Dudley has a utility function U(C, R) = C - (12 - R)², where R is leisure and C is consumption per day. He has 16 hours per day to divide between work and leisure. If Dudley has a nonlabor income of $35 per day and is paid a wage of $6 per hour, how many hours of leisure will he choose per day?

Question

Quizplus · Accepted Answer

Dudley maximizes his utility by setting the marginal utility of leisure equal to the wage rate. The derivative of U with respect to R is 2(12-R). Setting this equal to the wage rate of $6, we solve for R: 2(12-R) = 6, which gives R = 9.

Dudley Has a Utility Function U(C, R) = C -