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Difficulty: EasyMarket Equilibrium Price and Quantity

In a local market, the demand function for rice is given by Qd=80−4PQ_d = 80 - 4P and the supply function is given by Qs=20+6PQ_s = 20 + 6P, where PP is the price in Naira per bag. What is the market equilibrium price (in Naira)?

Answer: 6 Naira

Answer

The market equilibrium price is 6 Naira.
At market equilibrium, quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s). Setting 80−4P=20+6P80 - 4P = 20 + 6P leads to 60=10P60 = 10P, which gives an equilibrium price of 6 Naira.

Step-by-Step Solution

1
Equate the demand function and the supply function to establish market equilibrium.
80−4P=20+6P80 - 4P = 20 + 6P
Market equilibrium is defined as the price point where quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s).
2
Collect like terms with price (PP) on one side and constant numerical terms on the other side.
80−20=6P+4P  ⟹  60=10P80 - 20 = 6P + 4P \implies 60 = 10P
Moving −4P-4P to the right side changes its sign to +4P+4P, and moving 2020 to the left side changes its sign to −20-20.
3
Divide both sides by 10 to isolate PP.
P=6P = 6
Dividing 60 by 10 yields the exact equilibrium price of 6 Naira.

Key Concept

Market Equilibrium Price Determination
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Topics

Market Equilibrium Price and Quantity

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