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).

ENGR.ECONOMIC ANALYSIS
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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: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).
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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