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The price of a good rises from $10 to $12, causing quantity demanded to fall from 100 units to 80 units. Using the midpoint (arc) method, what is the price elasticity of demand for this good?

  1. A-1.00
  2. B-0.82
  3. C-2.00
  4. D-1.22
Show answer & explanation

Correct answer: D. -1.22

%ΔQ = (80-100)/[(80+100)/2] = -20/90 = -22.22%. %ΔP = (12-10)/[(12+10)/2] = 2/11 = 18.18%. Elasticity = -22.22%/18.18% = -1.22, indicating elastic demand.

Why the other options are wrong

  • A. Would imply unit elastic demand, which is not the case here.
  • B. Incorrect magnitude; underestimates the percentage change in quantity.
  • C. Overstates elasticity; does not match midpoint calculation.

Midpoint (Arc) Elasticity

A method for calculating price elasticity of demand that uses the average of starting and ending values as the base, avoiding directional bias.

  • %ΔQ uses average of Q1 and Q2 as denominator
  • %ΔP uses average of P1 and P2 as denominator
  • |E|>1 = elastic; |E|<1 = inelastic; |E|=1 = unit elastic

Memory trick: Midpoint avoids the 'direction bias' — average the base like averaging a road trip's start and end mileage.

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