Question

The city government is losing millions of dollars on its buses and subways. The government proposes to increase the fare by 20% to raise revenue and has asked for your advice. You know that the price elasticity of demand for mass transit in the city is approximately equal to 0.75. What do you think of the proposal to increase the fare to raise revenue for the city? Be as specific as possible.

Answer 1

Solution:

Price elasticity of demand = 0.75, which is inelastic.

Total revenue = price*quantity

So, percentage change in total revenue = percentage change in price + percentage change in quantity demanded

As price elasticity of demand = percentage change in quantity demanded/percentage change in price, with inelastic demand that is price elasticity of demand < 1, so

Percentage change in quantity demanded/percentage change in price < 1

Percentage change in quantity demanded < percentage change in price

So the percentage decrease in quantity demanded is less than 20%, implying that total revenue would increase. Mathematically, with given values and above formula, percentage change in quantity demanded = -0.75*20 = -15%

So, percentage change in total revenue = (-15) + 20 = +5%, so clearly total revenue will rise.

Economically, with an inelastic demand, since quantity demanded doesn't change much even with high change in prices as people cannot switch easily, it makes sense that high price would still capture enough demand to ultimately increase the revenue.