27) Consider the following consumer's problem facing a proportional tax. Utility function over consumption (C) and leisure (L) U(C,L) = C1/21 1/2 Total hours: H = 30 Labour hours: NS = H - L Proportional income tax rate = 0.1 Hourly wage: 5 Find the optimal C*, L*, NS*, and Tax revenue at the optimum. Answer: to be solved in class 28) Suppose the following model of government efficiency. Utility function over consumption of private goods (C) and public goods (G) U(C,L) = C1/2G1/2 Exogenous Income: Y = 50 Lump-sum tax: T Budget constraint: C + T = Y PPF: C = Y - G/q Government efficiency: q = 0.8 (This measures the number of public goods that can be produced from one unit of private consumption good) We want to maximize the representative consumer's utility and balance the government budget. Find C*, G*, T* Answer: to be solved in class 29) Consider the following two-period problem for the representative consumer Y1 = 50 T1 = 5 Y2 = 20 T2 = 10 r = 0.10 C1 = consumption in the first period C2 = consumption in the second period S = saving in the first period U(C1, C2) = min {C1, C2} What is the optimal saving, S*, that maximizes the representative consumer's lifetime utility? Answer: to be solved in class