At a price of $4.97 per pound, the supply for cherries is 16,289 pounds, and the demand is 10,218 pounds. When the price drops to $4.31 per pound, the supply decreases to 10,676 pounds and the demand increases to 12,992 pounds. Assume that the price-supply and price-demand equations are linear. What is the equilibrium quantity? Round to the nearest pound. pounds.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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In a free market economy, the price of a product is determined by the relationship between supply and demand.  Suppliers are more willing to supply a product at higher prices.  So when the price is high, supply is high.  On the other hand, consumers of a product are generally less willing to buy a product at higher prices.  So when the price is high, demand is low.

In a free competitive market, the price of a product tends to move toward an equilibrium price, in which the supply and demand are equal; that common value of the supply and demand is the equilibrium quantity.  To find the equilibrium price, we solve the system consisting of the price-supply and price-demand equations.

1. 

At a price of $4.97 per pound, the supply for cherries is 16,289 pounds, and the demand is 10,218 pounds.  When the price drops to $4.31 per pound, the supply decreases to 10,676 pounds and the demand increases to 12,992 pounds.  Assume that the price-supply and price-demand equations are linear.

What is the equilibrium quantity?  Round to the nearest pound.

                       pounds.

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