Givens: w * L+r+K min L>0, K > 0 s.t. %

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Question 40
Givens:
min
w * L+r * K
L>0, K >0
s.t.
• The marginal product of labor: MPL = .5 * *
• The marginal product of capital: MPK = .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 tem 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 did the new event affect total cost?
O Cannot be determined.
O Total cost remained unchanged.
O Total cost decreased.
O Total cost increased.
Transcribed Image Text:Question 40 Givens: min w * L+r * K L>0, K >0 s.t. • The marginal product of labor: MPL = .5 * * • The marginal product of capital: MPK = .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 tem 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 did the new event affect total cost? O Cannot be determined. O Total cost remained unchanged. O Total cost decreased. O Total cost increased.
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