Suppose that a firm has a production function given by: ? = ?^?.???^?.? . The wage...
Suppose that a firm has a production function given by: ? = ?^?.???^?.? . The wage rate is $18 and the rental rate is $9.
12. Suppose that the firm has 4 units of capital in the short run. Find the short run total cost function. ________________________________
13. Find the marginal product of labor (MPL) function. ________________________________
14. Solve the optimization condition for K and write that equation. ________________________________
15. Suppose the firm wants to minimize the cost of producing 100 units of output. Calculate the amount of labor the firm would hire as part of its production process. ______________________
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Suppose that a firm has a production function given by: ? =
?^?.???^?.? . The wage...
3. Suppose a firm has the production function Q = 50 KL 1) If the wage...
3. Suppose a firm has the production function Q = 50 KL 1) If the wage rate is $10 per unit of labor and the rental rate of capital is $5 per unit of capital, how much capital and labor should the firm employ in the long run to minimize the cost of producing 40,000 units? 2) Using the solution in part 1), what will the firm’s long-run total cost be?
Suppose that a firm had a production function given by q-21 K The rental rate for...
Suppose that a firm had a production function given by q-21 K The rental rate for the fim is $10 and the wage is s5 Solve the optimization condition for K and then fill in the value that appears in front of L K- Round to the nearest 2 decimal places if necessary.) Suppose that a firm had a production function given by q-L025k075. The wage rate (w) is $10 and the rental rate () is $10 Calculate the amount...
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...
Suppose a firm has the production function Q = 50KL with MP, = 50K and MP,...
Suppose a firm has the production function Q = 50KL with MP, = 50K and MP, = 50L . 1) If the wage rate is $10 per unit of labor and the rental rate of capital is $5 per unit of capital, how much capital and labor should the firm employ in the long run to minimize the cost of producing 40,000 units? 2) Using the solution in part 1), what will the firm's long-run total cost be?
Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the...
Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the firm has 256 units of capital. Find the Marginal Product of Labor (MPL). Fill in the appropriate numbers in the function below. MPL = ( ) L-0.5
A firm has the production function Q= 4LK. The marginal products are given by MPL =...
A firm has the production function Q= 4LK. The marginal products are given by MPL = 4K and MPK= 4L. Suppose that the prices of labour and capital are given by w and r. Solve for the quantities of L and K that minimize the cost of producing Q units of output. Provide an expression for the long run total cost function. What returns to scale are exhibited by this production function? What economies of scale are exhibited? Show the...
Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the...
Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the firm has 16 units of capital. Find the Marginal Product of Labor (MPL). Fill in the appropriate numbers in the function below. MPL = Answer ___ L-0.5 (Round to the nearest 2 decimal places if necessary.)
A firm uses capital and labor to produce output according to the production q = 4VLK...
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
Suppose that a firm had a production function given by: q=L025K0 75 The wage rate (...
Suppose that a firm had a production function given by: q=L025K0 75 The wage rate ( $10 and the rental rate (r) is $5 Calculate the amount of labor the firm would hire when it produces 400 units of output in a cost-minimizing way (Round to the nearest 2 decimal places if necessary.) Answer:
5. Suppose a firm has the production function Q = K1/2 L1/4 M1/4 The wage rate...
5. Suppose a firm has the production function Q = K1/2 L1/4 M1/4 The wage rate w = 16 , rental rate r = 2 , and the price of the materials m = 1. 1) Suppose in the short run, K is fixed at K *. What’s the solution to the firm’s short run cost-minimization problem? 2) What is the solution to the firm’s long run cost minimization problem given that the firm wants to produce Q units of...
Suppose that a firm had a production function given by q-21 K The rental rate for the fim is $10 and the wage is s5 Solve the optimization condition for K and then fill in the value that appears in front of L K- Round to the nearest 2 decimal places if necessary.) Suppose that a firm had a production function given by q-L025k075. The wage rate (w) is $10 and the rental rate () is $10 Calculate the amount...
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...
Suppose a firm has the production function Q = 50KL with MP, = 50K and MP, = 50L . 1) If the wage rate is $10 per unit of labor and the rental rate of capital is $5 per unit of capital, how much capital and labor should the firm employ in the long run to minimize the cost of producing 40,000 units? 2) Using the solution in part 1), what will the firm's long-run total cost be?
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
Suppose that a firm had a production function given by: q=L025K0 75 The wage rate ( $10 and the rental rate (r) is $5 Calculate the amount of labor the firm would hire when it produces 400 units of output in a cost-minimizing way (Round to the nearest 2 decimal places if necessary.) Answer:
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