Assume an individual has a utility function of this form
U(C, L) = 6 + CxL
This utility function implies that the individual’s marginal utility of leisure is C and her marginal utility of consumption is L. The individual has an endowment of V in non-labor income and T = 16 hours to either work (h) or use for leisure (L).
Assume the price of each unit of consumption good p = 2 and the wage rate for each hour of work w = 1, and V = 0. What is the optimal amount of consumption and leisure?