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Question-2 (Cost Minimization) A firm uses labor and machines to produce output according to the production function f(L, M) = 4L1/2 M¹/2, where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10. 1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $100 and another isocost line showing combinations that cost $200. 2. Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker. (Hint: The firm will produce at a point where the slope of the production isoquant equals the slope of the isocost line.) 3. Sketch the production isoquant corresponding to an output of 10. 1. Calculate the cost of producing 10 units at these factor prices: c(40; 10; 40)

Question-2 (Cost Minimization) A firm uses labor and machines to produce output according to the production function f(L, M) = 4L1/2 M¹/2, where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10. 1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $100 and another isocost line showing combinations that cost $200. 2. Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker. (Hint: The firm will produce at a point where the slope of the production isoquant equals the slope of the isocost line.) 3. Sketch the production isoquant corresponding to an output of 10. 1. Calculate the cost of producing 10 units at these factor prices: c(40; 10; 40)

ECON MICRO
ECON MICRO
5th Edition
ISBN:9781337000536
Author:William A. McEachern
Publisher:William A. McEachern
Chapter7: Production And Cost In The Firm
Section: Chapter Questions
Problem 3.7P
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Question-2 (Cost Minimization) A firm uses labor and machines to produce output according to the production function f(L, M) = 4L¹² M¹/², where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10. 1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. 2. Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker. (Hint: The firm will produce at a point where the slope of the production isoquant equals the slope of the isocost line.) 3. Sketch the production isoquant corresponding to an output of 10. 1. Calculate the cost of producing 10 units at these factor prices: c(40; 10; 40)
Transcribed Image Text:Question-2 (Cost Minimization) A firm uses labor and machines to produce output according to the production function f(L, M) = 4L¹² M¹/², where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10. 1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400 and another isocost line showing combinations that cost $200. 2. Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker. (Hint: The firm will produce at a point where the slope of the production isoquant equals the slope of the isocost line.) 3. Sketch the production isoquant corresponding to an output of 10. 1. Calculate the cost of producing 10 units at these factor prices: c(40; 10; 40)
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