Question

For each of the following demand curves:

i) Find the price-elasticity of demand in terms of P.

ii) Determine the range of P values for which the demand curve is perfectly elastic, elastic, unitary elastic, inelastic and perfectly inelastic (your answer will look like, the demand is inelastic for 0 < P < 10, unitary elastic at P = 10, etc). iii) Calculate the price-elasticity of demand at P = 3 and give an interpretation in words of what that means in terms of percentages.

(a) Q(P) = 77 − 2P

(b) Q(P) = 5P −1/4

(c) Q(P) = a − bP

Answer 1

(a) Q = 77 - 2P

(i) Price elasticity of demand (Ep) = (dQ/dP) x (P/Q) = -2 x [P / (77 - 2P) = -2P / (77 - 2P)

(ii) Demand is elastic (inelastic) if absolute value of elasticity is higher (lower) than 1. Demand is unit elastic if absolute value of elasticity equals 1.

(A) If demand is elastic,

[2P / (77 - 2P)] > 1

2P > (77 - 2P)

4P > 77

P > 19.25

(B) If demand is inelastic,

[2P / (77 - 2P)] < 1

2P < (77 - 2P)

4P < 77

P < 19.25

(C) If demand is unit elastic,

[2P / (77 - 2P)] = 1

2P = (77 - 2P)

4P = 77

P = 19.25

(iii) When P = 3,

Elasticity = -2P / (77 - 2P) = (-2 x 3) / [77 - (2 x 3)] = -6 / (77 - 6) = -6 / 71 = -0.08

Since absolute value of elasticity is lower than 1, demand is inelastic. This means that for every 1% increase (decrease) in price, quantity demanded will decrease (increase) by 0.08%. An increase (decrease) in price will increase (decrease) total revenue.

NOTE: As per Answering Policy, 1st sub-part (a) with multiple parts has been answered.