Problem:

Suppose a firm's short-run total product schedule is given in the table below. It sells its output in a competitive market for $1.50 each.

1. What is the marginal product of the first worker?
2. What is the marginal revenue product of the first worker?
3. Suppose the wage is $7. How many workers will this firm hire?
4. If the wage rises to $9, how will the firm adjust its employment?
5. Alternatively, suppose the firm sells its output according to the following demand schedule:

   Labor	Total Product	Product Price	Total Revenue	Marginal Revenue Product
   0	0	----
   1	8	$3.50
   2	18	2.80
   3	29	2.30
   4	39	1.90
   5	47	1.65
   6	52	1.50
   7	53	1.40

   Fill in the remaining two columns of the table. How many workers will be hired at a wage of $7?

Answer:

1. Marginal product is the addition to total output associated with the next worker. Total output rises from 0 to 8 with the addition of the first worker, so the marginal product is 8.
2. Marginal revenue product is the increase in total revenue associated with the next worker. For a competitive firm, this is product price times marginal product. The marginal revenue product of the first worker is $1.50 x 8 = $12.
3. To determine the profit-maximizing level of employment, it is necessary to find marginal revenue product and compare it to the wage rate. The completed table is below:

   Labor	Total Product	Marginal Product	Marginal Revenue Product
   0	0
   1	8	8	$12.00
   2	18	10	15.00
   3	29	11	16.50
   4	39	10	15.00
   5	47	8	12.00
   6	52	5	7.50
   7	53	1	1.50
   8	53	0	0.00

   Maximum profits are obtained by hiring only those workers whose marginal revenue products exceed the wage. In this example, 6 workers are hired.
4. The 6^th worker is no longer profitable. Reducing employment by 1 worker would save $9 in wages and "costs" the firm only $7.50 in lost revenue. Maximum profits are obtained with 5 workers.
5. The completed table is shown below: Total revenue is product price times total product and marginal revenue product is the change in total revenue from hiring an additional worker.

   Labor	Total Product	Product Price	Total Revenue	Marginal Revenue Product
   0	0	----	----	----
   1	8	$3.50	$28.00	$28.00
   2	18	2.80	50.40	22.40
   3	29	2.30	66.70	16.30
   4	39	1.90	74.10	7.40
   5	47	1.65	77.55	3.45
   6	52	1.50	78.00	.45
   7	53	1.40	74.20	–3.80

   Comparing MRP to the wage, the firm maximizes profits by hiring 4 workers.

Problem:

Suppose a firm hiring from a competitive labor market has the marginal revenue product schedule as given in the first two columns of the table below:

1. If this firm can hire labor competitively at a wage of $16, how many workers will it hire?

Alternatively, suppose the firm has monopsony power such that it must pay $6 to hire the first worker and must increase the wage rate by $2 to attract each successive worker, as shown in the third column of the table above.

2. What is the total labor cost of hiring one worker? Of two workers? What is the marginal labor cost of the second worker?
3. What is the total labor cost of hiring three workers? What is the marginal labor cost of the third worker? Fill in the remainder of the final two columns.
4. What level of employment maximizes this firm's profit?
5. What wage rate will the firm pay to attract the profit-maximizing number of workers? Compare this outcome with that in part a.

Answer:

1. It will hire 5 workers. The marginal revenue product of the sixth worker ($12) is less than his or her wage rate ($16). Therefore, hiring the sixth worker will reduce profits.
2. Total labor cost is found as the wage rate times the number of workers. The total labor cost of one worker is $6, while two workers cost $8 x 2 = $16. The marginal labor cost of the second worker is the change in total labor cost, or $10: $16 – $6 = $10.
3. Three workers cost $10 x 3 = $30. The marginal labor cost is the difference between this cost and the cost of hiring just 2: $30 – 16 = $14. The complete table is below. All numbers in the fourth column are the product of the wage rate and the corresponding number of workers; marginal labor cost is the difference in successive total wage costs.

   Labor	Marginal Revenue Product	Wage Rate	Total Labor Cost	Marginal Labor Cost
   0	$ 0		$ 0
   1	20	$ 6	6	$ 6
   2	24	8	16	10
   3	28	10	30	14
   4	24	12	48	18
   5	18	14	70	22
   6	12	16	96	26
   7	6	18	126	30

4. The firm expands employment until the marginal revenue product no longer exceeds the marginal labor cost. It hires the fourth worker ($24 > $18), but not the fifth ($14 < $22).
5. Note that the wage paid to attract the sixth worker is $16, the same as for the competitive firm hiring the profit-maximizing amount of labor. For the monopsony, only four workers are demanded. To attract exactly four workers, this firm pays the corresponding wage rate, or $12. Relative to an otherwise identical competitive firm, a monopsony hires fewer workers at a lower wage rate.