Suppose that a firm’s production function is q =L0.5K0.5. This means that the marginal rate of technical substitution is K/L.The cost of a unit of labour is $20 and the cost of a unit of capital is $80. The firm wants to produce 50 units of output. If both capital and labour are variable, how many units of labour (L) and how many units of capital (K) should be hired in the long run?   A. K = 25, L =100   B. K = 10, L = 100   C. K = 25, L =10   D. K = 7, L = 28

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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  1. Suppose that a firm’s production function is q =L0.5K0.5. This means that the marginal rate of technical substitution is K/L.The cost of a unit of labour is $20 and the cost of a unit of capital is $80. The firm wants to produce 50 units of output. If both capital and labour are variable, how many units of labour (L) and how many units of capital (K) should be hired in the long run?

      A.
    K = 25, L =100
      B.
    K = 10, L = 100
      C.
    K = 25, L =10
      D.
    K = 7, L = 28
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