How many units of consumption goods will be produced

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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?

Reference no: EM13982201

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