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 following table: If each case sells for $5 more than the cost of the materials used in producing it, and the competitive market wage is $625/week, then how many workers should Sam hire each week?

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 following table:  If each case sells for $5 more than the cost of the materials used in producing it, and the competitive market wage is $625/week, then how many workers should Sam hire each week?

Quizplus · Accepted Answer

To determine the optimal number of workers to hire, we must first calculate the marginal product of labor (MPL) and the value of the marginal product (VMP) for each additional worker, as shown in the following table:

Number of Workers | Weekly Output | MPL | VMP 
-----------------|--------------|-----|----- 
1                | 50           | N/A | N/A 
2                | 110          | 60  | $300 
3                | 160          | 50  | $250 
4                | 190          | 30  | $150 
5                | 205          | 15  | $75

The MPL is calculated by taking the change in output from hiring one more worker. The VMP is calculated by multiplying the MPL by the price of each case, which is $5 more than the cost of materials used, so VMP = MPL x $5.

The optimal number of workers to hire is the point where the VMP equals the wage rate of $625 per week. This occurs when 4 workers are hired, as their VMP is $600 ($150 x 4) which is just below the wage rate. Hiring a fifth worker would result in a VMP of only $75, which is not enough to cover the cost of their wage, so the optimal choice is B) 4 workers.

Sam Owns a Candy Factory and Hires Workers in a Competitive