At a price of $4.81 per pound, the supply for cherries is 16,130 pounds, and the demand is 10,348 pounds. When the price drops to $4.22 per pound, the supply decreases to 10,590 pounds and the demand increases to 12,824 pounds. Assume that the price-supply and price-demand equations are linear. What is the equilibrium price? $ per pound. Round to the nearest cent.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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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 $4.81 per pound, the supply for cherries is 16,130 pounds, and the demand is 10,348 pounds.  When the price drops to $4.22 per pound, the supply decreases to 10,590 pounds and the demand increases to 12,824 pounds.  Assume that the price-supply and price-demand equations are linear.

What is the equilibrium price?

$                       per pound.  Round to the nearest cent.

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