$\begin{array}{cc}
\begin{array}{cc}
\
\begin{array}{c}
\text { Wage nate } \
\text { (dollars per hour) }
\end{array} & \begin{array}{c}
\text { Labor demanded } \
\text { (workers) }
\end{array} \
\hline \$ 26 & 0 \
22 & 2 \
18 & 4 \
14 & 6 \
10 & 8
\end{array}
\begin{array}{cc}
\text{Total labor}\
\text{cost-hourly}&\text{Marginal wage}\
\text{(dollars per hour)}&\text{(dollars per worker)}\
\hline
-&....\
-&-\
-&-\
-&-\
-&-
\end{array}
\end{array}$
$\text { Table } 31.1$ 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.How many workers would the union want hired in Table 31.1 if its goal was to maximize the amount of dues collected?
A) 2.
B) 4.
C) 6.
D) 8.

Question

Quizplus · Accepted Answer

To compute the total wage bill, we need to multiply the wage rate by the number of workers hired at each wage rate. For example, at a wage rate of \$26, the firm is willing to hire 0 workers, so the total wage bill is 0. At a wage rate of \$22, the firm is willing to hire 2 workers, so the total wage bill is:

Total wage bill at \$22 = \$22 × 2 = \$44

Similarly, we can compute the total wage bill at each wage rate and fill in the table as follows:

$\begin{array}{cc}
\begin{array}{cc}
\
\begin{array}{c}
\text { Wage nate } \
\text { (dollars per hour) }
\end{array} & \begin{array}{c}
\text { Labor demanded } \
\text { (workers) }
\end{array} \
\hline \$ 26 & 0 \
22 & 2 \
18 & 4 \
14 & 6 \
10 & 8
\end{array}
\begin{array}{cc}
\text{Total labor}\
\text{cost-hourly}&\text{Marginal wage}\
\text{(dollars per hour)}&\text{(dollars per worker)}\
\hline
- & - \
\$ 0 & - \
\$ 72 & 25 \
\$ 72 & 17 \
\$ 84 & 9
\end{array}
\end{array}$

To compute the marginal wage, we need to find the change in the total wage bill divided by the change in the number of workers hired. For example, the marginal wage between a wage rate of \$22 and \$18 is:

Marginal wage at \$22 = (\$72 - \$44) ÷ (4 - 2) = \$14

Similarly, we can compute the marginal wage at each wage rate and fill in the table as follows:

$\begin{array}{cc}
\begin{array}{cc}
\
\begin{array}{c}
\text { Wage nate } \
\text { (dollars per hour) }
\end{array} & \begin{array}{c}
\text { Labor demanded } \
\text { (workers) }
\end{array} \
\hline \$ 26 & 0 \
22 & 2 \
18 & 4 \
14 & 6 \
10 & 8
\end{array}
\begin{array}{cc}
\text{Total labor}\
\text{cost-hourly}&\text{Marginal wage}\
\text{(dollars per hour)}&\text{(dollars per worker)}\
\hline
- & - \
\$ 0 & - \
\$ 72 & 25 \
\$ 72 & 17 \
\$ 84 & 9
\end{array}
\end{array}$

To compute the amount of union dues collected at each wage rate, we need to multiply the total wage bill at that wage rate by 1 percent. For example, at a wage rate of \$18, the total wage bill is \$72, so the amount of union dues collected is:

Union dues at \$18 = \$72 × 0.01 = \$0.72

Similarly, we can compute the amount of union dues collected at each wage rate and fill in the table as follows:

$\begin{array}{cc}
\begin{array}{cc}
\
\begin{array}{c}
\text { Wage nate } \
\text { (dollars per hour) }
\end{array} & \begin{array}{c}
\text { Labor demanded } \
\text { (workers) }
\end{array} \
\hline \$ 26 & 0 \
22 & 2 \
18 & 4 \
14 & 6 \
10 & 8
\end{array}
\begin{array}{cc}
\text{Total labor}\
\text{cost-hourly}&\text{Marginal wage}\
\text{(dollars per hour)}&\text{(dollars per worker)}\
\hline
- & - \
\$ 0 & - \
\$ 72 & 25 \
\$ 72 & 17 \
\$ 84 & 9
\end{array}
\begin{array}{c}
\text{Union dues}\
\text{(dollars per}\
\text{hour)}
\end{array}
\begin{array}{c}
- \
\$ 0.44 \
\$ 0.72 \
\$ 0.72 \
\$ 0.84
\end{array}
\end{array}$

To maximize the amount of union dues collected, the union would want to maximize the total wage bill, since the dues are proportional to the wage bill. This occurs at a wage rate of \$18, where the total wage bill is \$72 and the union collects \$0.72 in dues. At this wage rate, the firm would hire 4 workers, so the union would want 4 workers hired.

Therefore, the answer is C) 6.

Table 31.1\text { Table } 31.1 Table 31.1 Table 311 Shows the Number of Workers a Firm Is Willing

$\text { Table } 31.1$ Table 311 Shows the Number of Workers a Firm Is Willing