Question

Suppose the mythical Tight Jeans Corporation leased a sewing machine, giving it the following production function:

Number of workers: 0 1 2 3 4 5 6 7 8

Quantity of Output: 0 20 46 64 72 78 81 80 77
(a) At what level of employment does the law of diminishing returns become apparent?
(b) Assume the wage per worker is $24, please compute the marginal cost of each additional pair from 78 to 81 pairs of jeans.

Answer 1

(a) At L = 1; Marginal product = Change in total product/Change in output = (20-0)/(1-0) = 20
At L = 2; Marginal product = Change in total product/Change in output = (46-20)/(2-1) = 26
At L = 3; Marginal product = Change in total product/Change in output = (64-46)/(3-2) = 18
So, MP starts diminishing from 3rd unit. Thus, law of diminishing returns become apparent from 3rd level of employment.

(b) Q = 78; Total cost = wage*labor = 24*(5) = 120
Q = 81; Total cost = wage*labor = 24*(6) = 144

So, Marginal cost = Change in Total cost/Change in output = (144-120)/(81-78) = 24/3 = $8

Marginal cost = $8

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