Suppose the interior solution exists in the consumer's utility maximization problem. Find the optimal labor supply of the representative consumer. П wt ພ2(1- w² (1-t)+1 N8* = 1 - w² (1-t)+wπ N8* = 1 1 N8* ○ N8* = 1 πT 2w(1-t) w² (1−t)²+w(1−t)π w2 (1-t)²+1 Consider the decisions of a representative consumer whose preferences are given by: u(C,1) = In C+ Inl where C is the quantity of consumption and 1 is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the labor supply). Further, consumer take wages as given and obtain after-tax labor income that is equal to w(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint is given by C = w(1 − t)(1 − 1) + π where is the real dividend income received from the representative firm (i.e. firm profits).
Suppose the interior solution exists in the consumer's utility maximization problem. Find the optimal labor supply of the representative consumer. П wt ພ2(1- w² (1-t)+1 N8* = 1 - w² (1-t)+wπ N8* = 1 1 N8* ○ N8* = 1 πT 2w(1-t) w² (1−t)²+w(1−t)π w2 (1-t)²+1 Consider the decisions of a representative consumer whose preferences are given by: u(C,1) = In C+ Inl where C is the quantity of consumption and 1 is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the labor supply). Further, consumer take wages as given and obtain after-tax labor income that is equal to w(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint is given by C = w(1 − t)(1 − 1) + π where is the real dividend income received from the representative firm (i.e. firm profits).
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.1P
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Transcribed Image Text:Suppose the interior solution exists in the consumer's utility maximization problem. Find the
optimal labor supply of the representative consumer.
П
wt
ພ2(1-
w² (1-t)+1
N8* = 1 -
w² (1-t)+wπ
N8* = 1
1
N8*
○ N8*
= 1
πT
2w(1-t)
w² (1−t)²+w(1−t)π
w2 (1-t)²+1
Transcribed Image Text:Consider the decisions of a representative consumer whose preferences are given by:
u(C,1) = In C+ Inl
where C is the quantity of consumption and 1 is the quantity of leisure.
The consumer faces two constraints.
The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the labor
supply). Further, consumer take wages as given and obtain after-tax labor income that is equal to
w(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint is
given by
C = w(1 − t)(1 − 1) + π
where is the real dividend income received from the representative firm (i.e. firm profits).
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