ENGR.ECONOMIC ANALYSIS
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ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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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.](https://content.bartleby.com/qna-images/question/c3585354-64d7-4f4a-b055-4a9b75b3799d/9af016c8-466c-457c-b76a-e1b7ceb3d8b7/t6ywac5_processed.png)
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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