A health club sells 100 memberships when the monthly price is $70 and 120 memberships when the monthly price is $60. The price elasticity of demand for memberships at this health club is (using the midpoint formula):
A) 0.25.
B) 0.65.
C) 1.18.
D) 1.

Question

Quizplus · Accepted Answer

Using the midpoint formula:
Price elasticity of demand = [(Q2-Q1) / ((Q2+Q1)/2)] / [(P2-P1) / ((P2+P1)/2)]
Where:
Q1=100, P1=$70
Q2=120, P2=$60

Plugging in the values:
Price elasticity of demand = [(120-100)/((120+100)/2)] / [(60-70)/((60+70)/2)]
= [20/110] / [-10/65]
= (-20/110) * (65/-10)
= 1.18

Therefore, the price elasticity of demand for memberships at this health club is 1.18, which means that a 1% decrease in price would result in a 1.18% increase in quantity demanded, indicating the demand is elastic.

A Health Club Sells 100 Memberships When the Monthly Price