Economics 451
Exam 1
Spring 2005
Prof Montgomery
Answer all questions. 100 points possible. Explanations can be brief.
1. [22 points]
Consider a marriage market with 100 males and 120 females.
Suppose that any married couple would receive joint income Z
mf
= 40.
Within marriages,
this joint income will be split between the male and female so that Z
m
+ Z
f
= 40.
The
equilibrium income levels Z
m
* and Z
f
* are determined by market supply and demand.
The value of being single differs across males and across females.
(That is, Z
sm
differs
across males, and Z
sf
differs across females.)
For 80 males, the value of being single is
10.
For the other 20 males, the value of being single is 25.
For 70 females, the value of
being single is 5.
For the other 50 females, the value of being single is 25.
a) To analyze market equilibrium, plot the supply and demand for
husbands
.
[HINT: Be
sure to label your graph carefully (including labels on the axis and curves, and identifying
numerical coordinates of important points on each curve).] What is the equilibrium
income Z
m
* received by married men?
How many marriages occur in equilibrium?
[HINT: You have enough information to give
numerical
answers.]
b) How does your result in part (a) differ from the outcome discussed in lecture (where
we assumed that Z
sm
is the same for all males, that Z
sf
is the same for all females, and that
Z
sm
+ Z
sf
< Z
mf
)?
Briefly discuss.
2. [24 points]
Actor i is altruistic toward actor j if i’s utility depends positively on j’s
utility (that is,
∂
U
i
/
∂
U
j
> 0).
Analogously, we may say that actor i is
envious
toward actor
j if i’s utility depends negatively on j’s utility (that is,
∂
U
i
/
∂
U
j
< 0).
Consider a household with a parent who is altruistic toward two children, Tom and Jane.
Suppose that the parent’s income is much larger than the income of either child, so that
both Tom and Jane receive positive transfers from the parent.
Initially, both Tom and
Jane are selfish (their utility depends solely on their own consumption) but not envious of
each other.
a) Suppose that Tom becomes envious of Jane (while Jane remains merely selfish).
How
will this affect the transfers chosen by the parent?
Briefly explain. [HINT: You might
consider the case with additively separable utility functions.]
b) Suppose instead that both Tom and Jane became envious towards each other.
Would
the parent increase or decrease her own consumption?
Briefly explain.
c) How would you respecify the parent’s utility function if the parent disapproved of her
children’s envy?
How would this modify the parent’s optimal choices?
Briefly explain.
d) Does the Rotten Kid Theorem hold when children are envious?
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View Full Document3. [28 points]
Consider a marriage market with 7 males and 7 females.
The following
matrix gives the payoffs that would be received by each male and each female in each
potential match.
[Males are placed along the rows of the matrix, and females are placed
along the columns, so that each pair (m
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 Fall '07
 MONTGOMERY
 Economics, Game Theory, Utility, UW students

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