Let U(C, l) = C + l 0.5 . As usual, C is the representative agent's consumption,l is the representative agent's leisure, h = 1 is the time endowment, and ? is the prot generated by the representative rm which is distributed as dividend to the representative consumer. Let G denotes government expenditures. Set G = 0.1. Let TFP, z = 1 and the aggregate capital stock, K = 1. The representative rm's production function is given by Y = F(K, N) = zK0.5N0.5 , where N is labor demanded by the rm. Let T denotes lump sum taxes.
Given z = 1,K = 1,and G = 0.1, nd the competitive equilibrium values of C, l, w, N, ?, T. In order to do this you need to solve the consumer's optimization problem and the rm's prot maximization problem. You need to make sure the labor marker clears i.e. Ns = Nd (labor supply=labor demand) and the government runs balanced budget i.e. (G = T).
Now assume that there is a social planner who has full information about the representative consumer's preferences and budget constraints. The social planner also has full information about the rm's production technology and production costs. Finally, the social planner knows that government revenues should be equal to government expenditures. Now, following the steps we learned in Week 5 lectures, solve the social planner's problem and nd the socially optimum values of C, l, w, N, ?, T. Compare the competitive equilibrium outcome with those of the socially optimum outcome. Make a comment regarding your findings.
Let U(C, l) = C + l 0.5 . As usual, C is the representative agent's consumption,l is the representative agent's leisure, h = 1 is the time endowment, and ? is the prot generated by the representative rm which is distributed as dividend to the representative consumer. Let G denotes government expenditures. Set G = 0.1. Let TFP, z = 1 and the aggregate capital stock, K = 1. The representative rm's production function is given by Y = F(K, N) = zK0.5N0.5 , where N is labor demanded by the rm. Let T denotes lump sum taxes.
Given z = 1,K = 1,and G = 0.1, nd the competitive equilibrium values of C, l, w, N, ?, T. In order to do this you need to solve the consumer's optimization problem and the rm's prot maximization problem. You need to make sure the labor marker clears i.e. Ns = Nd (labor supply=labor demand) and the government runs balanced budget i.e. (G = T).
Now assume that there is a social planner who has full information about the representative consumer's preferences and budget constraints. The social planner also has full information about the rm's production technology and production costs. Finally, the social planner knows that government revenues should be equal to government expenditures. Now, following the steps we learned in Week 5 lectures, solve the social planner's problem and nd the socially optimum values of C, l, w, N, ?, T. Compare the competitive equilibrium outcome with those of the socially optimum outcome. Make a comment regarding your findings.
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