You are an efficiency expert hired by a firm that uses machines (K) and workers

Question

You are an efficiency expert hired by a firm that uses machines (K) and workers (L) as inputs. The firm has estimated that the marginal product of labor is MPL = A – 6 L, while the marginal product of capital is MPK = B – 3 K, and the volume of output produced is Q = 1500. The firm is currently using 16 units of L and 7 units of K, and has flexibility to substitute capital for labor and vice versa. The input prices are w = $30, r = $20:

a) If A = 246 and B = 91 the firm is minimizing the cost of producing the given quantity of output.

b) If A = 200 and B = 150, then the firm should use less L and more K to minimize the cost of producing the given quantity of output

c) the firm should use less K and more L to minimize the cost of producing the given quantity of output for any values of A and B

d) None of the above

Explanation / Answer

d) None of the above

Firm will minimize cost , when

MPL/MPK = W/r

(A- 6L)/(B - 3K) = 30/20

(A- 6*16)/(B - 3*7) = 3/2

(A - 96)/(B - 21) = 3/2

Putting A = 246 , and B = 91

  (246 - 96)/(91 - 21) = 3/2

150/70 not = 3/2

Now, putting A = 200, and B = 150

(200 - 96)/(150 - 21) = 3/2

104/129 Not = 3/2

If you don't understand anything then comment, I'ill revert back on the same. :)

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