An individual derives utility from consumption goods, X, and leisure time, N, to

Question

An individual derives utility from consumption goods, X, and leisure time, N, to maximize the daily utility level, u = XN. Outside income per day is $m and the price of consumption goods is $p. The individual can earn money each day by working at a wage rate of $w per hour, but working of course takes away from leisure time (which implies it causes disutility). The individual’s utility maximization problem is constrained by two things: (i) the budget constraint, pX = m + wL, and (ii) the “time constraint”, L + N = 24 . the production function produces consumption goods with labor (L) according to f(L)=100* square root L. How much time will they spend on leisure? How many units of consumption goods will be produced?

Explanation / Answer

Labor supply: L* = 24 - N*

=24 - (24w + m)/2w

=24-12-m/2w

=12 - m/2w

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