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Difficulty: HardMarket Equilibrium Price and Quantity

The market demand for soya beans in a regional market is given by Qd=350−5PQ_d = 350 - 5P, and the initial market supply function is Qs=−70+9PQ_s = -70 + 9P, where PP is the price per bag in Naira (N\text{N}). If an increase in fuel costs shifts the supply function to Qs=−140+9PQ_s = -140 + 9P, by how much will the equilibrium price change?

  1. Increase by N5\text{N}5Answer
  2. B
    Decrease by N5\text{N}5
  3. C
    Increase by N10\text{N}10
  4. D
    Increase by N35\text{N}35

Answer

The equilibrium price increases by N5\text{N}5.
Equating the demand function Qd=350−5PQ_d = 350 - 5P to the initial supply function Qs=−70+9PQ_s = -70 + 9P gives 14P=42014P = 420, yielding P1∗=N30P_1^* = \text{N}30. After the supply shift to Qs=−140+9PQ_s = -140 + 9P, setting 350−5P=−140+9P350 - 5P = -140 + 9P gives 14P=49014P = 490, yielding P2∗=N35P_2^* = \text{N}35. The net change in equilibrium price is N35−N30=N5\text{N}35 - \text{N}30 = \text{N}5 increase.

Step-by-Step Solution

1
Calculate the initial equilibrium price (P1∗P_1^*) by equating initial demand and supply functions.
350−5P=−70+9P  ⟹  14P=420  ⟹  P1∗=30350 - 5P = -70 + 9P \implies 14P = 420 \implies P_1^* = 30
Market equilibrium occurs where quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s).
2
Calculate the new equilibrium price (P2∗P_2^*) using the shifted supply function.
350−5P=−140+9P  ⟹  14P=490  ⟹  P2∗=35350 - 5P = -140 + 9P \implies 14P = 490 \implies P_2^* = 35
The shift in the supply function establishes a new market clearing price point.
3
Determine the magnitude of change in the equilibrium price (ΔP∗\Delta P^*).
ΔP∗=P2∗−P1∗=35−30=5\Delta P^* = P_2^* - P_1^* = 35 - 30 = 5
Subtracting the initial equilibrium price from the new equilibrium price gives the net price change.

Key Concept

Market Equilibrium Response to Supply Shifts
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Topics

Market Equilibrium Price and Quantity

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