Chapter 5.1, Problem 66PE

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 65–66 involve supply and demand.

The following models describe demand and supply for three-bedroom rental apartments.

$\begin{array}{l}\begin{array}{llll}DemandModel\hfill & \hfill & \hfill & SupplyModel\hfill \\ p=-50x+2000\hfill & \hfill & \hfill & p=50x\hfill \end{array}\\ \begin{array}{llll}Monthlyrentalprice\hfill & \hfill & \hfill & Monthlyrentalprice\hfill \end{array}\\ \begin{array}{llll}\begin{array}{l}Numberofapartments\\ demanded,inthousands\end{array}\hfill & \hfill & \hfill & \begin{array}{l}Numberofapartments\\ supplied,inthousands\end{array}\hfill \end{array}\end{array}$

a. Solve the system and find the equilibrium quantity and the equilibrium price.

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

When rents are ______ per month, consumers will demand _______ apartments and suppliers will offer ________ apartments for rent.