Suppose a rm uses both labor L and capital K as inputs to production. Its production function is of the Cobb-Douglas form, i.e. F (K; L) = K 1 3 L 2 3 The rm charges a price P for every good it sells, pays a nominal rental rate R to every unit of capital it hires and pays a nominal wage W to every unit of labor it hires. Assume the supply of capital is inelastic KS = 27 and the supply of labor is inelastic LS = 8. (a) Express the rms real revenues, real costs and real prots in terms of the variables dened above. (b) Assume the rm operates in goods markets, capital markets and labor markets that are perfectly competitive - that is, it takes R P and W P as given. Derive two conditions that will need to hold in order for the rm to maximize its prots ( Set the partial derivative of prots with respect to L equal to zero and the partial derivative of prots with respect to K equal to zero). The rst of these conditions should include the real wage rate W P as well as K and L. This is the labor demand equation. The second condition should involve the real rental rate of capital R P as well as K and L. This is the capital demand equation. (c) Focus rst on the capital market: plot the capital demand function when L = 8 (You need at least three points to plot this curve). On the same graph plot the capital supply function. Compute the equilibrium rental price of capital and show it on the graph. (d) Focus now on the labor market: plot the labor demand function when K = 27 (You need at least three points to plot this curve). On the same graph plot the labor supply function. Compute the equilibrium real wage and show it on the graph. 1(e) In equilibrium, how many goods will that rm supply to the market for goods? (f) Find real labor income W P L, real capital income R P K and use them to compute the rms real prots in equilibrium