Price Elasticity of Demand - Two Example Calculations

Here are two calculation questions using price elasticity of demand.

Cinema ticket prices

A cinema charges £8 per ticket for evening screenings and sells 250 tickets a night on average. They estimate that the price elasticity of demand for tickets is (-) 1.6. 

Calculate the expected number of tickets sold if they reduce the ticket price to £7.

Answer:

Ped = % change in Qty Demanded / % change in Price
% change in price = 12.5%
If Ped = (-) 1.6 then ticket sales will rise by 1.6 x 12.5% = 20%
20% of 250 is 50 extra tickets
Expected tickets sold rises to 300

Car parking charges

A local council raises the price of car parking from £3 per day to £5 per day and finds that usage of car parks contracts from 1,200 cars a day to 900 cars per day. 
Calculate the price elasticity of demand for this price change and calculate whether total revenue from the car park rises or falls.

Answer:

% change in price = (+) 66.7%
% change in demand = (-) 25%
PED = -25/66.7
= 0.375 (i.e. demand is price inelastic)

Total revenue:
@£3 per day – revenue = £3 x 1,200 = £3,600
@ £5 per day – revenue = £5 x 900 = £4,500
Revenue rises when Ped <1 and a business raises their average selling price.