QUESTION C2 20 marks total The demand for personalised point

QUESTION C2 (20 marks total) 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) (2 marks) What is the market price for an hour of taxi service? (b) (3 marks) 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) (3 marks) 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? (d) (2 marks) What must c be in order for (at least some) passengers to take a taxi from a taxi licence holder! e) (3 marks) Calculate the consumers\' surplus in the taxi market when c is at the the level you have calculated in part (d)

Solution

C2. a) The demand for taxi services is given as:P=100-Q

The taxi market in this case is highly competitive and the taxi drivers are willing to enter the market as long as they can earn a minimum of $30 per hour making the supply curve of taxi in the market horizantal or perfectly elastic.Therefore,the market price is fixed at $30 per hour and the equilibrium quantity or the hours of the taxi service is determined by the intersection of the demand and supply curve of taxi service in the market.

b) Now,the government issues licenses once a total of 30 hours taxi services have been rendered to the market.Hence,the total quantity of taxi services or Q is 30 to obtain a license in the market.

Hence,plugging Q=30 into the demand function,we get:-

P=100-Q

P=100-30

P=70

Thus,when 30 hours of taxi service is provided the market price is $70 per hour of service.

Total monetary value generated from all the taxi licenses=($70*30)=$2100

c) With the introduction of Umber,the drivers have to pay an extra cost c per hour to avoid being cost.Thus,now with high competition in the market,the drivers will enter the market as long as they can earn $(30+c) per hour.Therefore,ideally the supply of taxi now becomes $(30+c) per hour.

Now,when c=30 the minimum market price that the drivers would accept to enter the market=($30+$30)=$60

Hence,after the introduction of Umber and an additional cost to drivers to avoid being caught,the market price for taxi services or P will be $60.

Now,when new market price is 30 or P=30 as solved in part a) into the demand function for taxi services,we get:-

P=100-Q

30=100-Q

30-100=-Q

-70=-Q

70=Q

Notice that when the market price for taxi services is $30 as calculated in part a),the quantity demanded for hourly taxi services is 70 hours of taxi services.

d) After the launch of the Umber,we have already seen that the market price for taxi services becomes P=$(30+c)

Based on the market equilibrium condition of demand and supply we can state that:-

100-Q=(30+c)

100-Q=30+c

100-Q-30=c

70-Q=c and Q=70-c

Thus,at the equilibrium the minimum value of c is calculated as 70-Q for at least some passengers to avail the taxi from license holders.

d) Now,assuming that P=0 in the demand equation,we obtain:-

P=100-Q

0=100-Q

-100=-Q

100=Q

Again,if Q=0 in the demand equation,we get:-

P=100-Q

P=100-0

P=100

At equilibrium the market price of taxi service is P=$(30+c) and Q=70-c

Thus,Consumer Surplus in this case=0.5(70-c){100-(30+c)}

=0.5(70-c)(100-30-c)

=0.5(70-c)(70-c)

=0.5(4900-70c-70c+c^2)

=0.5(4900-140c+c^2)

=2450-70c+c^2/2