Question

Refer to the table below: Output Labor pt w 47 83 8 122 131 138 10 p* - market price of output w- market equilibrium wage Assuming that the firm is a profit-maximizing economic agent, what is the optimalamountolaborL,that it would hire?

Answer 1

In this case, we know that a profit maximizing agent would hire as long as marginal revenue product of labor (MRPL) is higher than or equal to its marginal cost i.e. wage rate.

So, first we calculate Marginal product of labor (MPL) and get Marginal Revenue Product of Labor by multiplying MPL with p*. We get the following schedule.

Q	Labor, L	MPL=Change in Q/Change in L	p*	MRPL=P*MPL	w
0	0		5		60
11	1	11	5	55	60
27	2	16	5	80	60
47	3	20	5	100	60
66	4	19	5	95	60
83	5	17	5	85	60
98	6	15	5	75	60
111	7	13	5	65	60
122	8	11	5	55	60
131	9	9	5	45	60
138	10	7	5	35	60

We observe that MRPL is higher than wage rate till L=7. After that MRPL<Wage rate.

So, a profit maximizing agent would hire 7 labor for profit maximization in this scenario.