Ms. Smith, the owner and manager of the Clear Duplicating Service located near a

Question

Ms. Smith, the owner and manager of the Clear Duplicating Service located near a major university, is contemplating keeping her shop open after 4 p.m. and until midnight. In order to do so, she would have to hire additional workers. She estimates that the additional workers would generate the following total output (where each unit of output refers to 100 pages duplicated). If the price of each unit of output is $10 and each worker hired must be paid $40 per day, how many workers should Ms. Smith hire?
Workers hired 0 1 2 3 4 5 6
Total product 0 12 22 30 36 40 42

Explanation / Answer

We know that at optimal level of worker hiring, the marginal revenue product by labor equals the wage rate. That is we have to find the level of workers where MRP = wage rate.

Wage is given as $40.

Marginal Revenue Product can be calculated by using the following formula:

MRP = Change in TR / Change in L

where MRP = Marginal Revenue Product; TR = Total revenue = Output*price and L = number of workers/labors.

Consider the following table in which MRP at each level is calculated:

We find out that at level of 5 labors MRP equals 40 which is also equal to wage rate. Thus optimal level of labor is 5 labor.

L TP TR MPR 0 0 0 0 1 12 120 120 2 22 220 100 3 30 300 80 4 36 360 60 5 40 400 40 6 42 420 20

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