

• straight line indifference curves

• if slope is –1, MRS = 1 (Coke-Pepsi)

Imperfect Substitutes

Coke, Cans

per week

(a) Perfect Substitutes

1 2 3 4 Pepsi, Cans per week

1

0

2 3 4

I1 I2 I3 I4

Perfect complements

• right-angle indifference curves

• MRS = 0 (Coffee-Cream)

Figure 4.4b Perfect Substitutes, Perfect Complements,

Imperfect Substitutes

Ice cream,

Scoops per week

(b) Perfect Complements

1 2 3 Pie, Slices per week

1 2 3

0

I1

I2

I3

a d

b

Imperfect substitutes

• convex indifference curves

• lies between the two extremes (straight and right-angle indifference curves)

Figure 4.4c Perfect Substitutes, Perfect Complements,

Imperfect Substitutes

B, Burritos

per semester

(c) Imperfect Substitutes

Z, Pizzas per semester

I

Application: Food vs clothing

• indifference curves of the average U.S

consumer between food consumed at home and clothing

• as we move away from the origin:

• I1 near right angles (perfect complements)

• I4 near straight lines (perfect substitutes)

• why: minimum levels of food and clothing are necessary to support life

Food at home

per year

Clothing per year

I4

I3

I2

I1

Utility

• numerical value that reflects relative rankings of various bundles of goods

• if Lisa prefers bundle a to b, then utility from a >

utility from b

• utility function:

• relationship between utility measure and every possible bundle of good

• succinct summary of information in indifference map

Ordinal preference

• ordinal scale maintains only ranking:

• letter grades

• utility

• cardinal scale maintains ranking and allows

absolute comparisons: money payments

Utility and indifference curves

• could plot utility and two goods in a 3D

figure: hill of happiness

• indifference curves are determined by taking parallel cuts of the hill of happiness

at some given level of utility

Utility and marginal utility

• marginal utility of Z

• change in utility from a small increase in Z

holding B fixed

Z

U MU

Z

∆

=

∆

U, Utils

∆U = 20 Utility function, U (10, Z )

∆Z =1

10 9 8 7 6 5 4 3 2 1

Z, Pizzas per semester

0

350

250 (a) Utility

230

, Marginal

MU Z

utility of pizza

MU Z

10 9 8 7 6 5 4 3 2 1

Z, Pizzas per semester

0

130

(b) Marginal Utility

20

Utility and marginal of substitution

Lisa trades from one bundle on an indifference curve to another by giving up some burritos to gain more pizza

Z B

B MU MRS

Z MU

∆

= = −

∆

Budget constraint

• Lisa spends all her income, Y, on pizza and

burritos

• her budget constraint is

p B + p Z = Y

Rewrite budget constraint

• suppose

• p Z= $1

• p B= $2

• Y = $50

• Plot this expression: Figure 4.6

Z B

Y p Z B

p

−

=

Figure 4.6 Budget Constraint

B, Burritos

per semester

Opportunity set

50 = Y/p Z

L1(p Z = $1, Y = $50)

25 = Y/p B

20

10

10

Z, Pizzas per semester

a

b

c

d

Opportunity set

• all bundles a consumer can buy

• includes bundles on and inside the budget constraint

Slope of budget constraint

• is called the marginal rate of transformation

• in our example:

Z B

MRT

∆

= = −

∆

Z B

p MRT

p

= − = − = −

Purchasing fractional quantities

• can buy fraction quantities because axes show a rate per time period

• effect of a change in price on consumption

One price rises

• price of burritos and income unchanged

• slope of the new budget line:

• budget constraint swings in toward origin

• opportunity set shrinks

Figure 4.7a Changes in the Budget Constraint

B, Burritos

per semester (a) Price of Pizza Doubles

Loss

50

L1(p Z= $1)

L2(p Z= $2) 25

25 0

Z, Pizzas per semester

Change in income

• consumer's income, Y, increases from $50 to $100

• ⇒ parallel shift out of budget line so MRT is

unchanged

• opportunity set grows ⇒ consumer can buy more

of all goods

• effectively, an increase in income is equivalent to

a comparable decrease in all prices

Figure 4.7b Changes in the Budget Constraint

B, Burritos

per semester (b) Income Doubles

Gain

100

L3(Y = $100)

L1(Y = $50)

50

25

50 0

Z, Pizzas per semester

Budget line meets indifference

curves

• maximize utility subject to the budget

constraint

• optimal bundle, two possibilities:

• interior solution: buy some units of all goods

• corner solution: buy only one good

Interior solution

• consumer buys some units of all goods

• optimum bundle, e, where highest

indifference curve touches the budget line

Figure 4.8a Consumer Maximization

B, Burritos

per semester

(a) Interior Solution

Budget line

10

20

25

50 30

10 0

Z, Pizzas per semester

I1

I2

I3

d

f c

e a g

A

B

Tangency property

• at interior optimum, indifference curve is tangent to budget line:

• last dollar spent on pizza gives as much extra utility as that spent on burrito

=

Summary: Utility maximized

consumers maximize their well-being subject to

the budget constraint where

• highest possible indifference curve hits budget

constraint

• indifference curve is tangent to budget constraint

(if both goods are purchased): MRS = MRT

• last dollar spent on one good gives as much extra

utility as the last dollar spent on any other

consumed good

Optimal bundle: Corner solution

• optimal bundle at point where highest indifference curve touches budget line

• Spenser's optimal bundle has a positive quantity

of only burritos

• reason: Spenser has flatter indifference curves than Lisa

• indifference curve at the budget line are not tangent at the optimal bundle

B, Burritos

per semester

(b) Corner Solution

Budget line 25

50

Z, Pizzas per semester

I1

I2

I3

e

Optimal bundles only on convex sections of indifference curves

• if indifference curves are smooth, then optimal bundles lie either

• on convex indifference curves or

• where the budget constraint hits an axis

• thus, if a consumer buys both goods, indifference curve is convex and tangent to budget line at optimal bundle

Figure 4.9a Optimal Bundles on Convex Sections of Indifference

Curves

B, Burritos

per semester

(a) Strictly Concave Indifference Curves

Z, Pizzas per semester

e

d

I2

Budget line

Figure 4.9b Optimal Bundles on Convex Sections of Indifference

Curves

e d

I2

I1

B, Burritos

per semester (b) Concave and Convex Indifference Curves

Z, Pizzas per semester

Budget line

Solved problem

show: if the consumer buys and consumes

both goods, consumers are not satiated

(more is preferred to less)

Answer

• suppose contrary: Lisa prefers fewer burritos to more

• show a contradiction: because burritos cost money, she's better off consuming no burritos

• though some consumers prefer less to more at some quantities, we do not observe consumers making purchases where that occurs

Solved problem

• Alexx's firm wants to transfer him from its

SF to its Paris office

• he doesn't care where he lives, but he cares

what he eats

• firm will pay him a salary in Euros such that

he can buy the same bundle of goods in

Paris that he is currently buying

• does he benefit from moving?

Restatement

• changes: ratio of price of American meals to price of French meals

• affects: Alexx's choice of his equilibrium bundle and his well being

Solved Problem 4.4

French meals

per year

American meals per year

a

f

LA

LF

I1I2

Solved problem: Food stamps

Are poor people necessarily better off receiving food stamps or a comparable amount of cash?

Answer

• cash gives a greater choice

• whether that greater choice matters depends

on the tastes of poor people (how much

food they eat)

Figure 4.10 Food Stamps Versus Cash

All other goods per month

Y Y + 100

Y + 100

Food per month

Budget line with food stamps Budget line with cash

Original budget line

A

B

f

d e

Y C

I1

I2

I3

Summary: 1 Preferences

• our analysis is based on 3 assumptions:

• completeness

• transitivity

• more is better

• indifference curve map summarizes

preferences

Indifference curve properties

1 being on a higher indifference curve is better

2 indifference curves do not cross

3 there is an indifference curve through every bundle

4 indifference curves have no thickness

5 indifference curves slope down

6 consumers purchase positive quantities only where their indifference curves are convex to origin

2 Utility

• utility is a numerical measure of the relative

ranking of bundles of goods

• utility is an ordinal measure

• marginal utility: extra utility from

consuming one more unit of a good holding

consumption of all other goods constant

3 Budget constraint

• consumer's opportunity set is greater, higher is income and lower are prices

• budget constraint shows bundles that a consumer can buy spending all income at given prices

• slope of budget line is marginal rate of transformation (MRT): rate at which Good 1 can

be exchanged for Good 2 in the market

4 Constrained maximizing

behavior

consumers maximize their well-being subject to

the budget constraint where:

• highest possible indifference curve touches budget

constraint,

• indifference curve is tangent to budget constraint

(if both goods are purchased): MRS = MRT

• last dollar spent on one good gives as much extra

utility as last dollar spent on any other consumed

good