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Difficulty: MediumMarket Equilibrium Price and Quantity

In a regional market for poultry feed, the daily quantity demanded is expressed as Qd=480−12PQ_d = 480 - 12P and the daily quantity supplied is expressed as Qs=−120+18PQ_s = -120 + 18P, where PP represents the price per bag in hundreds of Naira and QQ represents quantity in bags. What is the market equilibrium price per bag in hundreds of Naira?

Answer: 20 hundreds of Naira

Answer

The market equilibrium price is 20 (in hundreds of Naira).
Equilibrium price is established when quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s). Setting 480−12P=−120+18P480 - 12P = -120 + 18P yields 30P=60030P = 600, resulting in an equilibrium price of 20 (in hundreds of Naira).

Step-by-Step Solution

1
Equate the demand and supply equations to find market equilibrium.
480−12P=−120+18P480 - 12P = -120 + 18P
Market equilibrium occurs at the price level where the quantity buyers wish to purchase equals the quantity sellers wish to supply.
2
Rearrange the equation by grouping constant terms on one side and price variables on the other.
30P=60030P = 600
Adding 12P12P to both sides eliminates −12P-12P on the left, and adding 120120 to both sides eliminates −120-120 on the right.
3
Divide the total value by the coefficient of price to determine equilibrium price.
P=20P = 20
Dividing 600600 by 3030 isolates PP to give the equilibrium price.

Key Concept

Market Equilibrium Price Determination
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Topics

Market Equilibrium Price and Quantity

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