An agent has utility function u(c; l) = c l, where c is greater or equal to0 is a consumption

good, and l is greater or equal to0 is leisure. The agent initially has 24 hours of labor endowment per

day and 0 units of c. The unit price of the consumption good is 1 and the unit price of

leisure is r per hour.

(a) Formulate the agent's utility maximization problem.

(b) Obtain the first order condition and solve them. (You must also prove that the

solution to the first order conditions solves the utility maximization problem.)

(c) Suppose that the agent now has another option. He can quit his job (in which case

he has 24 hours of leisure) and obtain a welfare payment of W per day from the

government. Prove that if W > 6r then the agent would prefer to be on welfare

rather than work.