Problem 1 (9 points) Let Frank's utility function be U(C, L) = Cz+m2L2, where a: > 0 is some number. Suppose he has 110 hours to split between work and leisure and he has no non-labor income. (a) Derive Frank's optimal choice of consumption and leisure as a function of the wage. (6 points) (b) What is Frank's reservation wage? (3 points) Problem 2 (6 points) Alan earns $20 per hour for up to 40 hours of work each week. He is paid $30 per hour for every additional hourj in excess of the 40 hours. Alan faces a 20% tax rate and has to pay $5 in childcare expenses for every hour he works. He receives $200 in child support payments each week, regardless of how much he works. There are 100 hours in the week. Graph Alan's weekly budget line after tax and childcare expenses