Question

Table 18-12

The table displays data for a small, competitive, profit-maximizing firm that produces and sells envelopes. The time frame is one week.

Labor L	Marginal Product of Labor MPL	Wage W
0 workers
	134 boxes of envelopes	$600
1
	106	$600
2
	92	​$600
3
	84	$600
4
	78	$600
5

Refer to Table 18-12. Suppose the firm sells each box of envelopes that it produces for $7. Suppose also that the firm’s fixed costs amount to $400. How many workers should the firm hire in order to maximize profit, and what is the maximum profit?

a. The firm should hire 2 workers; its maximum profit is $80.

b. The firm should hire 2 workers; its maximum profit is $96.

c. The firm should hire 3 workers; its maximum profit is $96.

d. The firm should hire 3 workers; its maximum profit is $124.

Answer 1

In order to maximize profit a firm hires that amount of labor such that MRP = Wage rate and if there is no such amount of Labor at which MRP = wage then it will hire till MRP > wage rate

where MRP = Marginal Revenue Product = P*MPL , P = price of output = 7 and wage = 600.

We can see from above that when L = 3, MRP = P*MPL = 7*92 = 644 which is greater than wage rate( = 600). Hence he should hire 3rd worker

Also When L = 4, then MRP = P*MPL = 7*84 = 588 which is lesser than wage rate and hence he should not hire 4th worker.

Hence, he should hire 3 workers in order to maximize profit.

Profit = Price*Quantity - (wage*number of workers + Fixed Cost)

Quantity = Quantity of output = MPL for first 3 workers = 134 + 106 + 92 = 332

Hence, Profit = 7*332 - (600*3 + 400) = $124

Hence, the correct answer is (d) The firm should hire 3 workers; its maximum profit is $124.