Chapter 7.3, Problem 61E

An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The price at which supply and demand are equal is called the equilibrium price. The quantity supplied and demanded at that price is called the equilibrium quantity. Exercises 61-62 involve supply and demand.

The following models describe wages for low-skilled labor.

a. Solve the system and find the equilibrium number of workers, in millions, and the equilibrium hourly wage.

b. Use your answer from part (a) to complete this statement:

If workers are paid ____ per hour, there will be ____ million available workers and ____ million workers will be hired.

c. In 2007, the federal minimum wage was set at $5.15 per hour. Substitute 5.15 for p in the demand model, $p=-0.325x+5.8$, and determine the millions of workers employers will hire at this price.

d. At a minimum wage of $5.15 per hour, use the supply model, $p=0.375x+3,$ to determine the millions of available workers. Round to one decimal place.

e. At a minimum wage of $5.15 per hour, use your answers from parts (c) and (d) to determine how many more people are looking for work than employers are willing to hire.