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Difficulty: HardMarket Equilibrium Price and Quantity

The demand and supply functions for a commodity in a competitive market are given as Qd=180−8PQ_d = 180 - 8P and Qs=−20+12PQ_s = -20 + 12P, where PP is the price in Naira (₦), QdQ_d is the quantity demanded, and QsQ_s is the quantity supplied. If the government imposes a maximum price ceiling of ₦8, what is the resulting market condition?

  1. A shortage of 40 unitsAnswer
  2. B
    A surplus of 40 units
  3. C
    A shortage of 20 units
  4. D
    A surplus of 20 units

Answer

A shortage of 40 units
Evaluating the demand function at P=8P = 8 yields Qd=180−8(8)=116Q_d = 180 - 8(8) = 116 units. Evaluating the supply function at P=8P = 8 yields Qs=−20+12(8)=76Q_s = -20 + 12(8) = 76 units. Subtracting quantity supplied from quantity demanded (116−76116 - 76) reveals an excess demand (shortage) of 40 units.

Step-by-Step Solution

1
Calculate quantity demanded (QdQ_d) at the price ceiling of ₦8
Qd=180−8(8)=180−64=116Q_d = 180 - 8(8) = 180 - 64 = 116 units
Substitute P=8P = 8 into the demand function.
2
Calculate quantity supplied (QsQ_s) at the price ceiling of ₦8
Qs=−20+12(8)=−20+96=76Q_s = -20 + 12(8) = -20 + 96 = 76 units
Substitute P=8P = 8 into the supply function.
3
Calculate market shortage or surplus (Qd−QsQ_d - Q_s)
116−76=40116 - 76 = 40 units
Since quantity demanded exceeds quantity supplied (Qd>QsQ_d > Q_s), there is a market shortage of 40 units.

Key Concept

Market Disequilibrium and Shortage Calculation
Estimated Time:2m 0s
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Topics

Market Equilibrium Price and Quantity

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