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1. Consider a firm which produces according to the following production function by using labor and...
Consider a firm which produces according to the following production function just by using labor
Consider a firm which produces according to the following production function just by using labor f(L) = 4L^1/2 + k (a) Derive the short-run total cost, the short-run average cost, the shortrun marginal cost function of the firm under the assumption that capital is the fixed input. (b) Find short-run firm supply as a function of input prices, w and r, and output price, p.
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital,...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK...
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK . In the short-run, the firm's amount of capital equipment is fixed at K = 100. The rental rate of capital is r=$1, and the wage rate of labor is w=$4. a. Derive the firm's short-run total cost curve. What is the short-run average total cost? What is the short-run average variable cost? b. Find the short-run marginal cost function. What are the total...
21. 12 points Consider a firm that produces output using labor (L) and capital (K). Sup-...
21. 12 points Consider a firm that produces output using labor (L) and capital (K). Sup- pose the firm's production technology is f(L, K) = L+ VK and the input prices are w and r for the wage and rental rate of capital. Find the firm's profit maximizing demands for labor and capital. 2.c.K
a firm produces output according to the following function q= f(L,K) = L^1/2K^3/2. The cost of...
a firm produces output according to the following function q= f(L,K) = L^1/2K^3/2. The cost of labor is $2 per hour and the rental cost of capital is $12 per hour. a) Determine the returns to scale for this function. b) Suppose the firm wishes to produce at cost $56. How Much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b. d. Suppose that there are...
a firm produces output according to the following function q= f(L,K) = L^1/2K^3/2. The cost of...
a firm produces output according to the following function q= f(L,K) = L^1/2K^3/2. The cost of labor is $2 per hour and the rental cost of capital is $12 per hour. a) Determine the returns to scale for this function. b) Suppose the firm wishes to produce at cost $56. How Much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b. d. Suppose that there are...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
1. The production function of a firm is f(1,k) = Vlk where l is labor and...
1. The production function of a firm is f(1,k) = Vlk where l is labor and k is capital/machinery. a. In the short run, if the quantity of capital is fixed at 64, derive the short run total cost SC(q), average cost SAC(q), and marginal cost SMC(q) of this firm. Assume each input costs $1 per unit. At what output does the minimum of SAC(q) occur? b. If labor and capital cost r and w respectively, and the quantity of...
The production of Florida strawberries uses two inputs: labor (L) and capital (K). The following production...
The production of Florida strawberries uses two inputs: labor (L) and capital (K). The following production function describes how these inputs are combined to produce bushels of oranges. f(L,K) = 5(1/2 + 3K1/2 1) Determine what kind of returns to scale this production function exhibits (HINT: labor is the "x" variable - the one that goes on the horizontal axis). 2) What is the formula for that kind of returns to scale? (HINT: use f(L,K)) 3) What is the general...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK . In the short-run, the firm's amount of capital equipment is fixed at K = 100. The rental rate of capital is r=$1, and the wage rate of labor is w=$4. a. Derive the firm's short-run total cost curve. What is the short-run average total cost? What is the short-run average variable cost? b. Find the short-run marginal cost function. What are the total...
21. 12 points Consider a firm that produces output using labor (L) and capital (K). Sup- pose the firm's production technology is f(L, K) = L+ VK and the input prices are w and r for the wage and rental rate of capital. Find the firm's profit maximizing demands for labor and capital. 2.c.K
1. The production function of a firm is f(1,k) = Vlk where l is labor and k is capital/machinery. a. In the short run, if the quantity of capital is fixed at 64, derive the short run total cost SC(q), average cost SAC(q), and marginal cost SMC(q) of this firm. Assume each input costs $1 per unit. At what output does the minimum of SAC(q) occur? b. If labor and capital cost r and w respectively, and the quantity of...
The production of Florida strawberries uses two inputs: labor (L) and capital (K). The following production function describes how these inputs are combined to produce bushels of oranges. f(L,K) = 5(1/2 + 3K1/2 1) Determine what kind of returns to scale this production function exhibits (HINT: labor is the "x" variable - the one that goes on the horizontal axis). 2) What is the formula for that kind of returns to scale? (HINT: use f(L,K)) 3) What is the general...
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