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Econ 301  Homework #3
1.
Deriving Labor Supply
. Consider a consumer with preferences for consumption of a composite good
(Y) and leisure (N) given by the following utility function:
U
(
Y,N
) = 2
Y
2
/
3
N
1
/
3
Denote the consumer’s wage rate by
w
and total time available for labor and leisure is 24 hours. The
price of consumption is one. Denote the amount of labor supplied as N, so that
N
+
H
= 24. The
consumer also receives an unearned income of
I
.
a. Write out the budget constraint determining feasible allocations of leisure and consumption.
b. Using substitution method to derive the optimal bundle of labor supply
H
(
w,I
) and optimal
bundle of consumption
Y
(
w,I
) (
Hint
, only need to solve the interior solution where labor supply
and consumption are positive).
c. Derive the consumer’s leisure consumption function:
N
(
w,I
).
d.
Optional (5 extra points)
. Determine the eﬀect of increasing unearned income
I
on the supply
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 Summer '07
 CORINNELANGINIER
 Microeconomics, Utility

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