Suppose a firm has a production function given by Q = L1/2 K1/2. Therefore, MPL = K1/2 / 2L1/2 and MPK = L1/2 / 2K1/2 Th...

Question

Question

Suppose a firm has a production function given by Q = L^1/2 K^1/2.

Therefore,

MP_L = K^1/2 / 2L^1/2 and MP_K = L^1/2 / 2K^1/2

The firm can purchase labor, L at a price w = 36, and capital, K at a price of r = 9.

a) What is the firm’s Total Cost function, TC(Q)?

b) What is the firm’s marginal cost of production?

Answer 1

Answer #1

Answer Ca) Minimize TC w trk = 36L +9K Subjcct to hegrange is gives ey L 3L t 9k+ A(Q-L K Fivst Order Conditine K. 36 = 2) O

Answer 2

Similar Homework Help Questions

Suppose a firm has a production function given by Q = [1/2K1/2. Therefore, 8-1/2 21/2 MP=...

Suppose a firm has a production function given by Q = [1/2K1/2. Therefore, 8-1/2 21/2 MP= -1/2 and MPx=- 28-1/2 The firm can purchase labor, L at a price w = 36, and capital, K at a price of r = 9. a) What is the firm's Total Cost function, TC(Q)? b) What is the firm's marginal cost of production?
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor...

Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = ½ L-1/2K1/2and MPK = ½ L1/2K-1/2 a) Suppose the price of labor is w = 18, and the price of capital is r = 2. Derive the firm’s total cost function. b) What is the firm’s marginal cost? c) For this problem, you will sketch the graph of the firm’s isoquant for Q...
Suppose a good is produced according to the following production function: Q = L1/2K1/2 so...

Suppose a good is produced according to the following production function: Q = L1/2K1/2 so that the marginal product of labor and capital are MPL = (1/2)(K/L)1/2 MPK = (1/2)(L/K)1/2 If w = $8 and r = $4, determine the necessary conditions for the input choices, K and E to be cost-minimizing. In other words, what is the cost-minimizing ratio of K to E for this firm? Your answer will be in the form of 2L: 5K. You...

Consider a firm that faces the following production function: q = f(L, K) = L1/2 K1/2...

Consider a firm that faces the following production function: q = f(L, K) = L1/2 K1/2 where q is output, L is labor, and K is capital. Use this production function to answer the following questions. (a) What is the marginal product of labor (MPL)? (b) Does the MPL follow the law of diminishing returns? How do you know? (c) What is the marginal product of capital (MPK)? (d) Does the MPK follow the law of diminishing returns? How do...
Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and...

Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and that K is fixed at K = 36. If the price of Labor, w = $12 per unit of Labor, what is the firm’s Marginal Cost of production when the firm is producing 48 units of output? MC = ________________________
Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and...

Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and that K is fixed at K = 49. If the price of Labor, w = $6 per unit of Labor, what is the firm’s Marginal Cost of production when the firm is producing 28 units of output?

Assume that a firm’s production function Q = K1/2L1/2. a. Assume that the firm currently employs...

Assume that a firm’s production function Q = K1/2L1/2. a. Assume that the firm currently employs 200 units of capital and 100 units of labor. Determine the Average Product of Capital, Average Product of Labor, Marginal Product of Capital, and Marginal Product of Labor.
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...
A firm has the production function F(L, K) = L1/2 + K1/2. The price of labor...

A firm has the production function F(L, K) = L1/2 + K1/2. The price of labor is $30 and the price of capital is $10. The firm has a production goal of 100 units of output. a) Carefully write out this firm’s cost minimization problem, using the particulars of this problem. b) Give two equations—particular to this problem—that the solution satisfies. c) Solve for the firm’s optimal input bundle. d) Determine the firm’s cost of producing 100 units of output....

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...