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Consumer Preferences and Indifference Curves: An Economic Analysis, Study notes of Economics

University of California - BerkeleyEconomics

The concept of consumer preferences and indifference curves through an economic lens. The transitivity experiment, preference maps, indifference curve properties, and willingness to substitute. It also covers the relationship between utility and indifference curves, as well as the budget constraint and consumer maximization. Insights into how consumers make decisions regarding the allocation of resources based on their preferences.

Typology: Study notes

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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
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe

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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

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

Figure 4.1c Bundles of Pizzas and Burritos Lisa Might Consume

B , Burritos per semester

(c) Preference Map

15 25 30 Z , Pizzas per semester

25

20

15

10

0

d

I^0

I^1

I^2 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

15 25 30 Z , Pizzas per semester

25

20

15

10

0

d

I^0

I^1

I^2 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
Figure 4.2a Impossible Indifference Curves
B , Burritos
per semester
(a) Crossing
Z , Pizzas per semester
I^1
I^0
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
Figure 4.4a Perfect Substitutes, Perfect Complements,
Imperfect Substitutes
Coke, Cans
per week
(a) Perfect Substitutes
Pepsi, Cans per week
I^1 I^2 I^3 I^4

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
Pie, Slices per week
I^1
I^2
I

3

a
d
e c
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:
    • I

near right angles (perfect complements)

  • I^4 near straight lines (perfect substitutes)
  • why: minimum levels of food and clothing

are necessary to support life

Indifference Curves Between Food and Clothing
Food at home
per year
Clothing per year
I^4
I^3
I^2
I^1

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 =
Z , Pizzas per semester
(a) Utility

Slope of budget constraint

  • is called the marginal rate of transformation
  • in our example:
Z
B

B p

MRT

Z p

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 pizza doubles: p
Z

=$2 (up from $1)

  • price of burritos and income unchanged
  • slope of the new budget line:

MRT = -$2/$2 = -

  • 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
L

1

( p Z = $1)
L

2

( p Z = $2)
Z , Pizzas per semester

Change in income

  • consumer's income, Y , increases from $50 to $
  • ⇒ 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
L^3 ( Y = $100)
L^1 ( Y = $50)
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

0 10 30 50 Z , Pizzas per semester

I^1

I^2

I^3 d

c f

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

Z Z

B B

Z B

Z B

MU p

MRS MRT

MU p

MU MU

p p

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

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.
French meals
per year
American meals per year
a
L A f
L F
I
1 I^

2

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

0 100 Food per month

Budget line with food stamps

Budget line with cash

Original budget line

A

B

f

d

e Y

C

I^1

I^2

I^3

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