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Difficulty: MediumMarket Equilibrium Price and Quantity

The weekly demand function for cocoa in a competitive market is expressed as Qd=650−15PQ_d = 650 - 15P and the supply function is expressed as Qs=−150+25PQ_s = -150 + 25P, where PP represents the price in Naira per bag, QdQ_d is the quantity demanded, and QsQ_s is the quantity supplied. What is the market equilibrium quantity in bags?

Answer: 350 bags

Answer

The market equilibrium quantity is 350 bags.
Equating quantity demanded and quantity supplied (650−15P=−150+25P650 - 15P = -150 + 25P) gives 40P=80040P = 800, which results in an equilibrium price of P=20P = 20 Naira. Substituting P=20P = 20 into the demand function gives Q=650−15(20)=350Q = 650 - 15(20) = 350 bags.

Step-by-Step Solution

1
Equate quantity demanded (Q_d) to quantity supplied (Q_s) to solve for the market equilibrium price.
650 - 15P = -150 + 25P, which simplifies to 40P = 800, yielding P = 20 Naira.
Market equilibrium occurs at the price level where quantity demanded equals quantity supplied.
2
Substitute the calculated equilibrium price (P = 20) back into the demand or supply equation to compute the equilibrium quantity.
Q = 650 - 15(20) = 350 bags.
Evaluating either market function at the equilibrium price determines the quantity cleared by the market.

Key Concept

Market Equilibrium Price and Quantity Determination
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Topics

Market Equilibrium Price and Quantity

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