Question

The table below shows the weekly relationship between output and number of workers for a factory with a fixed size of plant.Number of Workers Output001502110330044505590666577008725971010705a. Calculate the marginal product of labor. b. At what point do diminishing returns set in? Explain. c. Based on the table above, if the wage rate is $500.00 and the price of output is $5, how many workers should the firm hire?

Answer 1

a) The marginal product of labor calculates the extra output generated by employing an additional unit of labor.

Marginal Product of Labor = (Change in Output) / (Change in Labor)

1st labor
(50 - 0) / (1 - 0) = 50
2nd labor
(110 - 50) / (2 - 1) = 60

Labor	Output	MPL
0	0
1	50	50
2	110	60
3	300	190
4	450	150
5	590	140
6	665	75
7	700	35
8	725	25
9	710	-15
10	705	-5

b) The marginal product of labor is rising initially but after one point it can be observed that the marginal output is actually decreasing. This is called as the 'law of diminishing returns'.

We can see that the output is rising with each additional labor up to labor 3 but after that it has fallen from 190 to 150 for the 4th labor.

c) The wage rate is $500 which means every additional labor costs $500.
The price of output is $5 which means marginal revenue is $5.

500 / 5 = 100

The firm will keep employing labor until marginal product of labor of an addition worker reaches to 100.
It will not be economical if the MPL is below 100 to hire an additional labor.

Labor	Output	MPL	MPL * Price	Profit
0	0			0
1	50	50	250	-250
2	110	60	300	-450
3	300	190	950	0
4	450	150	750	250
5	590	140	700	450
6	665	75	375	325
7	700	35	175	0
8	725	25	125	-375
9	710	-15	-75	-950
10	705	-5	-25	-1475

The firm will hire maximum 5 labors as MPL is above 100 up to that point.