Answer to Question #222861 in Microeconomics for arpan

Question

Your finance officer has just advised you that the public transport 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.

i. Explain why the estimated values for price elasticity of demand differ.
ii. Compute what will happen to ridership and revenue over the next few months if you decide to raise fares by 5%.
iii. Compute what will happen to ridership and revenue over the next few years if you decide to raise fares by 5%.
iv. What happens to total revenue now and after several years if you choose to raise fares?

Answer 1

Solution:

i.). This is because at the beginning of the price change, the public transport system is scarce and hence the price elasticity of demand will be more inelastic due to the lack of many options considering that transport is a basic necessity. After a few years, there will be more public transport systems charging slightly lower prices, therefore the inelastic price elasticity of demand will fall a little.

 

ii.). The formula for point PEd = $\frac{\triangle Q }{\triangle P}$

PEd = -0.3

-0.3 =$\frac{\triangle Q }{5}$

ΔQ = 5 x -0.3 = -1.5%

ΔQ = -1.5%

This means that the quantity of ridership will fall by 1.5% while revenue will also fall by 1.5% over the next few months.

 

iii.). The formula for point PEd = $\frac{\triangle Q }{\triangle P}$

PEd = -1.5

-1.5 = $\frac{\triangle Q }{5 }$

ΔQ = 5 x -1.5 = -7.5$\%$

ΔQ = -7.5$\%$

This means that the quantity of ridership will fall by 7.5$\%$ while revenue will also fall by 7.5$\%$ over the next few years.

 

iv.). If you choose to raise fares, the total revenue now will decrease by 1.5$\%$, while it decreases by 7.5$\%$ after a few years.