Suppose that capital and labor are prefect substitutes in a one-to-two ratio such that: Q =...
Suppose that capital and labor are prefect substitutes in a one-to-two ratio such that: Q = 2K + L. Currently, the wage rate is w=5 and the rental rate is r=8.
a) What is the minimum cost and method of producing Q=20 units of output?
b) Suppose that the price of capital increases to r=12. If we keep the total cost the same as in part (a), what level of output can now be produced and what method of production (input mix) is used?
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Suppose that capital and labor are prefect substitutes in a
one-to-two ratio such that: Q =...
Suppose the firm's production function is Q = K1/3L2/3. a. If the rental rate of capital...
Suppose the firm's production function is Q = K1/3L2/3. a. If the rental rate of capital R = $30 and the wage rate W = $40, what is the cost-minimizing capital-to-labor ratio? b. If the rental rate of capital R is $35 and the wage rate W is $70, and assuming the same production function, how many units of labor and capital should the firm use to produce 12 units of output? c. What is the total cost of producing...
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...
A firm produces output according to the production function: Q = F(K,L) = 2K + 2L....
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9. A firm produces output according to a production function Q = F(K,L) min [2K,4L]. a....
9. A firm produces output according to a production function Q = F(K,L) min [2K,4L]. a. How much output is produced when K-2 and L = 3? b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 4 units of output? How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on...
#6 6. A manufacturer uses labor and capital to produce widgets. Labor and capital are perfect...
#6
6. A manufacturer uses labor and capital to produce widgets. Labor and capital are perfect substitutes and the production function is Q-2K+IL a. Derive and graph the isoquants for Q-20 and 0-40 units of output (not all units of K will be whole numbers) (20 - 2K+ILK -10-0.5L.) 0-20 LK 040 LK 10 b. Suppose the price of labor is w 51 and the price of capital is for a total cost of $10 and $15. 51. Graph the...
A firm wishes to produce Q = 150 as cheaply as possible using only labor (L)...
A firm wishes to produce Q = 150 as cheaply as possible using only labor (L) and capital (K) with a relationship explained by the following production technology: Q = 15L + 25K. The prevailing market wage is $w/hr. You will need to work carefully to determine the wage rate but know that the rental rate of capital, r = 50. 1. Find w so that the firm can optimally employ 5 workers and 3 units of capital to produce...
Priyanka's company has the production function Q=100K^0.5L^0.5, where Q measures output, K measures machine hours, and...
Priyanka's company has the production function Q=100K^0.5L^0.5, where Q measures output, K measures machine hours, and L measures labor hours. Suppose that the rental rate of capital is R=$30, the wage rate is W=$15, and the firm wants to produce 5,000units of output. Use the Lagrange method to find the optimal input mix. What the optimal level of K & L?
Aamir's company has the production function Q=8K^0.75L^0.25, where Q measures output, K measures machine hours, and...
Aamir's company has the production function Q=8K^0.75L^0.25, where Q measures output, K measures machine hours, and L measures labor hours. Suppose that the rental rate of capital is R=$120, the wage rate is W=$20, and the firm wants to produce 800 units of output. Use the Lagrange method to find the optimal input mix. What the optimal level of K?
A cost minimizing firm’s production function is Q=2KL. The price of labor, w, is currently $4,...
A cost minimizing firm’s production function is Q=2KL. The price of labor, w, is currently $4, and the price of capital, r, is currently $1. At the firm’s current level of output, it has total costs of $160. Input prices change such that the wage rate is now 8 times the rental rate. The firm adjusts its input combination, but leaves total output unchanged. Answer the questions below as you solve for the cost - minimizing input combination after the...
Tiffany's company has the production function Q=2K^0.5L^0.5, where Q measures output, K measures machine hours, and...
Tiffany's company has the production function Q=2K^0.5L^0.5,
where Q measures output, K measures machine hours, and L measures
labor hours. Let the wage rate be W, and suppose that the rental
rate of capital is R=$20 and the firm wants to produce 400 units of
output. Use the Lagrange method to find the demand curve for labor
as a function of the wage rate. Your answer will have L on the left
hand side of the equation. On the right...
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...
9. A firm produces output according to a production function Q = F(K,L) min [2K,4L]. a. How much output is produced when K-2 and L = 3? b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 4 units of output? How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on...
#6
6. A manufacturer uses labor and capital to produce widgets. Labor and capital are perfect substitutes and the production function is Q-2K+IL a. Derive and graph the isoquants for Q-20 and 0-40 units of output (not all units of K will be whole numbers) (20 - 2K+ILK -10-0.5L.) 0-20 LK 040 LK 10 b. Suppose the price of labor is w 51 and the price of capital is for a total cost of $10 and $15. 51. Graph the...
Tiffany's company has the production function Q=2K^0.5L^0.5,
where Q measures output, K measures machine hours, and L measures
labor hours. Let the wage rate be W, and suppose that the rental
rate of capital is R=$20 and the firm wants to produce 400 units of
output. Use the Lagrange method to find the demand curve for labor
as a function of the wage rate. Your answer will have L on the left
hand side of the equation. On the right...
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