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Economics 11: Microeconomic Theory 1
Professor Christian Hellwig
Practice Problems Week 5, Answer Key
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.
d)
How does the labor supply of each individual change with changes in the
wage rates, and changes in the outside income M. Explain your result in terms
of income and substitution effects.
a)
The household’s income consists of the two members’ wage incomes and the
additional outside income M. If person 1 consumes X
1
hours of leisure, she works T
1
X
1
hours, and earns w
1
(T
1
 x
1
) dollars. Similarly, if person 2 consumes X
2
hours of leisure,
he works T
2
 X
2
hours, and earns w
2
(T
2
 X
2
) dollars. The budget constraint then is
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This note was uploaded on 04/05/2009 for the course ECON 11 taught by Professor Cunningham during the Spring '08 term at UCLA.
 Spring '08
 cunningham
 Economics

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