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Difficulty: EasyMarket Equilibrium Price and Quantity

In a market for cassava flakes, the daily quantity demanded is given by the linear demand function Qd=120−4PQ_d = 120 - 4P and the daily quantity supplied is given by the linear supply function Qs=30+5PQ_s = 30 + 5P, where PP is the price per bag in Naira (N\text{N}). What is the market equilibrium price?

  1. N10\text{N}10Answer
  2. B
    N15\text{N}15
  3. C
    N90\text{N}90
  4. D
    N150\text{N}150

Answer

The market equilibrium price is N10\text{N}10.
Market equilibrium is established at the price where quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s). Equating 120−4P=30+5P120 - 4P = 30 + 5P gives 90=9P90 = 9P, which yields P=10P = 10. Therefore, N10\text{N}10 is the correct equilibrium price.

Step-by-Step Solution

1
Set quantity demanded equal to quantity supplied to find market equilibrium (Qd=QsQ_d = Q_s).
120−4P=30+5P120 - 4P = 30 + 5P
Market equilibrium occurs where the quantity demanded equals the quantity supplied.
2
Collect like terms by moving price terms to one side and constant terms to the other.
120−30=5P+4P  ⟹  90=9P120 - 30 = 5P + 4P \implies 90 = 9P
Grouping algebraic terms isolates the price variable PP.
3
Solve for the price PP.
P=909=10P = \frac{90}{9} = 10
Dividing both sides by 9 yields the equilibrium price of N10\text{N}10.

Key Concept

Market Equilibrium Price Determination
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Topics

Market Equilibrium Price and Quantity

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