Economics 101A – Fall 2008
Problem Set Number 7
Due: Tuesday November 4 in class
1. Two roommates, 1 and 2, have preferences over leisure (x) and the cleanliness of their room,
c.
Suppose c = y
1
+ y
2
, where y
i
is the amount of time spent by roommate i
in cleanup activities.
Each roommate has a total of 1 unit of time available (per week): thus x
1
+ y
1
=1 and similarly for
roommate 2.
Let 1's preferences be given by
U(x
1
, c) = x
1
+ 1/2 log(c)
and let 2's preferences be given by
V(x
2
, c) = x
2
+ 1/2 log(c)
a.
Suppose 1 and 2 take each other’s clean up effort as given.
Derive the optimal effort of 1 as a
function of 2's effort.
Find the symmetric Cournot equilibrium
.
Are there other Cournot
equilibria?
b.
Suppose 1 and 2 agree on a schedule of clean up that maximizes the sum
of their utilities.
What is the optimal level of cleanliness, c
*
?
c.
Suppose that 1 thinks 2 is following the jointly optimal policy agreed in part b.
What is 1's
optimal choice?
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 Fall '08
 Staff
 Economics, Supply And Demand, economic surplus, jointly optimal cleanliness, jointly optimal policy

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