Concept explainers
Systems of equations play an important role in the analysis of supply and demand. For example, suppose that a theater company wants to set an optimal price for tickets to a show. If the theater sells tickets for $1 each, there would be a high demand and many people would buy tickets. However, the revenue brought in would not cover the expense of the show. Therefore, the theater is not willing to offer (supply) tickets at this low price. If the theater sells tickets for $10,000 each, chances are that no one would buy a ticket (demand would be low).
In an open market, the price of an item is dependent on the demand by consumers and the supply offered by producers. Competition between buyers and sellers streers the price toward an equilibrium price-that is, the price where supply equals demand. The number of items offered and sold at the equilibrium price is the equilibrium quantity. Use this information for Exercises 87-88.
Suppose that the price p (in $) of theater tickets is influenced by the number of tickets x offered by the theater and demanded by consumers.
Solve the system of equations defined by the supply and demand models.
What is the equilibrium price?
What is the equilibrium quantity?

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