Question

You are the owner of a small puzzle manufacturer that currently hires 10 employees. You operate in a very competitive industry, and the typical wage rate paid to employees in your industry is $500 per week per unit of labor. (You can assume that is the current equilibrium weekly wage rate.)The table below provides information about the weekly productivity of workers at your company.  

Labor (L)	Output per week (Q)
0	0
1	150
2	310
3	400
4	475
5	535
6	590
7	630
8	660
9	680
10	690

1. What is the marginal productivity associated with each unit of labor? Add your answers to a “Marginal Product of Labor” column and support your answer with a graph of the marginal product of labor. (4 points)
2. If you currently sell each puzzle for $10, what does your demand for labor look like? (Derive the value of marginal product and provide a graph that includes at least 3 points you would find on the demand curve for labor.) (3 points)
3. At the going wage rate ($500 per week), how many workers will you hire? Relate your answer to marginal analysis in making decisions. (2 points)
4. You’re considering offering a training program to your employees that is expected to double productivity. Explain and show graphically how you expect this to affect your demand for labor, the level of labor you will hire, and the level of output you will produce. Calculate explicitly how many workers you will now hire. (4 points)

Answer 1

1. The table would be as below.

L	Q	MPL
0	0	-
1	150	150
2	310	160
3	400	90
4	475	75
5	535	60
6	590	55
7	630	40
8	660	30
9	680	20
10	690	10

The MPL is calculated as . The graph is as below.

2. For the price be $10, the VMP is as below.

L	MPL	VMPL
0	-	-
1	150	1500
2	160	1600
3	90	900
4	75	750
5	60	600
6	55	550
7	40	400
8	30	300
9	20	200
10	10	100

The VMPL is calculated as . The demand for labor is where wage is equal to VMPL, provided the VMPL is not increasing with labor. The graph is as below.

Note that the the labor demand starts from L=2, since at L=1, the firm is facing increasing marginal returns, and the firm would employ at least that amount of labor after which the marginal product of labor is decreasing.

3. The firm would hire 6 workers. The reason being that, if the firm hires 7 workers, it's increase in revenue (the VMPL of $400) would be less than the wage (of $500) provided to the 7th worker, and as that means the cost exceeds the revenue, the firm would reduce the level of employment. If the firm hires 5 workers, it would have an incentive of employing another worker since another worker would still increase their revenue by (the VMP of $550) more than the cost paid (wage of $500). Hence, the firm would employ 6 workers.

Also, the firm would hence produce 59 units.

4. The table would be as below.

L	Q	MPL	VMPL
0	0	-	-
1	300	300	3000
2	620	320	3200
3	800	180	1800
4	950	150	1500
5	1070	120	1200
6	1180	110	1100
7	1260	80	800
8	1320	60	600
9	1360	40	400
10	1380	20	200

The increase in productivity would result in doubling of output and hence the doubling of MPL. The VMP would also be doubled.

The labor demand schedule would be as below.

The labor hired in this case would be 8. Again, the firm would not hire 9 workers since the cost (wage) exceeds the revenue increased (VMP of $400), and the firm would not hire 7 workers since firm can employ one more worker and still earn more (by VMP of $600) than it pays (the wage of $500). The firm would now produce 1320 units when L=8.