Consider the consumer's optimization problem: the consumer makes a consumption-leisure choice to maximize his utility U(C, l) subject to the budget constraint C + wl = wh + T. Assume the utility function is U(C, l) = log(C) + log(l). Under this utility function, MRSl,c = C/l. Therefore, the consumer's optimality condition implies MRSl,c = C/l = w.

(a) Use the consumer's optimality condition and budget constraint, solve for consumer's optimal choice of C and l. (Hint: for you to check your answer, you should get C = wh+T 2 .)

(b) Assume T = 0, show that the substitution effect and income effect cancel out. That is, show that a change of w has no impact on consumer's leisure choice.