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Difficulty: HardPrice Controls: Ceilings and Floors

The market demand and supply equations for cassava in a regional economy are given as Qd=800−10PQ_d = 800 - 10P and Qs=200+15PQ_s = 200 + 15P, where PP is the price per kilogram in Naira (N\text{N}) and QQ is the quantity in metric tonnes. If the government imposes a price floor of N32\text{N}32 per kilogram to support cassava farmers and guarantees to purchase all unsold produce, what is the total monetary outlay required by the government to buy the surplus cassava?

  1. N6,400Answer
  2. B
    N4,800
  3. C
    N15,360
  4. D
    N2,560

Answer

The total monetary outlay required by the government to buy the surplus cassava is N6,400.
The correct answer is obtained by first calculating the market equilibrium price (N24\text{N}24) to confirm that the price floor of N32\text{N}32 is binding. Substituting P=32P = 32 into the demand and supply equations gives a quantity demanded of 480 metric tonnes480\text{ metric tonnes} and a quantity supplied of 680 metric tonnes680\text{ metric tonnes}. This creates a market surplus of 680−480=200 metric tonnes680 - 480 = 200\text{ metric tonnes}. Since the government guarantees to buy all unsold produce at the floor price of N32\text{N}32 per kg, the total expenditure is 200×32=N6,400200 \times 32 = \text{N}6,400.

Step-by-Step Solution

1
Determine the equilibrium price to verify that the price floor is binding.
Set Qd=Qs  ⟹  800−10P=200+15P  ⟹  25P=600  ⟹  P=N24Q_d = Q_s \implies 800 - 10P = 200 + 15P \implies 25P = 600 \implies P = \text{N}24.
A price floor is binding (effective) only when set above the market equilibrium price of N24\text{N}24.
2
Calculate quantity demanded (QdQ_d) and quantity supplied (QsQ_s) at the price floor of N32\text{N}32.
Qd=800−10(32)=480 metric tonnesQ_d = 800 - 10(32) = 480\text{ metric tonnes}, and Qs=200+15(32)=680 metric tonnesQ_s = 200 + 15(32) = 680\text{ metric tonnes}.
Evaluating demand and supply functions at the imposed floor price determines the resulting disequilibrium.
3
Calculate the excess supply (surplus) resulting from the price floor.
Surplus=Qs−Qd=680−480=200 metric tonnes\text{Surplus} = Q_s - Q_d = 680 - 480 = 200\text{ metric tonnes}.
At the price floor, producers supply more cassava than consumers demand, creating a surplus.
4
Calculate total government financial outlay to absorb the surplus.
Total Outlay=Surplus×Pf=200×N32=N6,400\text{Total Outlay} = \text{Surplus} \times P_f = 200 \times \text{N}32 = \text{N}6,400.
The government must purchase the entire unsold surplus of 200 metric tonnes at the official floor price of N32\text{N}32 per kilogram.

Key Concept

Price Floor Surplus and Government Subsidy Absorption
Estimated Time:2m 0s
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Topics

Price Controls: Ceilings and Floors

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