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Suppose that a firm's production function is: Its marginal product functions are: MPL = 5K0.5/L0.5 = 0.5q/L and q=10L 0.5K0.5 MPK = 5L0.5/K0.5 = 0.5q/K. The cost of a unit of labor, w, is $80 and the cost of a unit of capital, r, is $20. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 7 and 28, respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require 27.99 units of labor. (Enter your response rounded to two decimal places.) K If the marginal rate of technical substitution is find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is units. (Enter your responses as integers.)

Suppose that a firm's production function is: Its marginal product functions are: MPL = 5K0.5/L0.5 = 0.5q/L and q=10L 0.5K0.5 MPK = 5L0.5/K0.5 = 0.5q/K. The cost of a unit of labor, w, is $80 and the cost of a unit of capital, r, is $20. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 7 and 28, respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require 27.99 units of labor. (Enter your response rounded to two decimal places.) K If the marginal rate of technical substitution is find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is units. (Enter your responses as integers.)

Economics:
Economics:
10th Edition
ISBN:9781285859460
Author:BOYES, William
Publisher:BOYES, William
Chapter22: Supply: The Costs Of Doing Business
Section: Chapter Questions
Problem 11E
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Suppose that a firm's production function is: Its marginal product functions are: MP₁ = 5K05/L0.5 = 0.5q/L and 9= 10L 0.5 0.5 MPK = 5L0.5/K0.5 = 0.5q/K. The cost of a unit of labor, w, is $80 and the cost of a unit of capital, r, is $20. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 7 and 28, respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require 27.99 units of labor. (Enter your response rounded to two decimal places.) K If the marginal rate of technical substitution is find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is integers.) units. (Enter your responses as K, Units of capital 112 98- 84- 70- 56+ 42+ 28- 14- 0- 0 14 28 42 56 70 L, Units of labor 84 -q=280 q#140 98 112 Ⓡ
Transcribed Image Text:Suppose that a firm's production function is: Its marginal product functions are: MP₁ = 5K05/L0.5 = 0.5q/L and 9= 10L 0.5 0.5 MPK = 5L0.5/K0.5 = 0.5q/K. The cost of a unit of labor, w, is $80 and the cost of a unit of capital, r, is $20. Isoquants for output of 140 and 280 are illustrated in the figure to the right. Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 7 and 28, respectively. Suppose now that the firm wants to increase output to 280 units. If capital is fixed in the short run, how much labor will the firm require? The firm will now require 27.99 units of labor. (Enter your response rounded to two decimal places.) K If the marginal rate of technical substitution is find the optimal level of capital and labor required to produce the 280 units of output. The optimal level of capital is units and the optimal level of labor is integers.) units. (Enter your responses as K, Units of capital 112 98- 84- 70- 56+ 42+ 28- 14- 0- 0 14 28 42 56 70 L, Units of labor 84 -q=280 q#140 98 112 Ⓡ
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