For the closed-economy one-period model, suppose the consumer's preferences are given by: U(c,l)=L= lnc+lnl

and the aggregate production function is given by Y=F(K,N_d)= K^1/3N_d^2/3

There is no government in the economy and K=1, h=1 are exogenous and given.

(a) Are all assumptions for the aggregate production function hold for the function given by 2nd equation?

(b) Define the competitive equilibrium for this economy

(c) Characterize the competitive equilibrium. Derive the equilibrium profit for the firm and the equation that would be used to solve for wages for this economy.

(d) Draw a diagram with consumer indifference curve(IC) and the production possibilities frontier (PPF) and show competitive equilibrium in this diagram. (You need to derive the equations for IC and PPF)

(e) Suppose the economy is at this competitive equilibrium and capital K increases. Using a diagram illustrate the change in equilibrium.Provide and explain the changes (increase or decrease) in equilibrium values for c,l,and w