A perfectly competitive firm produces output y using labour and capital, L, K, as inputs. The technology of the firm can be described by the production function f(L,K) = BLK-a. (1) The factor prices are denoted by (w,r) > 0. Output price is p > 0. a) Derive the conditional factor demands and show that the cost function of the firm is given by c(y) = y with = (69)**(**) + (max. 7 points) b) Derive the marginal cost function. What do you observe regarding its slope? How does this relate to the firm's technology! (max. 4 points) c) Determine the optimal supply of the firm for all possible prices. (max. 5 points) Suppose the firm sells its product on the world market. There is only one competitor which produces in some other country using labour Lf as input (labour is immobile across countries). This firm has a decreasing returns to scale production function ff(Lf). Both firms are price takers. Demand at the world market can be described by a decreasing demand function D(p). d) Suppose both firms produce in equilibrium, thus p = . The following equations determine the equilibrium on the world market aff(Lf) - wf = 0 (3) f(L,K) + f(LF) = D(p) Explain both equations. How do they determine the equilibrium values of the endogenous variables? (max. 8 points) e) Suppose the price for labour wg in the foreign country increases, while w and r are unaffected. Perform a comparative static analysis to determine the effect on the output quantities of both firms and total output. (max. 9 points) P alf A perfectly competitive firm produces output y using labour and capital, L, K, as inputs. The technology of the firm can be described by the production function f(L,K) = BLK-a. (1) The factor prices are denoted by (w,r) > 0. Output price is p > 0. a) Derive the conditional factor demands and show that the cost function of the firm is given by c(y) = y with = (69)**(**) + (max. 7 points) b) Derive the marginal cost function. What do you observe regarding its slope? How does this relate to the firm's technology! (max. 4 points) c) Determine the optimal supply of the firm for all possible prices. (max. 5 points) Suppose the firm sells its product on the world market. There is only one competitor which produces in some other country using labour Lf as input (labour is immobile across countries). This firm has a decreasing returns to scale production function ff(Lf). Both firms are price takers. Demand at the world market can be described by a decreasing demand function D(p). d) Suppose both firms produce in equilibrium, thus p = . The following equations determine the equilibrium on the world market aff(Lf) - wf = 0 (3) f(L,K) + f(LF) = D(p) Explain both equations. How do they determine the equilibrium values of the endogenous variables? (max. 8 points) e) Suppose the price for labour wg in the foreign country increases, while w and r are unaffected. Perform a comparative static analysis to determine the effect on the output quantities of both firms and total output. (max. 9 points) P alf