Suppose a firm 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 firm 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.

1. Express the firm’s real revenues, real costs and real profits in terms of the variables defined above.

2. Assume the firm operates in goods markets, capital markets and labor markets that are perfectly competitive - that is, it takes P , R and W as given. Derive two conditions that will need to hold in order for the firm to maximize its profits ( Set the partial derivative of profits with respect to L equal to zero and the partial derivative of profits with respect to K equal to zero).

3. The first 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. Let us assume that labor is fixed L = 8 and focus on the capital demand equation. Plot the capital demand function when L = 8 (Show at least three points of the curve).

4. Suppose the supply of capital is inelastic and given by Ks = 27. Plot the capital supply line on the same graph as the capital demand curve. Find the real rental rate of capital that clears the market and show it on the graph.

5. How many goods will that firm produce?