Consider the following production function: Q=(K1/2+L1/2)2.
Consider the following production function: Q=(K1/2+L1/2)2. Find the cost (wL+rK) minimizing quantities of capital (K) and...
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 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 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?
Consider a production function of three inputs, labor, capital, and materials, given by Q= LKM. The marginal products associated with this production function are as follows: MPL = KM, MPk = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials. (a) Suppose that the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q....
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?
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 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...
1. Consider the following production function: Q = f(K, L) = (K^1/2) (L^1/2) a) Place capital on the vertical axis and labor on the horizontal axis. Determine the marginal rate of technical substitution. b) Suppose that the price of capital is $10, 000, and the price of labor is $10, 000. What is the ratio of capital to labor that allows the firm to produce any given quantity of output as cheaply as possible. c) Suppose that the price of...
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....
Derive the cost function associated with the production function in questions 2 is C(q) = 4 + 2q and in questions 3 is C=wL+rK=1*8+2*4=16. The cost function is of the general form C(Q) = xQ. What is the value of x? 2. The inverse market demand function is given by P()-20 q. Would consumers prefer to face a monopolist in this market with a cost function given by C(g)4+ 2q, or a perfectly competitive firm with a cost function given...
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...