Homework Answers
From the production function we have
MRTS = MPL/MPK
= 100 * 0.8 L^-0.2 K^0.4 / 100 x 0.4 L^0.8 K^-0.6
= 2K/L
Wage rental ratio is 5/5 = 1
At the optimum choice of labor and capital MRTS = w/r
2K/L = 1
2K = L
Hence labor units are 2*100 = 200
Labor input = 200 units.
Add Answer to:
Consider the following production function: 9 = 100L0.860.4. Currently the wage rate (w) is $5.00 and...
AUS electronics manufacturer is considering moving its production abroad. Suppose its production function is q=L0604 In...
AUS electronics manufacturer is considering moving its production abroad. Suppose its production function is q=L0604 In the United States, w = $6 and 4 In Mexico, the wage is 10% lower than in the United States but the firm faces the same cost of capital w = 55.40 and r = 4 What are Land K and what is the cost of producing 100 units in both countries? (for all of the following questions, enter a numeric response using a...
1. Consider the following production functions. In each case determine if: • the function is Cobb...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
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...
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...
4. Consider a production process where capital and labor are perfect complements – two units of...
4. Consider a production process where capital and labor are perfect complements – two units of capital are required for each unit of labor to produce four units of output. 1) Derive the production function for this production process. 2) If the wage rate is $5 per unit of labor and the rental rate of capital is $8 per unit of capital, how much capital and labor should the firm employ to minimize the cost of producing 100 units? 3)...
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...
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...
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?
1. Consider the following production function: Y = A min{2N, K} (1) where A measures productivity,...
1. Consider the following production function: Y = A min{2N, K} (1) where A measures productivity, N is labor employed by the firm, and K is capital. The firm chooses labor and capital, taking productivity as given. Labor can be purchased at a constant wage, W, and capital at a constant rate, R. (a) Derive the cost function C = C(W,R,Y) for the firm. (b) Show that costs decrease in productivity, A. (c) Consider two companies with cost functions Yị...
Assume the wage rate is w=$2, and the rental rate of capital is r=$7. The marginal...
Assume the wage rate is w=$2, and the rental rate of capital is r=$7. The marginal product of labor is MPL=30, and the marginal product of capital is MPK=90. If the firm wishes to minimize its production costs, and continue to produce the same level of output, it should: a) increase capital, reduce labor b) increase labor, reduce capital c) do nothing d) increase both capital and labor
AUS electronics manufacturer is considering moving its production abroad. Suppose its production function is q=L0604 In the United States, w = $6 and 4 In Mexico, the wage is 10% lower than in the United States but the firm faces the same cost of capital w = 55.40 and r = 4 What are Land K and what is the cost of producing 100 units in both countries? (for all of the following questions, enter a numeric response using a...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
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...
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...
1. Consider the following production function: Y = A min{2N, K} (1) where A measures productivity, N is labor employed by the firm, and K is capital. The firm chooses labor and capital, taking productivity as given. Labor can be purchased at a constant wage, W, and capital at a constant rate, R. (a) Derive the cost function C = C(W,R,Y) for the firm. (b) Show that costs decrease in productivity, A. (c) Consider two companies with cost functions Yị...
Most questions answered within 3 hours.
-
You have been asked to develop a new line of organic skincare
products. Spend time with...
asked 40 minutes ago -
Summerdahl Resort's common stock is currently trading at $37 a
share. The stock is expected to...
asked 1 hour ago -
To an economist, the field of industrial organization answers
which of the following questions?
asked 1 hour ago -
How could meeting industry expectations, propel managers into
challenging and possible conflict of interest situations? How...
asked 1 hour ago -
You have been married to your spouse for 10 years. You have two
small children (ages...
asked 3 hours ago -
Spiderman makes a leap from one building to
another. He starts on one building that is...
asked 3 hours ago -
A
symbol is something that stands for something else. What are the
symbols in education?what are...
asked 3 hours ago -
The charge to the left in the figure above has a
magnitude of 2.90 nC, and...
asked 5 hours ago -
Verify the MIRR is 9.29% given cash flows in years 1 and 2 of
$1,000 each,...
asked 5 hours ago -
Calculate the pH of a 5.7 M solution of aniline (C6H5NH2; Kb =
3.8 x 10^-10)
asked 7 hours ago -
LSL R3, R3, R12
Memory
Address
Orig.
Data
Updated
Data
Register
Orig.
Data
Updated
Data
0x84F0...
asked 7 hours ago -
Air at 100 kPa and density of 1.2 kg/m3 flows upward through a
5-cm diameter inclined...
asked 8 hours ago