Last semester there were 5,000 parking spaces available on campus.The price of a parking permit was $80 per semester,and the quantity demanded equaled the quantity supplied at this price.Suppose the number of parking spaces increases by 10% and the elasticity of demand for parking is 0.5.Parking Services should ________ the price of a permit by ________ to guarantee that quantity demanded will equal quantity supplied.
A) decrease; 10%
B) decrease; 20%
C) decrease; 5%
D) increase; 10%

Question

Quizplus · Accepted Answer

With a 10% increase in the number of parking spaces, the new total number of parking spaces available will be 5,500. However, with an elasticity of demand of 0.5, we can expect demand for parking to increase by only 5% (half of the 10% increase in supply).

Therefore, the new quantity demanded for parking will be:
5,000 x 1.05 = 5,250

To ensure that quantity demanded equals quantity supplied, Parking Services will need to decrease the price of a permit. Using the formula for price elasticity of demand:
% change in quantity demanded = % change in price x elasticity of demand
We can solve for the necessary % change in price:
5% = % change in price x 0.5
% change in price = 10%

Therefore, Parking Services should decrease the price of a permit by 20% in order to guarantee that quantity demanded will equal quantity supplied.

Last Semester There Were 5,000 Parking Spaces Available on Campus