Question

Imagine a country where plane and train services between two main cities are both completely provided by private companies, and, from a consumer perspective these services are perceived as substitutes. The demand for plane trips services is:

?1 = 3,000 − 200?1 + 30?2 + 2?

(1) Where D1 is annual demand for plane trips, P1 is price of plane trips, P2 is price of train trips and Y is average annual consumer income. Assume the supply of plane trips by the industry can be described by:

?1 = 300?1

(2) Where S1 is the number of plane trips, and the market clears so:

?1 = ?1

(3) Assume the average annual income, Y, is $80,000 and the price of train trips is P2 = $500. Further, assume the market always clears, there are no empty planes and trains, and producers are competitive. Ignore externalities such as pollution.

Assume the government puts a $120 tax on each plane trip, which is levied on airline companies. Answer the following questions:

1. What is the new price of plane trips to consumers? (5 Marks)

2. What is the new price of plane trips to airline companies? (5 Marks)

3. How many plane trips are now supplied and bought? (5 Marks)

4. Present the relevant diagram. (5 Marks)

5. How much tax revenue is raised? (5 Marks) Section C (25 Marks)

Answer 1

D1 = 3,000 - 200P1 + 30 x 500 + 2 x 80,000 = 3,000 - 200P1 + 15,000 + 160,000 = 178,000 - 200P1

S1 = 300P1

In pre-tax equilibrium, D1 = S1

178,000 - 200P1 = 300P1

500P1 = 178,000

P1 = 356

Q1 = 300 x 356 = 106,800

(1)

After tax, new supply curve is

S2 = 300 x (P - 120) = 300P - 36,000

Setting D1 = S2,

178,000 - 200P = 300P - 36,000

500P = 214,000

P = 428 (Price paid by buyers)

(2)

Price received by sellers = 428 - 120 = 308

(3)

Q = 178,000 - 200 x 428 = 178,000 - 85,600 = 92,400

(4)

In following graph, D0 and S0 are initial demand and supply curves intersecting at point E with price P0 (= $356) and quantity Q0 (= 106,800). When the tax shifts supply curve leftward to S1, it intersects D0 at point F with higher price P1 (Price paid by buyers = $428) and lower quantity Q1 (= 392,4009.67). Price received by sellers is P2 (= $308). Tax revenue equals area P1FGP2.

P Si So А E Pi Po 22 Do B 0 91 go

(5)

Tax revenue = 120 x 92,400 = 11,088,000