Question

The demand for personalised point-to-point passenger transportation (traditionally known as “taxi”)

service is given by

P = 100 − Q

where P and Q are the price ($ per hour) and quantity (in hours) of taxi service, respectively. There are infinitely many people who are willing to supply taxi service as long as they can get $30 per hour for driving a taxi. In other words, the market supply of taxi service is horizontal at P = 30.

All passengers and drivers in the taxi markets are price-takers. However, one must have a taxi licence in order to drive a taxi. The government issues taxi licences to the effect that at most 30 hours of taxi services can be provided to the market.

(a) What is the market price for an hour of taxi service? (b) Calculate the total value of all taxi licences.

Technological innovation has allowed consumers to hire a taxi service from drivers without a taxi licence through an app called “Umber”. For the remaining parts of the questions, assume that Umber cannot set a price for its drivers, nor does it charge any person (passengers and drivers alike) anything for using its app. Also assume that passengers consider the service from Umber drivers the same as that from drivers with a taxi licence.

At first, the government makes driving for Umber illegal. As such, Umber drivers need to spend an extra cost of c per hour to avoid being caught. In other words, there are infinitely many drivers who are willing to provide a taxi service through Umber for $(30 + c) per hour.

(c) Suppose c = 30. What is the new market price for taxi service? If taxi licence holders continue to charge the price you solved in part (a), would any passenger take a taxi from a taxi licence holder?

4. (d) What must c be in order for (at least some) passengers to take a taxi from a taxi licence holder?

5. (e)   Calculate the consumers’ surplus in the taxi market when c is at the the level you have calculated in part (d).

6. After some consideration, the government decides to legalise the use of Umber while imposing a per unit tax of $30 on taxi service (whether or not the driver holds a taxi licence). Umber drivers no longer have to pay the amount c

7. (f) Find the amount of tax revenue collected. Would the tax revenue be enough to compensate taxi licence owners for the amount they have paid for their licences (i.e., the amount you solved in part (b))?

8. (g) Calculate the consumers’ surplus in the taxi market under this per unit tax scheme. Is it higher, lower or the same as the amount you have calculated in part (e)?

Answer 1