Question

​)AJ Corp sells speakers and has observed a recent drop in sales from 800 units a month to 650 units, reducing its revenue by £18,000 (with no change in its price). Assuming its price elasticity to be -1.6, calculate the necessary price that AJ must charge to restore its sales volume to its previous level.

Answer 1

Let price be P per unit.

Initial revenue = P x Q0 = 800P

New revenue = P x Q1 = 650P

800P - 650P = 18,000

150P = 18,000

P = 120

Let new price to be charged be P1. Using midpoint method,

Elasticity = [(Q1 - Q0) / (Q1 + Q0)] / [(P1 - P0) / (P1 + P0)]

- 1.6 = [(650 - 800) / (650 + 800)] / [(P1 - 120) / (P1 + 120)]

- 1.6 = [- 150 / 1,450] / [(P1 - 120) / (P1 + 120)]

- 1.6 = [- 150 x (P1 + 120)] / [(1,450 x (P1 - 120)]

- 1.6 = (- 150P1 - 18,000) / (1,450P1 - 174,000)

- 2,320P1 + 278,400 = - 150P1 - 18,000

2,170P1 = 296,400

P1 = 136.59