Question

Suppose the demand for crossing the Chargem Bridge is given by Q = 10,000 – 1,000P where P is in $/car and Q is the number of cars per day.

1. If the toll (P) is $2/car, how much revenue is collected daily?

2. What is the price elasticity of demand at this point?

3. Could the bridge authorities increase their revenues by changing their price?

4. The Crazy Canuck Lines, a ferry service that competes with the Chargem Bridge begins operating hovercrafts that make commuting by ferry much more convenient. How will this affect the elasticity of demand for trips across the Chargem Bridge?

Answer 1

A)if p=2$

Then Q=10,000-1000*2=8000

Total revenue=2*8000=16,000

B) elasticity of Demand=(∆Q/∆p)*(P/Q)

∆Q/∆p=-1000

Q=8000

P=2

Elasticity of demand=(-1000)*(2/8000)-2000/8000=-0.25

So demand is inelastic.

C)When demand is inelastic ,which means Percentage change in quantity will be lower than perfect change in price, which means increase in price will result in relatively lower Decrease in quantity. as a result total revenue will increase ,when price increase .

So authority can increase total revenue by increasing price.

For example if they increase price to 3$

Q=10,000-1000*3=7000

Total revenue=3*7000=21,000

D) Because of this now , there will be a substitute of Chargem Bridge, which result in increase in elasticity of demand at all prices, means demand is now more relatively elastic.

Increase in price of toll will decrease real income of users ,so quantity demanded will decrease.

But now there is additional substitution effect, increase in price toll will make Crazy Canuck Lines relatively cheaper,so Consumer will shift to crazy Canucks lines ,so quantity demanded will decrease more.

So demand of chargam bridge will become more elastic.