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Difficulty: Very hardConcept and Law of Supply

A commercial cassava processing firm operates under a linear supply function Qs=a+bPQ_s = a + bP, where QsQ_s represents the quantity supplied in bags and PP represents the market price per bag in Naira (N\text{N}). Operational market records show that when the price of cassava flour was N400\text{N}400, the firm supplied 1,200 bags1,200\text{ bags}. When the market price rose to N550\text{N}550, the quantity supplied increased to 1,800 bags1,800\text{ bags} in accordance with the law of supply. What is the reservation price (the minimum threshold price) below which the firm will offer zero bags to the market?

  1. N100\text{N}100Answer
  2. B
    N150\text{N}150
  3. C
    N200\text{N}200
  4. D
    N400\text{N}400

Answer

The reservation price below which the firm will offer zero supply is N100\text{N}100.
The slope of the supply function is derived as b=ΔQΔP=600150=4b = \frac{\Delta Q}{\Delta P} = \frac{600}{150} = 4. Substituting into Qs=a+bPQ_s = a + bP yields an intercept a=−400a = -400, giving the supply equation Qs=−400+4PQ_s = -400 + 4P. Setting Qs=0Q_s = 0 gives 4P=4004P = 400, which solves to a reservation price of N100\text{N}100.

Step-by-Step Solution

1
Calculate the slope coefficient bb using the law of supply relationship.
b=ΔQsΔP=1,800−1,200550−400=600150=4b = \frac{\Delta Q_s}{\Delta P} = \frac{1,800 - 1,200}{550 - 400} = \frac{600}{150} = 4
The slope bb reflects how quantity supplied changes in response to price changes according to the law of supply.
2
Substitute b=4b = 4 and a known point (P=400,Qs=1200)(P=400, Q_s=1200) into Qs=a+bPQ_s = a + bP to find the autonomous supply constant aa.
1,200=a+4(400)  ⟹  1,200=a+1,600  ⟹  a=−4001,200 = a + 4(400) \implies 1,200 = a + 1,600 \implies a = -400
Finding the intercept aa defines the full explicit linear supply function: Qs=−400+4PQ_s = -400 + 4P.
3
Determine the reservation price by setting quantity supplied Qs=0Q_s = 0.
0=−400+4P  ⟹  4P=400  ⟹  P=N1000 = -400 + 4P \implies 4P = 400 \implies P = \text{N}100
The reservation price is the minimum market price required to induce producers to supply the first unit of output.

Key Concept

Derivation and analysis of linear supply functions and reservation price under the Law of Supply
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Topics

Concept and Law of Supply

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