Givens: min w + L+r*K L20, K 20 s.t. 9o SK L5 • The marginal product of labor: MPL = .5 %3D • The marginal product of capital: MPK = .5 %3D • Baseline Scenario: w $10, r = $10 and qo = 200 %3D • New Scenario: w = $10, r $2.50 and qo 200 %3D 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 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: How has the new scenario changed the isocost line, if at all?
Givens: min w + L+r*K L20, K 20 s.t. 9o SK L5 • The marginal product of labor: MPL = .5 %3D • The marginal product of capital: MPK = .5 %3D • Baseline Scenario: w $10, r = $10 and qo = 200 %3D • New Scenario: w = $10, r $2.50 and qo 200 %3D 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 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: How has the new scenario changed the isocost line, if at all?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
4
Transcribed Image Text:TIA
Givens:
min
w * L+r * K
L20, K >0
s.t.
• The marginal product of labor: MPL = .5 *
%3D
• The marginal product of capital: MPK = .5*
K
• Baseline Scenario: w = $10, r = $10 and qo = 200
• New Scenario: w = $10, r $2.50 and qo = 200
%3D
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 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: How has the new scenario changed the isocost line, if at all?
Transcribed Image Text:The new event caused the isocost line to rotate, altering the slope of the isocost line and facilitating a new input
bundle that will reduce cost.
The new event caused the isocost line to shift in a parallel manner, facilitating a new input bundle that will
increase cost.
The new event caused the isocost line to shift in a parallel manner, facilitating a new input bundle that will reduce
cost.
The new event caused the isocost line to rotate, altering the slope of the isocost line and facilitating a new input
bundle that will increase cost.
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