Economics 11: Microeconomic Theory 1
Professor Christian Hellwig
Practice Problems Week 5
1)
A particular household consists of two individuals who are both potential workers and who pool
their budgets. The household’s preferences are represented by a single utility function U(X
0
, X
1
,
X
2
), where X
1
is the amount of leisure enjoyed by person 1, X
2
is the amount of leisure enjoyed by
person 2, and X
0
is the amount of the single composite consumption good enjoyed by the
household. The two members of the household each have 24 hours which can either be enjoyed as
leisure, or spent in paid work. The hourly wage rates for the two individuals are w
1
and w
2
,
respectively, and they jointly have nonwage income of M. The price of the composite consumption
good is
1
.
a)
Write down the household budget constraint
b)
The household utility function takes the form:
U (X
0
, X
1
, X
2
) =
β
0
log (X
0

α
)+
β
1
log X
1
+
β
2
log X
2
Solve for the household’s optimal choice of X
1
,X
2
,X
0
c)
Derive the household’s supply of the labor of individuals 1and 2.
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 Spring '08
 cunningham
 Economics, Supply And Demand, Household Utility Function, household budget constraint

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