Question

You are the manager of a large but privately held online retailer that currently uses 17 unskilled workers and 6 semiskilled workers at its warehouse to box and ship the products it sells online. Your company pays its unskilled workers the minimum wage but pays the semiskilled workers \(9.75 per hour. Thanks to government legislation, the minimum wage in your state will increase from \)7.25 per hour to $8.15 per hour on July 24, 2013. Discuss the implications of this legislation for your company’s operations and in particular the implications for your optimal mix of inputs and long-run investment decisions.

Short answer

Following government legislation, the corporation would prefer to keep total costs low while maintaining high production quality. As a result, the company should hire more semi-skilled workers and fewer unskilled ones.

Step-by-step solution

Find the total labor cost 

Given that the company employs 17 unskilled and 6 semiskilled workers. Unskilled workers are given a minimum wage of per hour, which will rise to in the future. Semi-skilled workers, on the other hand, are paid per hour.

Using this information, we can figure out the firm's cost structure through following calculation:

$\begin{array}{rcl}TotalLaborCost& =& UnskilledWorkers\text{'}Cost+SemiskilledWorkers\text{'}Cost\\ & =& quantityofunskilledworkers\times wage+quantityofsemiskilledworkers\times wage\\ & =& \text{17}\times \text{7.25 + 6}\times \text{9.75}\\ & =& 123.25+58.5\\ & =& \text{181.75}\\ & & \end{array}$

Therefore, the total labor cost before the government legislation is $\text{\$ 181.75}.$

$\begin{array}{rcl}TotalLaborCost& =& UnskilledWorkers\text{'}Cost+SemiskilledWorkers\text{'}Cost\\ & =& quantityofunskilledworkers\times wage+quantityofsemiskilledworkers\times wage\\ & =& \text{17}\times 8.\text{15 + 6}\times \text{9.75}\\ & =& 138.55+58.5\\ & =& 197.05\\ & & \end{array}$

Therefore, the total labor cost after the government legislation is $\text{\$ 197.05}.$

Long-run investment decisions

The new minimum wage law imposition resulted in the increased cost of unskilled labor. Hence, the company will now hire more skilled labor than unskilled workers because paying higher wages to unproductive workers increases the firm's cost without much gains from production. While hiring skilled, productive workers will increase the production of the firm, which in turn will increase the profits gained. Hence, the company will terminate its unskilled workers and hire more skilled workers at the cost of unskilled ones.

Hence, firm will hire $\left(138.55÷9.75\right)\simeq 14$skilled workers in place of 17 unskilled ones.