Sam owns a candy factory and hires workers in a competitive labor market to pack cases of candy.The company's weekly output of cases of candy varies with the number of workers hired,as shown in the table: $$\begin{array} { c c }
\text { Number of workers } & \text { Cases/week } \
0 & 0 \
1 & 160 \
2 & 310 \
3 & 450 \
4 & 580 \
5 & 700 \
6 & 810
\end{array}$$
If each case sells for $5 more than the cost of the materials used in producing it and the competitive market wage is $650/week,how many workers should Sam hire?

Question

Sam owns a candy factory and hires workers in a competitive labor market to pack cases of candy.The company's weekly output of cases of candy varies with the number of workers hired,as shown in the table: $$\begin{array} { c c } 
\text { Number of workers } & \text { Cases/week } \
0 & 0 \
1 & 160 \
2 & 310 \
3 & 450 \
4 & 580 \
5 & 700 \
6 & 810
\end{array}$$
If each case sells for $5 more than the cost of the materials used in producing it and the competitive market wage is $650/week,how many workers should Sam hire?

Quizplus · Accepted Answer

First, let's find the marginal product of labor (MPL) by finding the additional output produced by each additional worker.

$$\begin{array} { c c c } 
\text { Number of workers } & \text { Additional output } & \text{MPL} \
1 & 160 & 160 \
2 & 150 & 75 \
3 & 140 & 46.7 \
4 & 130 & 32.5 \
5 & 120 & 24 \
6 & 110 & 18.33
\end{array}$$

As we can see, MPL decreases as more workers are hired. This means that the total product of labor (TPL) increases at a decreasing rate, which indicates that there are diminishing returns to labor.

Next, let's find the value of the marginal product (VMP), which is the additional revenue generated by each additional worker:

$$\begin{array} { c c c } 
\text { Number of workers } & \text { Additional revenue } & \text{VMP} \
1 & 800 & 800 \
2 & 1550 & 775 \
3 & 2250 & 750 \
4 & 2900 & 725 \
5 & 3500 & 700 \
6 & 4050 & 675
\end{array}$$

VMP is decreasing as more workers are hired, which means that the marginal revenue product (MRP) is also decreasing. MRP is the additional revenue generated by the last worker hired.

To determine the optimal number of workers to hire, we need to compare the MRP to the wage rate. If MRP is greater than the wage rate, then hiring an additional worker would increase profit. If MRP is less than the wage rate, then it would be more profitable to hire fewer workers.

In this case, the wage rate is $650/week. We can see from the table that MRP is greater than $650 for the first four workers, but drops below $650 for the fifth and sixth worker. Therefore, the optimal number of workers to hire is 4.

Sam Owns a Candy Factory and Hires Workers in a Competitive