A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = √LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $60 per worker-hour and the cost of capital is $15 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 10,000 plastic bins? Hint: The marginal products are MP₁ = = and MPK 2√√I = 2√√K
A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = √LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $60 per worker-hour and the cost of capital is $15 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 10,000 plastic bins? Hint: The marginal products are MP₁ = = and MPK 2√√I = 2√√K
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter7: Proudction Costs
Section: Chapter Questions
Problem 2SQ
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Transcribed Image Text:A firm produces plastic bins using labor (measured in man-hours) and capital (measured in
machine-hours), according to the production function Q = f(L,K) = √LK, where Q is the
number of plastic bins produced. Suppose that the cost of labor is $60 per worker-hour and the
cost of capital is $15 per machine-hour.
What is the cost minimizing input combination if the firm wants to produce 10,000 plastic
bins? Hint: The marginal products are MP₁ =
=
and MPK
2√√I
=
2√√K
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