Transcript Lecture Slides 9/2/2015

Chapter 3
CONSUMER CHOICE
Chapter Outline
4-2
1.
Preferences.
2.
Utility.
3.
Budget Constraint.
4.
Constrained Consumer Choice.
5.
Behavioral Economics.
Premises of Consumer Behavior
4-3
The model of consumer behavior is based on the
following premises:
 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.
Five Properties of Consumer Preferences
4-4

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.
Five Properties of Consumer Preferences
4-5

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.
Five Properties of Consumer Preferences
4-6

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
Concentrate on goods
Five Properties of Consumer Preferences
4-7

Continuity- if a consumer prefers Bundle a to
Bundle b, then the consumer prefers Bundle c to b is
c is very close to a.
 The
purpose of this assumption is to rule out sudden
preference reversals in response to small changes in the
characteristics of a bundle
Five Properties of Consumer Preferences
4-8

Strict Convexity- means that consumers prefer
averages to extremes, i.e. more balanced baskets
that have some of each good.
 For
example if Bundle a and Bundle b are distinct
bundles and the consumer prefers both of these bundles
to Bundle c, then the consumer prefers a weighted
average of a and b, βa+(1-β)b, to Bundle c.
Preference Maps
4-9



To summarize information about a consumer’s
preferences is to create a graphical representationa map-of them
Example: Each semester, Lisa, who lives for fast
food, decides how many pizzas and burritos to eat.
The various bundles of pizzas and burritos she might
consume are shown in panel a of Figure 3.1
Figure 3.1 Bundles of Pizzas and Burritos Lisa Might
Consume
25
Lisa prefers any
bundle in area A
(b)
over e
A
f
20
15
e
a
d
10
b
5
B
15
25
30
Z, Pizzas per semester
4-10
If Lisa
Lisa
prefers
is indifferent
bundle e bundles
between
to any e, a,
bundle
and
c …..
in area B
B, Burritos per semester
B, Burritos per semester
(a)
Which
Which of
of these
these
two
two bundles
bundles
would
would be
be
preferred
c
preferred by
by
Lisa?
Lisa?
c
25
20
Lisa prefers
bundle
feover
over
15
bundle e,
d, since fe
has more
of both
10
goods: Pizza and
Burritos
e
a
b
15
25
I1
30
Z, Pizzas per semester
we can draw an
indifferent curve over
those three points
Indifference Curves
4-11

Indifference curve - the set of all bundles of goods
that a consumer views as being equally desirable.
 The
figure shows indifference curves that are continuous
(have no gaps).

Indifference map - a complete set of indifference
curves that summarize a consumer’s tastes or
preferences
Properties of Indifference Maps
4-12
1.
2.
3.
4.
5.
Bundles on indifference curves farther from the
origin are preferred to those on indifference
curves closer to the origin. (more is better)
There is an indifference curve through every
possible bundle.
Indifference curves cannot cross.
Indifference curves slope downward.
Indifference curves can not be thick.
Figure 3.1 Bundles of Pizzas and Burritos Lisa
Might Consume
4-13
(c)
A
c
25
f
20
15
e
a
d
10
b
B, Burritos per semester
B, Burritos per semester
(a)
25
c
f
20
I2
e
15
a
10
d
I1
5
I0
B
15
25
30
Z, Pizzas per semester
15
25
30
Z, Pizzas per semester
we can draw an
indifferent curve over
those three points
Fig 3.2 Impossible Indifference Curves
4-14
B, Burritos per semester

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. ( More-is-better)

e
b
a
I1
I0
Z, Pizzas per semester
Indifference curves can not cross:
A given bundle cannot be on two
indifference curves
Therefore, indifference curves must slope
downward to the right
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
If they sloped upward, they would violate the assumption that more
is preferred to less
 Some points that had more of both goods would be indifferent to a
basket with less of both goods

To consume more food, the consumer is willing to give up some units of
clothing consumption and still get the same utility. In other words, if
food consumption is decreased, the consumer needs to obtain more
units of clothing to keep the same level of utility.
15
4-16

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, Burritos per semester
Impossible Indifference Curves
b
a
I
Z, Pizzas per semester
Impossible Indifference Curves
4-17
Solved Problem 3.1
4-18


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
Solved Problem 3.1
B, Burritos per semester
4-19

b
Consumer is indifferent
between b and a since
both points are in the
same indifference curve…

a
I
Z, Pizzas per semester
But this contradicts the
“more is better” assumption
since b has more of both
and hence it should be
preferred over a.
Utility
4-20


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)
Consumer Preferences
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
Utility
A
numerical score representing the satisfaction that a
consumer gets from a given market basket
 If buying 3 copies of Microeconomics makes you
happier than buying one shirt, then we say that the
books give you more utility than the shirt
21
Utility Function: Example
4-22

Suppose that the utility Lisa gets from pizzas and
burritos is
u  q1q2


Question: Can we 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.
Utility
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


Although we numerically rank baskets and
indifference curves, numbers are ONLY for ranking
A utility of 4 is not necessarily twice as good as a
utility of 2
There are two types of rankings
 Ordinal
ranking
 Cardinal ranking
23
Ordinal Preferences
4-24



If we know only consumers’ relative rankings of
bundles, our measure of pleasure is ordinal rather
than cardinal
An ordinal measure is one that tells us the relative
ranking of two things but does not tell us how much
more one rank is than another
A cardinal measure is one by which absolute
comparisons between ranks may be made
Utility measures are not unique
Willingness to Substitute between goods
4-25



Marginal Rate of Substitution- maximum amount
of one good that a consumer will sacrifice (trade)
to obtain one more unit of another good Slope of
the indifference curve
Indifference curve is downward sloping, hence a
negative MRS
We will use calculus to determine MRS at a point on
Lisa’s indifference curve
Marginal Rate of Substitution
4-26
MRS at e = - slope of
indifference curve at e
= - dB/dP
=-dq2/dq1
Utility - Example
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Clothing
Basket
C
A
B
15
U = FC
25 = 2.5(10)
25 = 5(5)
25 = 10(2.5)
C
10
U3 = 100
A
5
B
0
5
10
U2 = 50
15
27
U1 = 25
Food
Marginal Utility
4-28


MRS depends on how much extra utility Lisa gets from
a little more of each good
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.
Lisa’s utility function is:
MU pizza
U
U

MU burritos 
q1
q 2
As Lisa consumes more
pizza, holding her
consumption of burritos
constant at 10, her
total utility, U,
increases…


4-29
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.
350
Utility function, U (10, Z )
250
230
0
U = 20
MU Z 
Z = 1
1
2
3
4
5
6
7
8
9
10
Z, Pizzas per semester
(b) Marginal Utility
MU Z, Marginal utility of pizza

U, Utils
Utility and
Marginal Utility
(a) Utility
130
20
0
MU Z
1
2
3
4
5
6
7
8
9
10
Z, Pizzas per semester
U
Z
(a) MRS along an Indifference curve
4-30
B, Burritos per semester
Indifference Curve Convex to the Origin
8
5
3
2
0

The MRS from bundle a to
bundle b is -3.
From bundle a to
bundle b, Lisa is
a
 This is the same as the slope
of the indifference curve
willing to give up 3
Burritos in exchange between those two points.
–3
for 1 more Pizza…
b
From bundle c  From b to c,
1
to bundle d,
-2
 MRS = -2.
c
Lisa is willing to  This is the same as the slope
1
d give up 1
-1
of the indifference curve
Burritos in
1
between those two points.
I
exchange for 1
3 4 5 6
more Pizza…
Z, Pizzas per semester
Marginal Rate of Substitution
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
Indifference curves are typically convex (bowed
inward).
 As
more of one good is consumed, a consumer would
prefer to give up fewer units of a second good to get
additional units of the first one (property of diminishing
MRS)

In other words, consumers generally prefer a
balanced market basket
31
Marginal Rate of Substitution
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
The MRS decreases as we move down the
indifference curve
 Along
an indifference curve there is a diminishing
marginal rate of substitution.
 The MRS went from 3 to 2 to 1
32
Diminishing MRS along an Indifference curve
4-33
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B, Burritos per semester
Indifference Curve Convex to the Origin At point a, the consumer has many
units of burritos and few units of
pizza and therefore, it is reasonable
to assume that s/he may value
pizza relatively more than burritos:
s/he would give up a lot of burritos
(3 units) to obtain 1 additional unit
of pizza and still be able to keep
the same level of utility.
a
8
–3
b
5
1
-2
c
3
1
-1
2
0
However, at point c, s/he has few burritos and a lot of pizza.
She’s only willing to give up a small amount of burritos for
an additional unit of pizza, making the slope very flat.
d Therefore, it is reasonable to assume that MRS diminishes
as we move down the indifference curve.
1
3
4
5
I
6
Z, Pizzas per semester
33
(b) Marginal Rate of Substitution with concave
indifference curves
4-34
B, Burritos per semester
(b) Indifference Curve Concave to the Origin

a
7
Nevertheless, from b
to c she is willing to
give up 3 Pizzas for 1
burrito.
 This is very unlikely

–2
b
5
1
–3
c
2
1

I
0
From bundle a to
bundle b, Lisa is
willing to give up 2
Pizzas for 1 Burrito.
3
4
5
6
Z, Pizzas per semester
Could you think why?
Diminishing marginal rate of substitution
4-35


When we have CONVEX preferences (as in the
normal case) 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?
Exercise:
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Suppose that utility function of a consumer is give by U(F,C)=
FC.




Draw the indifference curve associated with a utility level of 12 and
the indifference curve associated with the utility level of 24.
Show that the indifference curves are convex. Use indifference curve
for utility level 12 as an example to show this.
Find the equation for the indifference curve for utility level equal to
12 and find the MRS at (F,C) = (3,4).
Find the MRS at point (F,C) = (2,3). You will have to derive the
equation for indifference curve that goes through the point first, then
find the MRS at that point.
36
Willingness to Substitute between goods
4-37
Suppose more generally we have an indifference curve:
Then once we select a value for q1, then the point q2 is
determined by the equation of the indifference curve, so we
can write q2 as a function of q1, i.e. q2(q1)
(Example: U=FC; For utility=25, indifference curve is FC=25, or
C=25/F)
Where U1 is MU of
good 1
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Marginal Utility and Consumer
Choice

It must be the case along an indifference curve that
0  MUF(F)  MUC(C)
No change in total utility along an indifference curve.
Trade off of one good to the other leaves the consumer
just as well off.
38
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Marginal Utility and Consumer
Choice

Rearranging:
C / F   MU F / MU C
Since
 C / F   MRS of F for C
We can say
MRS  MUF/MUC
39
Solved Problem 3.2
4-40
Suppose that Jackie has what is known as a CobbDouglas utility function:
where a is a positive constant, q1 is the number of
CDs she buys a year and q2 is the number of movie
DVDs she buys. What is her MRS?
Answer:
Curvature of Indifference Curves.
4-41


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

Figure 3.4a Perfect Substitutes
Coke, Cans per week
4-42

4
3
2
Straight, parallel lines
with an MRS (slope) of
−1.
 Bill is willing to exchange
one can of Coke for one
can of Pepsi.

1
I1
0
Bill views Coke and
Pepsi as perfect
substitutes: can you tell
how his indifference
curves would look
like?
1
I2
I3
I4
2
3
4
Pepsi, Cans per week
Figure 3.4b Perfect Complements
Ice cream, Scoops perweek
4-43
d
2
a
1
0
c
e
3
1
b
I3
I2
I1
2
3
Pie, Slices per week
 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.
EXERCISE
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

Suppose a consumer’s utility of consuming good-X and
good-Y is given by
U(X,Y) = min{X,2Y}
Where, X is the amount of good-X and Y is the amount of
good-Y. The function “min” is a function that chooses the
smallest value in the bracket. For example min{2,3} =2,
min(3,2}=2, min{100,3} =3.
44
Figure 3.4c Imperfect Substitutes
4-45
B, Burritos per semester
f

The standard-shaped,
convex indifference
curve in panel lies
between these two
extreme examples.

I
Z, Pizzas per semester
Convex indifference
curves show that a
consumer views two
goods as imperfect
substitutes.
Application: Indifference Curves Between Food and
Clothing
4-46
Research has
shown that at low
(subsistence) levels
of income (I1),
there is little
willingness to
substitute between
food and clothing.
Consumer Preferences:
An Application
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

An analysis of consumer preferences would help to
determine where to spend more on changes in car
design: performance or styling
Some consumers will prefer better styling and some
will prefer better performance in their car
47
Consumer Preferences:
An Application
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Styling
These consumers
place a greater
value on
performance
than styling
Performance
48
Consumer Preferences:
An Application
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Education, Inc.
Styling
These consumers
place a greater
value on styling than
performance
Performance
49
Problems: constructing indifference curves
4-50
1.
2.
3.
Don is altruistic. Show the possible shape of his
indifference curves between charity and all other
goods.
Miguel considers tickets to the Houston Grand
Opera and to Houston Astros baseball games to be
perfect substitutes. Show his preference map.
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?
Budget Constraint
4-51


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
Budget Constraint
4-52

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.
Budget Constraint (cont).
4-53

How many burritos can Lisa buy?

To answer solve budget constraint for B (quantity of
burritos):
PB B  PZ Z  Y
PB B  Y  PZ Z
Y  PZ Z
B
PB
Budget Constraint (cont).
4-54

From previous slide we have:
Y  PZ Z
B
PB

If pZ = $1, pB = $2, and Y = $50, then:
$50  ($1 Z )
B
 25  0.25Z
$2
B, Burritos per semester
Figure 3.5 Budget Constraint
 From previous slide we
have that if:
Amount of Burritos
consumed if all income
is allocated for
Burritos.
25 = Y/pB
20
– pZ = $1, pB = $2, and Y =
$50, then the budget
constraint, L1, is:
$50  ($1 Z )
B
 25  0.25Z
$2
a
b
L1
c
10
Amount of Pizza
consumed if all income
is allocated for Pizza.
Opportunity set
d
0
4-55
10
30
50 = Y /pZ
Z, Pizzas per semester
Budget Constraints: Budget Line
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
Letting x and y be the goods on the x- and y-axis
respectively:




The vertical intercept, I/Py, illustrates the maximum amount of
good y that can be purchased with income I
The horizontal intercept, I/Px, illustrates the maximum amount
of x that can be purchased with income I
The slope of the line measures the relative cost of food
and clothing; it’s the relative price of the good on the xaxis.
The slope is the negative of the ratio of the prices of
the two goods; it’s –Px/Py
56
The Slope of the Budget Constraint
4-57

We have seen that the budget constraint for Lisa is given by
the following equation:
Y
PZ
B

Z
PB PB
Slope = B/Z = MRT

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
Table: Allocations of a $50 Budget Between Burritos
and Pizza
4-58
(a) Changes in the Budget Constraint: An increase in the
Price of Pizzas.
B, Burritos per semester
4-59
Slope = -$1/$2 = -0.5
25
L1 (pZ = $1)
$2
Y - PZ = $1
PB
PB
B=
If the price of Pizza
doubles, (increases
from $1 to $2) the
slope of the budget
line increases
Loss
L2
(pZ = $2)
0
Slope = -$2/$2 = -1
Z
25
50
Z, Pizzas per semester
This area represents
the bundles she can
no longer afford!!!
(b) Changes in the Budget Constraint: Increase in
Income (Y)
4-60
B, Burritos per semester
$100
$50
B= P B
50
L3 (Y = $100)
25
If Lisa’s income
increases by $50 the
budget line shifts to
the right (with the
same slope!)
Gain
L1 (Y = $50)
0
PZ
Z
PB
50
100
Z, Pizzas per semester
This area represents
the new consumption
bundles she can now
afford!!!
Solved Problem
4-61

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?
Solved Problem
4-62
Figure 3.6 (a) Consumer Maximization: Interior Solution
B, Burritos per semester

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

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.

25
c
20
e
d
A
0
f
B
10
4-63

10
Would Lisa be able to
consume any bundle along
I1 ?
 Yes; she could afford
bundles d, c, and a.
a
30
I3
I2
I1
50
Z, Pizzas per semester
B, Burritos per semester
Consumer Maximization: Interior Solution
 The budget constraint and the indifference curve
have the same slope at the point e where they
touch.
 Therefore, at point e:
MU Z
PZ
MRS  

 MRT
MU B
PB
25
Slope of I2
e
I2
0
4-64
50
Z, Pizzas per semester
Slope of BL
Figure 3.6 (b) Consumer Maximization:
Corner Solution
B, Burritos per semester
4-65
25
e
I3
I2
Budget line
I1
50
Z, Pizzas per semester
Solved Problem 3.3
4-66

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.
Solved Problem 3.3
4-67
Figure 3.7 Optimal Bundles on Convex Sections of
Indifference Curves
4-68
Maximizing utility subject to a constraint
using calculus
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Lisa’s objective is to maximize her utility, U(q1, q2),
subject to (s.t.) her budget constraint:
Here the control variables are q1 and q2.
Lisa has no control over the prices she faces, p1
and p2, or her income, Y.
Two methods of solving the problem. We’ll focus on
the substitution method only.
Substitution
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First, we can substitute the budget constraint into the
utility function. Using algebra we can rewrite the budget
constraint as q1 = (Y-p2q2)/p1 and substitute this
expression for q1 in the utility function
Using standard maximization techniques we can solve
this problem. (i.e. take the first derivative of the utility
function with respect to q2 and set it equal to zero)
Substitution
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By rearranging terms in the above equation, we get the
same condition for an optimum that we obtained using a
graphical approach.
When we combine the MRS=MRT condition with the budget
constraint we have two equations in two unknowns , q1 and
q2. So we can solve for the optimal q1 and q2 as function of
prices, p1 and p2, and income
Minimizing Expenditure
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We have shown how Lisa chooses quantities of goods so as to
maximize her utility subject to a budget constraint.
There is a related or dual constrained maximization problem
where she finds the combination of goods that achieve a
particular level of utility for the least expenditure.
Earlier we showed that Lisa maximized her utility by picking a
bundle of q1 = 30 and q2 = 10 at the indifference curve I2
Now we see: How can Lisa make the lowest possible expenditure
to maintain her utility at a particular level which corresponds to
indifference curve I2?
Fig. 3.8 Minimizing Expenditure
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The figure shows three possible
budget lines corresponding to
budgets or expenditures E1, E2 and
E3.
E1 lies below I2.
E2 and E3 both cross I2. However the
BL with E2 is the least expensive way
for her to stay on I2.
The rule for minimizing expenditure while achieving a given level of utility is to
choose the lowest expenditure such that the budget line touches-is tangent to-the
relevant indifference curve
Minimizing Expenditure
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Solving either of the two problems yields the same optimal
values.
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More useful to use the expenditure minimizing approach
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We can use calculus to solve the expenditure minimizing problem
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The solution of this problem gives us the expenditure function: the
relationship showing the minimal expenditures necessary to
achieve a specific utility level for a given set of prices.
Food Stamps
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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.
Food Stamps (cont).
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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?
All other goods per month
Food Stamps Versus Cash
Budget line with cash
Y + 100
f
Y
C
e
I3
d
I2
I1
B
Budget line with
food stamps
A
0
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Original
budget line
100
Y
Y + 100
Food per month
Behavioral Economics
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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