Economics 451
Exam 1
Spring 2007
Prof Montgomery
Answer all questions.
100 points possible.
1) [10 points]
Briefly evaluate and discuss the following claim:
Economic models of the
family cannot adequately address “power differentials” between family members.
2) [30 points]
Consider a household composed of a husband and a wife.
Each member
of the household allocates his/her time to produce market goods (M) and household
goods (H), and time inputs are chosen to maximize overall household utility (which
depends on total M and total H produced by the household members).
Assuming that the
husband has
increasing
returns to production in each sector, while the wife has
constant
returns to production in each sector, their individual production possibilities curves
(PPCs) are given below.
Further assume that the horizontal intercepts (labeled a) and the
vertical intercepts (labeled b) are the same on both diagrams.
M
husband’s PPC
M
wife’s PPC
(convex)
(linear)
b
b
a
H
a
H
a) In Chapter 2 of Becker’s
Treatise
, he considers the case where
both
members of the
household have
constant
returns to production in both sectors.
Given this assumption,
what result does he state regarding the optimal division of labor within households?
[NOTE:
I’m asking about his initial result, where coefficients of production are taken as
given,
not
his subsequent result when individuals choose to invest in human capital.]
b) Will Becker’s result (discussed in part a) still hold given the individual PPCs shown
above?
If you answered no, what result
does
hold?
If you answered yes, can you state a
stronger
result than Becker’s?
In either case, explain your answer.
[HINT: Consider a
potential outcome where both members allocate time to both sectors.
Is the household
behaving efficiently?]
c) Draw the household’s overall PPC.
Then, for each segment of this curve, indicate
which members of the household are working in which sector(s).
[HINT:
Your graph
doesn’t need to be perfect, but should be properly labeled, and the overall PPC must have
the correct shape.]
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View Full Document3) [30 points]
Consider a marriage market with 4 men and 4 women.
The following
matrix gives the payoffs received by each man and woman in each potential match.
[The
matrix specifies the payoffs (m
ij
, f
ji
) given a match between man i and woman j.
The first
column gives payoffs if each man remains single; the first row gives payoffs if each
woman remains single.]
Assume that utility is
not
transferable.
w
o
m
e
n
1
2
3
4
men
4
3
2
1
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
)
6
,
4
(
)
2
,
9
(
)
5
,
5
(
)
6
,
3
(
1
)
2
,
5
(
)
3
,
7
(
)
2
,
6
(
)
3
,
8
(
4
)
1
,
9
(
)
5
,
4
(
)
1
,
5
(
)
4
,
6
(
2
)
4
,
7
(
)
7
,
2
(
)
9
,
6
(
)
5
,
4
(
5
3
4
3
2
.
a) Is the match structure {M1F4, M2F3, M3F1, M4F2} stable?
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 Fall '07
 MONTGOMERY
 Economics, Utility, religious participation

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