Suppose the firm's production function is given by f(L,K) = 5LK. C represents the total cost of production; the price of L is PL and the price of K is PK. Plot an isoquant from this specific production function. Using graphical analysis derive the firm's conditional demand curve for L in both the short and long run. Explain.
Suppose the firm's production function is given by f(L,K) = 5LK. C represents the total cost...
1. (1 p) A firm's production function is given by F(K,L)= K+ vKL. The per period price of a unit of labour services is w1 and that for capital services is r 2. Assuming that the amount of capital is fixed at K 4, derive the firm's short-run average cost curve and explain its shape.
Suppose the firm's production function is given by f(K,L) = min {K",L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
Consider a firm using two inputs; capital (K) and labor (L) in production. The firm's production technology is characterized by the following production function: Q = F(K, L) = 40K L In the short run (SR), the quantity of the capital (K) that the firm uses is fixed at K = 10 whereas the quantity of the labor input can be varied. Price of labor is $4,000 per worker and the price of capital is $2,000 per capital. (PL=$4,000 and...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
5. Let the firm's production function be given by y = + x2. Note that the inputs 2 and 2 are perfect substitutes in this production process. Suppose w = 2 and we = 1. (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price of...
Suppose the firm's production function is Q = 2KL where Q is units of output, K is units of capital (which are fixed at 2), and L is units of labor. a. What is the firm’s short-run production function? b. Over the labor input usage range of 0 to 5, that is L ranging from 0 to 5, graph the firm’s Total Product curve. c. Derive and graph the firm’s Average Product curve and the Marginal Product curve. Graph/plot them...
5. Let the firm's production function be given by y 1+2. Note that the inputs r1 and 2 are perfect substitutes in this production process. Suppose wi 2 and w2 1 (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price of the second input, w2,...