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The production function is given by f (L) = 6L^2/3 . Suppose that the cost per...

  1. The production function is given by f (L) = 6L^2/3 . Suppose that the cost per unit of labour is $16 and the price of output is $12. How many units of labour will the firm hire?
  1. 54
  2. 27
  3. 13.50
  4. 81
  5. 9
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Answer #1

Ans. b. 27

the production function, f (L) = 6 L2/3  

  df(L) – 4L-1/3 d

MPL = 4 L- 1/3

the cost per unit of labor, W = $16

the price of output, P = $12

then The optimum labor usage level of the profit-maximizing firm where

MRP = W [ MRP = Marginal revenue product ]

MPL x P = W [ MRP = MPL x P ]

4 L-1/3  x $12  = $16

  $48/ L1/3 = $16

$48/ $16 = L1/3

3 = L1/3

apply cube both side, we have

27 = L

L = 27

Hence, the firm will hire 27 units of labour.

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