Chapter Four
ConsumerChoice
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Chapter Outline
1. Preferences.
2. Utility.
3. Budget Constraint.
4. Constrained Consumer Choice.
5. Behavioral Economics.
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Premises of Consumer Behavior
Individual preferences determine the amount of pleasure people derive from the goods and services they consume.
Consumers face constraints or limits on their choices.
Consumers maximize their well-being or pleasure from consumption, subject to the constraints they face.
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Utility Theories
Cardinal Utility Theory Measurable Jeremy Bentham
Ordinal Utility Theory Only requires ordering of preferences
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Ordinal Utility Theory
Preference assumptionsCompleteness
Transitivity
More is Better
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Properties of Consumer Preferences
Completeness - when facing a choice between any two bundles of goods, a consumer can rank them so that one and only one of the following relationships is true: The consumer prefers the first bundle to the second, prefers the second to the first, or is indifferent between them.
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Properties of Consumer Preferences
Transitivity - a consumer’s preferences over bundles is consistent in the sense that, if the consumer weakly prefers Bundle z to Bundle y (likes z at least as much as y) and weakly prefers Bundle y to Bundle x, the consumer also weakly prefers Bundle z to Bundle x.
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Properties of Consumer Preferences
More Is Better - all else being the same, more of a commodity is better than less of it (always wanting more is known as nonsatiation). Good - a 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
Are these statements consistent with the pervious assumptions?
I like a scoop of chocolate ice cream the same as a scoop of vanilla ice cream. I am indifferent between having a scoop of chocolate ice cream or a scoop of vanilla
ice cream. However, I prefer a scoop of vanilla ice cream to a scoop of strawberry ice cream and I prefer a scoop of strawberry ice cream to chocolate ice cream.
I prefer an ice cream cone with one scoop of ice cream over one with two scoops. I don’t know whether I want to spend another 50 cents for another scoop of ice
cream. I can’t decide. I am indifferent between the small serving size and the medium serving size. I don’t know whether I really like rocky road ice cream. I have never tasted it. I like ice cream flavored with real vanilla beans more than ice cream flavored with
an artificial vanilla flavoring, but I don’t think it is worth the extra cost. I can’t look at another plate of ice cream. I am willing to pay someone to get it out
of my sight. I am indifferent between a plate of ice cream containing one scoop of chocolate and
two scoops of vanilla and a plate containing one scoop of vanilla and two scoops of chocolate. However, I prefer a plate containing one scoop of chocolate and three scoops of vanilla to a plate containing one scoop of vanilla and three scoops of chocolate.
I hate ice cream.
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Preference Maps
Indifference curve - the set of all bundles of goods that a consumer views as being equally desirable. Indifference map - a complete set of
indifference curves that summarize a consumer’s tastes or preferences
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Figure 4.1 Bundles of Pizzas and Burritos Lisa Might Consume
B, B
urr i
tos
per
sem
este
r
(a)
302515
Z, Pizzas per semester
25
20
15
10
5
da
b
e
c
f
A
B
B, B
urri
tos
per
sem
este
r
(b)
302515
Z, Pizzas per semester
25
20
15
10
a
b I1
e
c
Which of these two bundles would be preferred by Lisa?
Lisa prefers bundle e over bundle d, since e has more of both goods: Pizza and Burritos
Lisa prefers bundle e to any bundle in area B
Which of these two bundles would be preferred by Lisa?
Lisa prefers bundle f over bundle e, since f has more of both goods: Pizza and Burritos
Lisa prefers any bundle in area A over e
If Lisa is indifferent between bundles e, a, and c …..
we can draw an indifferent curve over those three points
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Figure 4.1 Bundles of Pizzas and Burritos Lisa Might Consume
B, B
urr i
tos
per
sem
este
r
(a)
302515
Z, Pizzas per semester
25
20
15
10
5
da
b
e
c
f
A
B
B, B
urri
tos
per
sem
este
r
(c)
302515
Z, Pizzas per semester
25
20
15
10d
a
b I1
e
c
f
we can draw an indifferent curve over those three points
I2
I0
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Properties of Indifference Maps
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 slope downward.
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Impossible Indifference Curves
Lisa is indifferent between e and a, and also between e and b… so by transitivity she
should also be indifferent between a and b…
but this is impossible, since b must be preferred to a given it has more of both goods.
B, B
urr
itos
per
sem
est
er
Z, Pizzas per semester
I1
I0a
be
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Impossible Indifference Curves
Lisa is indifferent between b and a since both points are in the same indifference curve… But this contradicts
the “more is better” assumption. Can you tell why?
Yes, b has more of both and hence it should be preferred over a.
B, B
urr
itos
per
sem
est
er
Z, Pizzas per semester
I
a
b
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Figure 4.2 Impossible Indifference Curves
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Solved Problem 4.1
Can indifference curves be thick? Answer:
Draw an indifference curve that is at least two bundles thick, and show that a preference property is violated
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Solved Problem 4.1
Consumer is indifferent between b and a since both points are in the same indifference curve… But this contradicts the
“more is better” assumption since b has more of both and hence it should be preferred over a.
B, B
urr
itos
per
sem
est
er
a
b
Z, Pizzas per semester
I
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Willingness to Substitute Between Goods
marginal rate of substitution (MRS) - the maximum amount of one good a consumer will sacrifice to obtain one more unit of another good.
The slope of the indifference curve!
Z
BMRS
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Figure 4.3 (a) MRS along an Indifference curve
B, B
urr i
tos
per
sem
este
r
Indifference Curve Convex to the Origin
5
3
8
1
-11
12
0
-2
–3
3 4 5 6
Z, Pizzas per semester
a
b
c
d
I
From bundle a to bundle b, Lisa is willing to give up 3 Burritos in exchange for 1 more Pizza…
From bundle b to bundle c, Lisa is willing to give up 2 Burritos in exchange for 1 more Pizza…
From bundle c to bundle d, Lisa is willing to give up 1 Burritos in exchange for 1 more Pizza…
The MRS from bundle a to bundle b is -3. This is the same as the
slope of the indifference curve between those two points.
From b to c, MRS = -2. This is the same as the
slope of the indifference curve between those two points.
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Figure 4.3 (b) Marginal Rate of Substitution
From bundle a to bundle b, Lisa is willing to give up 2 Pizzas for 1 Burrito. Nevertheless, from
b to c she is willing to give up 3 Pizzas for 1 burrito.
This is very unlikely Could you think
why?
B, B
urri
tos
per
sem
este
r
(b) Indifference Curve Concave to the Origin
5
7
1
1
2
0
–2
–3
3 4 5 6
Z, Pizzas per semester
a
b
c
I
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Diminishing marginal rate of substitution
The marginal rate of substitution approaches zero as we move down and to the right along an indifference curve.
Discussion: could you imagine a good that does not exhibit this property?
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Curvature of Indifference Curves.
Casual observation suggests that most people’s indifference curves are convex.
Exceptions:
Perfect substitutes - goods that a consumer is completely indifferent as to which to consume.
Perfect complements - goods that a consumer is interested in consuming only in fixed proportions
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Figure 4.4a Perfect Substitutes
Bill views Coke and Pepsi as perfect substitutes: can you tell how his indifference curves would look like? Straight, parallel lines
with an MRS (slope) of −1.
Bill is willing to exchange one can of Coke for one can of Pepsi.
Cok
e, C
ans
per w
eek
1 2 3 4
Pepsi, Cans per week
1
0
2
3
4
I 1 I2 I3 I 4
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Figure 4.4b Perfect ComplementsIc
e cr
eam
, Sco
ops
per w
eek
1 2 3
Pie, Slices per week
1
2
3
0
I1
I2
I3
a
d
e c
b
If she has only one piece of pie, she gets as much pleasure from it and one scoop of ice cream, a, as from it and two
scoops, d, or as from it and
three scoops, e.
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Figure 4.4c Imperfect Substitutes
The standard-shaped, convex indifference curve in panel lies between these two extreme examples. Convex indifference
curves show that a consumer views two goods as imperfect substitutes.
B, B
urri
tos
per
sem
este
r
f
Z, Pizzas per semester
I
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Application: Indifference Curves Between Food and Clothing
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Problems: constructing indifference curves
1. Don is altruistic. Show the possible shape of his indifference curves between charity and all other goods.
2. Miguel considers tickets to the Houston Grand Opera and to Houston Astros baseball games to be perfect substitutes. Show his preference map.
3. If Joe views two candy bars and one piece of cake as perfect substitutes, what is his marginal rate of substitution between candy bars and cake?
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Utility
Utility - a set of numerical values that reflect the relative rankings of various bundles of goods.
utility function - the relationship between utility values and every possible bundle of goods.
U(B, Z)
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Utility Function: Example
Question: Can determine whether Lisa would be happier if she had Bundle x with 9 burritos and 16 pizzas or Bundle y with 13 of each?
Answer: The utility she gets from x is 12utils. The utility she gets from y is 13utils. Therefore, she prefers y to x.U= BZ.
BZu
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Marginal utility
marginal utility - the extra utility that a consumer gets from consuming the last unit of a good. the slope of the utility function as we hold the
quantity of the other good constant.
Marginal Utility of good Z is:
Z
UMUZ
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Figure 4.5 Utility and Marginal Utility As Lisa consumes
more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases… and her marginal
utility of pizza, MUZ, decreases (though it remains positive).
Marginal utility is the slope of the utility function as we hold the quantity of the other good constant.
MU
Z,
Mar
gina
l util
ity o
f pi
zza
MUZ
10987654321
Z, Pizzas per semester
0
130
(b) Marginal Utility
20
U,
Util
s
U = 20
Utility function, U (10, Z)
Z = 1
10987654321
Z, Pizzas per semester
0
350
250
(a) Utility
230
Z
UMU Z
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Utility and Marginal Rates of Substitution
The MRS is the negative of the ratio of the marginal utility of another pizza to the marginal utility of another burrito.
Formally,
B
Z
MU
MU
Z
BMRS
Movement along an indifference curve
Trade off B for Z so as to leave utility constant
As B declines MUB increases
As Z increases MUZ decreases
(MUZ /MUB) decreases
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Derive MRS of Burritos for Pizza
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B
Z
ZB
ZB
ZB
MU
MU
Z
B
MUZMUB
MUZMUB
U
MUZMUBU
0
0
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Budget Constraint
budget line (or budget constraint) - the bundles of goods that can be bought if the entire budget is spent on those goods at given prices.
opportunity set - all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint
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Budget Constraint
If Lisa spends all her budget, Y, on pizza and burritos, then
pBB + pZZ = Y
where pBB is the amount she spends on burritos and pZZ is the amount she spends on pizzas.
This equation is her budget constraint. It shows that her expenditures on burritos and pizza use
up her entire budget.
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Budget Constraint (cont).
How many burritos can Lisa buy? To answer solve budget constraint for B (quantity of
burritos):
ZP
P
P
YB
P
ZPYB
ZPYBP
YZPBP
B
Z
B
B
Z
ZB
ZB
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Budget Constraint (cont).
From previous slide we have:
If pZ = $1, pB = $2, and Y = $50, then:
B
Z
P
ZPYB
ZZ
B 5.0252$
)1($50$
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Figure 4.6 Budget Constraint From previous slide we have
that if:– pZ = $1, pB = $2, and Y = $50,
then the budget constraint, L1, is:
ZZ
B 25.0252$
)1($50$
B, B
urr
itos
per
sem
est
er
Opportunity set
50 = Y /pZ
L1
25 = Y/pB
20
10
100 30
Z, Pizzas per semester
a
b
c
d
Amount of Burritos consumed if all income is allocated for Burritos.
Amount of Pizza consumed if all income is allocated for Pizza.
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The Slope of the Budget Constraint
We have seen that the budget constraint for Lisa is given by the following equation:
The slope of the budget line is also called the marginal rate of transformation (MRT)
rate at which Lisa can trade burritos for pizza in the marketplace
ZP
P
P
YB
B
Z
B
Slope = B/Z = MRT
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Table 4.1 Allocations of a $50 Budget Between Burritos and Pizza
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Budget Constraint
5.
2
125$
50$,1$,2$
b
z
zb
b
z
b
zb
p
pMRT
ZB
Bpp
Zp
p
p
YB
ZpBpY
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Figure 4.7(a) Changes in the Budget Constraint: An increase in the Price of Pizzas.
B, B
urr
itos
per
sem
est
er
Loss
50
L1 (pZ = $1)
L2 (pZ = $2)
25
250
Z, Pizzas per semester
B = YPB
- PZ = $1
PB
Z
If the price of Pizza doubles, (increases from $1 to $2) the slope of the budget line increases
This area represents the bundles she can no longer afford!!!
$2Slope = -$1/$2 = -0.5
Slope = -$2/$2 = -1
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Figure 4.7(b) Changes in the Budget Constraint: Increase in Income (Y)
Gain
L3 (Y = $100)
L1 (Y = $50)
0
B = $50PB
- PZ PB
Z
If Lisa’s income increases by $50 the budget line shifts to the right (with the same slope!)
$100
This area represents the new consumption bundles she can now afford!!!
10050
Z, Pizzas per semester
B, B
urrit
os
per
sem
este
r
50
25
Changes in Budget Constraint
Change in relative prices Rotates the budget constraint
Change in income Parallel shift in budget constraint
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Solved Problem 4.2
A government rations water, setting a quota on how much a consumer can purchase. If a consumer can afford to buy 12 thousand gallons a month but the government restricts purchases to no more than 10 thousand gallons a month, how does the consumer’s opportunity set change?
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Solved Problem 4.2
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Figure 4.8(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
Z, Pizzas per semester
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.
Maximize Utility Given a Budget Constraint
Two possible solutions Interior solution
Some of both goods are consumed
Corner solution Only one of two goods is consumed
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The budget constraint and the indifference curve have the same slope at the point e where they touch. Therefore, at point e:
Slope of I2
Figure 4.8(a) Consumer Maximization: Interior Solution
B,
Bu
rr ito
s p
er
sem
est
er
25
500
Z, Pizzas per semester
I2
e
MRTP
P
MU
MUMRS
B
Z
B
Z
Slope of BL
Constrained Utility Maximization
A•
I
C•
•B
II
R
T
Quantity of burgers
Qu
anti
ty o
f piz
zas
0 8020 10040 60
10
20
30
40
50
7010 9030 50
•E
III
•DIV
45
15
MRS<MRT
MRS>MRT
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Consumer Equilibrium (recap)
ation transformof ratemarginal
RatiohangeMarket Exc
ConstraintBudget
b
z
b
z
b
zb
p
pMRT
Zp
p
p
YB
ZpBpY
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Consumer Equilibrium (recap)
b
z
zb
zb
MU
MU
Z
BMRS
ZMUBMU
ZMUBMUU
0
Holding utility constant along an indifference curve
Consumer Equilibrium
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b
b
z
z
b
z
b
z
p
MU
p
MU
p
p
MU
MU
MRTMRS
•Individuals that face identical prices have the same MRS
•For each individual the last dollar spent on each and every good at the same amount to utility
Consumer Equilibrium
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b
b
z
z
b
z
b
z
b
z
b
z
p
MU
p
MU
p
p
MU
MU
p
p
MU
MU
MRTMRS
When the indifference curve is steeper than the budget constraint
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Figure 4.8(b) Consumer Maximization: Corner Solution
B,
Bu
rrito
s p
er
sem
est
er
Budget line
25
50
Z, Pizzas per semester
I1
I2
I3
e
For the first dollar spent on Z the MUz/Pz < MUb/Pb
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Solved Problem 4.3
Nigel, a Brit, and Bob, a Yank, have the same tastes, and both are indifferent between a sports utility vehicle (SUV) and a luxury sedan.
Each has a budget that will allow him to buy and operate one vehicle for a decade.
For Nigel, the price of owning and operating an SUV is greater than that for the car.
For Bob, an SUV is a relative bargain because he benefits from lower gas prices and can qualify for an SUV tax break.
Use an indifference curve–budget line analysis to explain why Nigel buys and operates a car while Bob chooses an SUV.
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Solved Problem 4.3
•With perfect substitutes a corner solution maximizes utility•Only consume the good that is relatively cheaper
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Figure 4.9 Optimal Bundles on Convex Sections of Indifference Curves
Interior solution minimizes welfare
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Solved Problem 4.4
Alexx doesn’t care about where he lives, but he does care about what he eats. Alexx spends all his money on restaurant meals at either American or French restaurants.
His firm offers to transfer him from its Miami office to its Paris office, where he will face different prices.
The 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 in Miami.11 Will Alexx benefit by moving to Paris?
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Solved Problem 4.4
•Bundle “a” maximizes welfare in U.S.•Price of U.S. food higher in France•Employer increases his income so that he can consume the same bundle in France•Is he better off?
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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 (Sullivan and Choi, 2002).
Households that meet income, asset, and employment eligibility requirements receive coupons that can be used to purchase food from retail stores.
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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.
Questions: 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?
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Figure 4.10 Food Stamps Versus Cash
All
othe
r go
ods
per
mon
th
Y Y + 100
Y + 100
0 100
Food per month
Budget line withfood stamps
Budget line with cash
Originalbudget line
A
B
f
deY
C
I 1
I2I3
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Behavioral Economics
behavioral economics - by adding insights from psychology and empirical research on human cognition and emotional biases to the rational economic model, economists try to better predict economic decision making
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