Problem 1

Let Frank's utility function be ( C, L) = C^2+ x^2L^2, where x 0 is some number. Supposehe 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. (6points)

(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 hourfor every additional hour, in excess of the 40 hours. Alan faces a 20% tax rate and has topay $ 5 in childcare expenses for every hour he works. He receives $ 200 in child supportpayments each week, regardless of how much he works. There are 100 hours in the weekGraph Alan's weekly budget line after tax and childcare expenses