Question 3 (30 points)

Question 3 (30 points). Consider the real inter-temporal model of investment that lasts for two periods. The representative consumer is endowed with h units of time in each period. The consumer's preference over consumptions and leisures for all periods is u(C,1) + Bu(C',1'), = where 0 <B<1 and u(C, 1) = y In C + (1 - 7) Inl, 0 <7<1. The representative firm's production function in each period is F(K, N) KaNl-a, where 0<a < 1. The firm owns capital K and chooses the capital stock K' for the future period. The government finances its expenditures G, G' with proportional taxes on labor income T, T' in both periods. (a) Define competitive equilibrium for this economy (6) Write down the equations that characterize the equilibrium allocation (C,C,1,1", K') (c) 'Define Pareto efficiency for this economy (d) Write down the social planner's problem for this economy (e) Is the competitive equilibrium allocation Pareto efficient? Explain why or why not using the social planner's problem.