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Difficulty: MediumMarket Equilibrium Price and Quantity

In a local agricultural market, the demand function for yam tubers is given by Qd=500−20PQ_d = 500 - 20P and the supply function is Qs=−100+40PQ_s = -100 + 40P, where PP represents the price per tuber in Naira (₦₦). If the market price is set at ₦8₦8, which of the following best describes the resulting market condition?

  1. An excess demand of 120 tubersAnswer
  2. B
    An excess supply of 120 tubers
  3. C
    An excess demand of 340 tubers
  4. D
    A market equilibrium of 300 tubers

Answer

An excess demand of 120 tubers
To evaluate the market condition at P=₦8P = ₦8, calculate quantity demanded: Qd=500−20(8)=340Q_d = 500 - 20(8) = 340 tubers, and quantity supplied: Qs=−100+40(8)=220Q_s = -100 + 40(8) = 220 tubers. Subtracting quantity supplied from quantity demanded yields 340−220=120340 - 220 = 120 tubers of excess demand.

Step-by-Step Solution

1
Calculate quantity demanded (QdQ_d) at price P=8P = 8
Qd=500−20(8)=500−160=340Q_d = 500 - 20(8) = 500 - 160 = 340 tubers
Substitute P=8P = 8 into the given demand function.
2
Calculate quantity supplied (QsQ_s) at price P=8P = 8
Qs=−100+40(8)=−100+320=220Q_s = -100 + 40(8) = -100 + 320 = 220 tubers
Substitute P=8P = 8 into the given supply function.
3
Determine market disequilibrium condition
Qd−Qs=340−220=120Q_d - Q_s = 340 - 220 = 120 tubers (Excess Demand)
Since quantity demanded exceeds quantity supplied, there is a shortage (excess demand) of 120 tubers.

Key Concept

Market Shortage and Excess Demand at Disequilibrium Price
Estimated Time:1m 30s
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Topics

Market Equilibrium Price and Quantity

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