equalibrian, Microeconomics

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Imagine a country where plane and train services between two main cities are both provided by private companies, and, from a consumer perspective these services are viewed as substitutes.
The demand for plane trips is:
(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 income.
Assume the supply of plane trips by the aviation industry can be described by:
(2)
Where S1 is plane trips per year and the market clears so:
(3)
Assume average annual income, Y, is $75,000 and the price of train trips is P2 = $500. Further, assume the market always clears, there are no empty planes or theft of rides and producers are competitive. Ignore externalities such as anti-social behaviour and pollution.
Answer the following questions:

1. What is the equilibrium price of plane trips?
2. How many plane trips are provided and purchased?
3. Calculate the producer surplus for the plane trips providers (airways companies).

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