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Chapter 8: Costs R2.1) A firm produces according to Q = RL, with MP, = and...
A firm applies a production technology to produce units of output (q) according to the production...
A firm applies a production technology to produce units of output (q) according to the production function q = 20 x L^.5 x K^.5 , where L is a variable input and K is a fixed input. Assume K = 100 in the short run. solve for the short-run average product of labor (AP L) and the marginal product of labor (MP L) functions. If L = 100, what are the numerical values of AP L and MP L?
1. An engineering firm has estimated the production function for your firm to be Q =...
1. An engineering firm has estimated the production function for your firm to be Q = VKL. This production function has marginal products given by MP = 0.5 MPx = 0.55 resulting in MRTS = K/L. The price of capital is r and the price of labor is w. In the short run, capital is fixed at K = 36 a. Find the short run production function. b. Find the short run cost function. c. Ifr = 100 and w...
Consider a firm which produces according to the following production function just by using labor
Consider a firm which produces according to the following production function just by using labor f(L) = 4L^1/2 + k (a) Derive the short-run total cost, the short-run average cost, the shortrun marginal cost function of the firm under the assumption that capital is the fixed input. (b) Find short-run firm supply as a function of input prices, w and r, and output price, p.
Problem 1 Your firm produces output of some generic manufactured good Q according to the following...
Problem 1 Your firm produces output of some generic manufactured good Q according to the following production function: Q(L,K) = 2L1/451/2 Assume the wage paid to labor is $10, the rental rate of capital is $40, and the price of your product is $200. (a) What is the technical rate of substitution for this production function? (b) Suppose you have 80 units of capital in the short run. Find the profit maximizing amount of labor you should employ. (c) Find...
1. Suppose a firm is producing output according to Q=1001KL. A. Draw a sketch of this...
1. Suppose a firm is producing output according to Q=1001KL. A. Draw a sketch of this firm's isoquant map B. What equation do you use to find a cost-minimizing combination of inputs for a certain output level Q.? K C. The marginal products of labor and capital are given by MP, = 50, and L MPK = 50, L respectively. The price of labor is $5 per unit, and the price of K capital is $20 per unit. What is...
1. Consider a firm which produces according to the following production function by using labor and...
1. Consider a firm which produces according to the following production function by using labor and capital: f(1,k) = klid (e) Suppose the wage rate of labor is 2 TL, the rental rate of capital is 2 TL and fixed capital input, k, is 2 units. What amount of output minimizes short-run average cost? What is the minimum possible short-run average cost? (f) Find short-run firm supply as a function of input prices, w and v, and output price, p....
Costs — End of Chapter Problem Peter's Pipers produces plumbing pipe. The long-run total cost of...
Costs — End of Chapter Problem Peter's Pipers produces plumbing pipe. The long-run total cost of Peter's pipes is LTC = 20,000Q – 200Q2 +Q3 where Q is measured as thousands of feet of piping. The long-run marginal cost of Peter's pipes is LMC = 20,000 – 400Q +3Q? a. Divide total cost by Q to obtain Peter's long-run average cost of producing pipe. Average cost = $ b. Exploit the relationship between LMC and LAC to find the quantity...
Practice Problem 1 (continued from Chapter 21) A firm produces computers with two factors of production:...
Practice Problem 1 (continued from Chapter 21) A firm produces computers with two factors of production: labor(I) and capital (k). Its technology is represented by the production function -0.1lk Suppose that the prices of the inputs are 10 and 100 dollars, respectively. What is the firm's long run supply curve? Suppose further that the amount of capital is fixed at 1 unit. What is the firm's short run supply curve? (b)
NEED ANSWERS OF PART (f,g,h,j) Problem 2 [21 marks] Consider a firm that uses two inputs. The quantity used of input 1...
NEED ANSWERS OF PART (f,g,h,j)
Problem 2 [21 marks] Consider a firm that uses two inputs. The quantity used of input 1 is denoted by x, and the quantity used of input 2 is denoted by x2. The firm produces and sells one good using the production function f(x1, x2)-4x053x25. The final good is sold at price P $10. The prices of inputs 1 and 2 are w$2 and w2 $3, respectively. The markets for the final good and both...
8.13. A firm produces a product with labor and capital. Its production function is described by...
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. Let w= 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q when the prices labor and capital are w = 1 and...
1. An engineering firm has estimated the production function for your firm to be Q = VKL. This production function has marginal products given by MP = 0.5 MPx = 0.55 resulting in MRTS = K/L. The price of capital is r and the price of labor is w. In the short run, capital is fixed at K = 36 a. Find the short run production function. b. Find the short run cost function. c. Ifr = 100 and w...
Problem 1 Your firm produces output of some generic manufactured good Q according to the following production function: Q(L,K) = 2L1/451/2 Assume the wage paid to labor is $10, the rental rate of capital is $40, and the price of your product is $200. (a) What is the technical rate of substitution for this production function? (b) Suppose you have 80 units of capital in the short run. Find the profit maximizing amount of labor you should employ. (c) Find...
1. Suppose a firm is producing output according to Q=1001KL. A. Draw a sketch of this firm's isoquant map B. What equation do you use to find a cost-minimizing combination of inputs for a certain output level Q.? K C. The marginal products of labor and capital are given by MP, = 50, and L MPK = 50, L respectively. The price of labor is $5 per unit, and the price of K capital is $20 per unit. What is...
1. Consider a firm which produces according to the following production function by using labor and capital: f(1,k) = klid (e) Suppose the wage rate of labor is 2 TL, the rental rate of capital is 2 TL and fixed capital input, k, is 2 units. What amount of output minimizes short-run average cost? What is the minimum possible short-run average cost? (f) Find short-run firm supply as a function of input prices, w and v, and output price, p....
Costs — End of Chapter Problem Peter's Pipers produces plumbing pipe. The long-run total cost of Peter's pipes is LTC = 20,000Q – 200Q2 +Q3 where Q is measured as thousands of feet of piping. The long-run marginal cost of Peter's pipes is LMC = 20,000 – 400Q +3Q? a. Divide total cost by Q to obtain Peter's long-run average cost of producing pipe. Average cost = $ b. Exploit the relationship between LMC and LAC to find the quantity...
Practice Problem 1 (continued from Chapter 21) A firm produces computers with two factors of production: labor(I) and capital (k). Its technology is represented by the production function -0.1lk Suppose that the prices of the inputs are 10 and 100 dollars, respectively. What is the firm's long run supply curve? Suppose further that the amount of capital is fixed at 1 unit. What is the firm's short run supply curve? (b)
NEED ANSWERS OF PART (f,g,h,j)
Problem 2 [21 marks] Consider a firm that uses two inputs. The quantity used of input 1 is denoted by x, and the quantity used of input 2 is denoted by x2. The firm produces and sells one good using the production function f(x1, x2)-4x053x25. The final good is sold at price P $10. The prices of inputs 1 and 2 are w$2 and w2 $3, respectively. The markets for the final good and both...
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. Let w= 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q when the prices labor and capital are w = 1 and...
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