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.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.2P
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1. An individual derives utility from the consumption of a basket of goods, c and leisure
time, given by
U(c, l) =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.
(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, given by U(c, l) =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. (a) Solve for the optimal labor supply.
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