Consider the following Cobb-Douglas production function: Y = 10L04K04. Suppose that the price of labor is w = 20 and the price of capital if r = 40. %| a- Derive the total cost curve for this production function. b- Derive the marginal cost curve for this production function. c- Plot the marginal and total cost curves for q = 1, 2, 3, 4, 5. What does it tell you about economies of scale for the production function?

Microeconomic Theory
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ISBN:9781337517942
Author:NICHOLSON
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Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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Consider the following Cobb-Douglas production function: Y = 10L04K04. Suppose that the
price of labor is w = 20 and the price of capital ifr = 40.
%3D
a- Derive the total cost curve for this production function.
b- Derive the marginal cost curve for this production function.
c- Plot the marginal and total cost curves for q = 1, 2, 3, 4, 5. What does it tell you
about economies of scale for the production function?
d- Suppose that the wage rate went up from 20 to 30. What would happen to the total
wage bill relative to total costs,
wL
? What would happen to total costs?
wL+rK
Transcribed Image Text:Consider the following Cobb-Douglas production function: Y = 10L04K04. Suppose that the price of labor is w = 20 and the price of capital ifr = 40. %3D a- Derive the total cost curve for this production function. b- Derive the marginal cost curve for this production function. c- Plot the marginal and total cost curves for q = 1, 2, 3, 4, 5. What does it tell you about economies of scale for the production function? d- Suppose that the wage rate went up from 20 to 30. What would happen to the total wage bill relative to total costs, wL ? What would happen to total costs? wL+rK
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