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Givens: w*L+r* K min L20, K 20 s.t. • The marginal product of labor: MPL = .5 • The marginal product of capital: M PK = .5 * • Baseline Scenario: w = $10, r = $10 and go = 200 • New Scenario: w = $10, r = $2.50 and go = 200 Equation Description: A firm is attempting to minimize total cost subject to sufficiently employing units of labor and units of capital to produce an output level at least as large as a specified output quota. Total cost equals the cost to employing units of labor plus the cost to employing units of capital. A firm's production function is the product of two terms: the first term is units of capital raised to the .5 power; and, the second term is units of labor raised to the .5 power. The marginal product of labor equals the product of three terms: the first term is .5; the second term is units of capital raised to the .5 power; the third term is units of labor raised to the -5 power. The marginal product of capital equals the product of three terms: the first term is .5; the second term is units of labor raised to the .5 power; the third term is units of capital raised to the -5 power. As a baseline scenario: The wage rate is $10 per unit of labor; the rental rate is $10 per unit of capital; and, the output quota is 200 units. As a new scenario: The wage ate is $10 per unit of labor: the rental rate is $2.50 per unit of capital; and, the output quota is 200 units. Question: Comparing the baseline scenario to the new scenario, how are capital and labor related?

Givens: w*L+r* K min L20, K 20 s.t. • The marginal product of labor: MPL = .5 • The marginal product of capital: M PK = .5 * • Baseline Scenario: w = $10, r = $10 and go = 200 • New Scenario: w = $10, r = $2.50 and go = 200 Equation Description: A firm is attempting to minimize total cost subject to sufficiently employing units of labor and units of capital to produce an output level at least as large as a specified output quota. Total cost equals the cost to employing units of labor plus the cost to employing units of capital. A firm's production function is the product of two terms: the first term is units of capital raised to the .5 power; and, the second term is units of labor raised to the .5 power. The marginal product of labor equals the product of three terms: the first term is .5; the second term is units of capital raised to the .5 power; the third term is units of labor raised to the -5 power. The marginal product of capital equals the product of three terms: the first term is .5; the second term is units of labor raised to the .5 power; the third term is units of capital raised to the -5 power. As a baseline scenario: The wage rate is $10 per unit of labor; the rental rate is $10 per unit of capital; and, the output quota is 200 units. As a new scenario: The wage ate is $10 per unit of labor: the rental rate is $2.50 per unit of capital; and, the output quota is 200 units. Question: Comparing the baseline scenario to the new scenario, how are capital and labor related?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question 39 Givens: min w *L+r* K L> 0, K >0 % < K5 » L5 s.t. • The marginal product of labor: MPL = .5 * * • The marginal product of capital: MPK = .5 * • Baseline Scenario: w = $10, r = $10 and qo = 200 • New Scenario: w = $10, r = $2.50 and go = 200 Equation Description: A firm is attempting to minimize total cost subject to sufficiently employing units of labor and units of capital to produce an output level at least as large as a specified output quota. Total cost equals the cost to employing units of labor plus the cost to employing units of capital. A firm's production function is the product of two terms: the fırst term is units of capital raised to the .5 power; and, the second term is units of labor raised to the 5 power. The marginal product of labor equals the product of three terms: the first term is .5; the second term is units of capital raised to the .5 power; the third term is units of labor raised to the -.5 power. The marginal product of capital equals the product of three terms: the first term is .5; the second term is units of labor raised to the 5 power; the third term is units of capital raised to the -.5 power. As a baseline scenario: The wage rate is $10 per unit of labor; the rental rate is $10 per unit of capital; and, the output quota is 200 units. As a new scenario: The wage rate is $10 per unit of labor; the rental rate is $2.50 per unit of capital; and, the output quota is 200 units. Question: Comparing the baseline scenario to the new scenario, how are capital and labor related? O Capital and labor are substitutes in production. O Capital and labor are inferior. O Cannot be determined. O Capital and labor are unrelated O Capital and labor are complements in production.
Transcribed Image Text:Question 39 Givens: min w *L+r* K L> 0, K >0 % < K5 » L5 s.t. • The marginal product of labor: MPL = .5 * * • The marginal product of capital: MPK = .5 * • Baseline Scenario: w = $10, r = $10 and qo = 200 • New Scenario: w = $10, r = $2.50 and go = 200 Equation Description: A firm is attempting to minimize total cost subject to sufficiently employing units of labor and units of capital to produce an output level at least as large as a specified output quota. Total cost equals the cost to employing units of labor plus the cost to employing units of capital. A firm's production function is the product of two terms: the fırst term is units of capital raised to the .5 power; and, the second term is units of labor raised to the 5 power. The marginal product of labor equals the product of three terms: the first term is .5; the second term is units of capital raised to the .5 power; the third term is units of labor raised to the -.5 power. The marginal product of capital equals the product of three terms: the first term is .5; the second term is units of labor raised to the 5 power; the third term is units of capital raised to the -.5 power. As a baseline scenario: The wage rate is $10 per unit of labor; the rental rate is $10 per unit of capital; and, the output quota is 200 units. As a new scenario: The wage rate is $10 per unit of labor; the rental rate is $2.50 per unit of capital; and, the output quota is 200 units. Question: Comparing the baseline scenario to the new scenario, how are capital and labor related? O Capital and labor are substitutes in production. O Capital and labor are inferior. O Cannot be determined. O Capital and labor are unrelated O Capital and labor are complements in production.
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