JAMB 2023 Economics · Question 12

If demand function for a product is Qd = 30 - 4P, and the price and quantity of products is 4 and 14…

Question

If demand function for a product is Qd = 30 - 4P, and the price and quantity of products is 4 and 14 respectively. What is the price elasticity of demand for the product?

  1. A.1.14
  2. B.7.1
  3. C.14.1
  4. D.1.7

Answer: A. 1.14

Explanation written with AI and checked against the answer key

Analyze the question: We are given a linear demand function Qd = 30 - 4P, and the point P = 4, Q = 14. We need the price elasticity of demand at that point.

Concept: Point price elasticity of demand:

Ed = (dQ/dP) × (P/Q)

For a linear demand function, dQ/dP is the coefficient of P, which is -4.

Solution:

  1. Check the point: Qd = 30 - 4(4) = 30 - 16 = 14. This matches the given quantity.
  2. dQ/dP = -4
  3. Ed = -4 × (4/14) = -16/14 = -1.14

Ignoring the negative sign (as is usual in exams, where we take the absolute value), |Ed| = 16/14 ≈ 1.14.

Since 1.14 > 1, demand is elastic at this point.

Answer: Option A (1.14).

Tip: For linear demand Qd = a - bP, elasticity at any point is b × P/Q. Always plug the price into the function first to check that Q matches. Options like 7.1 and 14.1 are distractors from mistakes such as inverting or misusing the numbers (for example, forgetting to divide by Q).

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