1 One-Period Model 1. * a Consider a one-period model. A rep- resentative consumer has preferences represented by u(C, z) = c + x/l + 1000, where C denotes a numraire composite goods and 1 denotes the hours of leisure. She is allotted h = 1000 hours of time. She works for N 5 hours at the wage rate of 10. In addition to her labor income, she earns the dividend 11' and pays T for tax. Write her utility maximization problem. 3. i: a Suppose that a representative firm's production function is given by zF(K, Nd) :2 KM, with total factor productivity 2* = 2 and capital K = . N d denotes labor demand. Write the prot maximization problem. 7. xxk 22 Let G = 2. Compute the equilib rium. Tip I've left you figure I just to help you check your answer. Do not quote it in your an- swer, which should be derived from the equilib rium conditions, not from a graph. You can solve items 1 and 3 combined (slower), or item 6 alone (quicker). If you go for the latter, be sure to quote an appropriate theorem in your answer. 14 51 Indifference Curves Budget Constraint 12 C=zF(K, h-I)-G 40 54 10 8 45 42 51 6 A 2 39 A 45 36- 33 . 42 0 -2 0 200 400 600 800 1000 I [hours]