Question

You are now ready to play the part of the manager of the public transit system. Your finance officer has just advised you that the system faces a deficit. Your board does not want you to cut service, which means that you cannot cut costs. Your only hope is to increase revenue. Would a fare increase boost revenue? You consult the economist on your staff who has researched studies on public transportation elasticities. She reports that the estimated price elasticity of demand for the first few months after a price change is about −0.3, but that after several years, it will be about −1.5. Explain why the estimated values for price elasticity of demand differ. Compute what will happen to ridership and revenue over the next few months if you decide to raise fares by 5%. Compute what will happen to ridership and revenue over the next few years if you decide to raise fares by 5%. What happens to total revenue now and after several years if you choose to raise fares?

Answer 1

Price elasticity of demand = % Change in Qty demanded / % Change in Price

Let us assume that at present Price is 100 and Qty. demanded is 100. So after 5% increase price will be 105. Now given that

in short term price elasticity is 0.3.

So, 0.3 = x/ 5
x = 0.3 * 5 = 1.5. Thus qty demanded is changed by 1.5 % in short term. So new qty will be 98.5.

Short term Revenue after price change = 105* 98.5 = 10342.5

in long term price elasticity is 1.5.

So, 1.5 = x/ 5
x = 1.5 * 5 = 7.5. Thus qty demanded is changed by 7.5 % in long term. So new qty will be 92.5.

Long term Revenue after price change = 105* 92.5 = 9712.5

Thus in short term revenue increases whereas in long term it will decrease.

This happens because in the short term some people stick to the old ways because they dont have an alternate so change in qty demanded is lesser as compared to change in price whereas in the long term people have time to find an alternate thus percentage change in qty demanded decreases as compared to price.