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Difficulty: MediumConcept and Law of Supply

A small-scale manufacturer of woven baskets in Anambra State observes that at a market price of N2,000\text{N}2,000 per basket, weekly supply is 250250 units. When the market price rises to N5,000\text{N}5,000 per basket, weekly supply increases to 850850 units. Assuming a linear supply relationship of the form Qs=c+dPQ_s = c + dP, what is the value of the autonomous supply constant cc?

  1. −150-150Answer
  2. B
    150150
  3. C
    0.20.2
  4. D
    −400-400

Answer

The autonomous supply constant cc is −150-150.
The linear supply function is defined as Qs=c+dPQ_s = c + dP. Determining the price responsiveness parameter d=ΔQsΔP=850−2505,000−2,000=0.2d = \frac{\Delta Q_s}{\Delta P} = \frac{850 - 250}{5,000 - 2,000} = 0.2, and substituting this back into 250=c+2,000(0.2)250 = c + 2,000(0.2) yields c=250−400=−150c = 250 - 400 = -150.

Step-by-Step Solution

1
Set up linear supply equations using given price and quantity pairs
Equation 1: 250=c+2,000d250 = c + 2,000d; Equation 2: 850=c+5,000d850 = c + 5,000d
The linear supply function follows the formula Qs=c+dPQ_s = c + dP.
2
Calculate the slope coefficient dd
d=ΔQsΔP=850−2505,000−2,000=6003,000=0.2d = \frac{\Delta Q_s}{\Delta P} = \frac{850 - 250}{5,000 - 2,000} = \frac{600}{3,000} = 0.2
The slope dd measures the change in quantity supplied per unit change in price.
3
Substitute d=0.2d = 0.2 into Equation 1 to solve for the autonomous supply constant cc
250=c+2,000(0.2)  ⟹  250=c+400  ⟹  c=250−400=−150250 = c + 2,000(0.2) \implies 250 = c + 400 \implies c = 250 - 400 = -150
Isolating cc provides the baseline intercept parameter of the supply function.

Key Concept

Linear Supply Function Parameters (Qs=c+dPQ_s = c + dP)
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Topics

Concept and Law of Supply

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