Table 31.1 shows the number of workers a firm is willing to hire per hour at different wage rates. Complete the table by computing the total wage bill (total labor cost) and the marginal wage. Assume the union collects dues of 1 percent of the total wage bill. At what wage in Table 31.1 would the union maximize the amount of dues it collects?
A) $10 per hour.
B) $14 per hour.
C) $18 per hour.
D) $22 per hour.

Question

Table 31.1 shows the number of workers a firm is willing to hire per hour at different wage rates. Complete the table by computing the total wage bill (total labor cost) and the marginal wage. Assume the union collects dues of 1 percent of the total wage bill. At what wage in Table 31.1 would the union maximize the amount of dues it collects?
A) $10 per hour. 
B) $14 per hour. 
C) $18 per hour. 
D) $22 per hour.

Quizplus · Accepted Answer

To find the total wage bill we need to multiply the wage rate with the number of workers hired.

For example, at a wage rate of $10 per hour, the firm is willing to hire 0 workers, so the total wage bill is 0.

At a wage rate of $12 per hour, the firm is willing to hire 50 workers, so the total wage bill is 50 x $12 = $600.

Similarly, we can compute the total wage bill for all the other wage rates in the table:

- At $14 per hour, the total wage bill is 100 x $14 = $1,400.
- At $16 per hour, the total wage bill is 150 x $16 = $2,400.
- At $18 per hour, the total wage bill is 200 x $18 = $3,600.
- At $20 per hour, the total wage bill is 250 x $20 = $5,000.
- At $22 per hour, the total wage bill is 300 x $22 = $6,600.

To compute the marginal wage, we need to find the additional cost of hiring one more worker.

For example, between a wage rate of $10 and $12, the firm is willing to hire 50 workers for an additional cost of $600 - $0 = $600. So the marginal wage is ($600/1) = $600.

Similarly, we can compute the marginal wage for all the other wage rates in the table:

- Between $12 and $14, the firm is willing to hire 50 more workers for an additional cost of $1,400 - $600 = $800. So the marginal wage is ($800/1) = $800.
- Between $14 and $16, the firm is willing to hire 50 more workers for an additional cost of $2,400 - $1,400 = $1,000. So the marginal wage is ($1,000/1) = $1,000.
- Between $16 and $18, the firm is willing to hire 50 more workers for an additional cost of $3,600 - $2,400 = $1,200. So the marginal wage is ($1,200/1) = $1,200.
- Between $18 and $20, the firm is willing to hire 50 more workers for an additional cost of $5,000 - $3,600 = $1,400. So the marginal wage is ($1,400/1) = $1,400.
- Between $20 and $22, the firm is willing to hire 50 more workers for an additional cost of $6,600 - $5,000 = $1,600. So the marginal wage is ($1,600/1) = $1,600.

To find the wage rate at which the union would maximize the amount of dues it collects, we need to calculate the total wage bill for each wage rate, then subtract 1% of that amount to get the union dues.

For example, at a wage rate of $10 per hour, the total wage bill is 0, so the union dues are also 0.

At a wage rate of $14 per hour, the total wage bill is $1,400, so the union dues are ($1,400 x 0.01) = $14.

Similarly, we can compute the union dues for all the other wage rates in the table:

- At $18 per hour, the total wage bill is $3,600, so the union dues are ($3,600 x 0.01) = $36.
- At $22 per hour, the total wage bill is $6,600, so the union dues are ($6,600 x 0.01) = $66.

Since the goal is to maximize the amount of dues collected, the answer is the wage rate with the highest union dues, which is B) $14 per hour.

Table 311 Shows the Number of Workers a Firm Is Willing