1. An individual derives utility from the consumption of a basket of goods, c and leisure time, & given by U(c₂l) = cºl(¹-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L + l = 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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1. An individual derives utility from the consumption of a basket of goods, \( c \), and leisure time, \( \ell \), given by

\[
U(c, \ell) = c^\alpha \ell^{(1-\alpha)}
\]

where \( 0 < \alpha < 1 \), is a constant; and must decide how to allocate her time between work, \( L \), and leisure to maximize her utility. The individual has a total of 24 hours in a day (\( L + \ell = 24 \)) and total consumption is constrained by her income; i.e., \( c = wL \), where \( w \) the wage per hour, is taken as given.

(a) Solve for the optimal labor supply.
Transcribed Image Text:1. An individual derives utility from the consumption of a basket of goods, \( c \), and leisure time, \( \ell \), given by \[ U(c, \ell) = c^\alpha \ell^{(1-\alpha)} \] where \( 0 < \alpha < 1 \), is a constant; and must decide how to allocate her time between work, \( L \), and leisure to maximize her utility. The individual has a total of 24 hours in a day (\( L + \ell = 24 \)) and total consumption is constrained by her income; i.e., \( c = wL \), where \( w \) the wage per hour, is taken as given. (a) Solve for the optimal labor supply.
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