Question 2. You manage Flying Scotsman, a small rail company connecting London to Edinburgh. You determine that the demand for a one-way ticket to Edinburgh from Seniors (> 60 years of age) and from the rest of the population is:

General public Seniors

Off-peak 280 -2P 240 -4P

Peak 680 - 2P 200-4P

P denotes the price of the one-way ticket. The marginal cost of an additional passenger is zero, but the train only has a capacity of 280 seats. No standing passengers are permitted so the maximum number of tickets sold is 280.

(a)Can you charge a different price to different markets of passengers? If yes, how?

(b)Find the profit maximizing prices for Seniors and for the general public both for peak and off-peak travel.

(c)Flying Scotsman has a contract with Scottish Shine, a firm that cleans the train in Edinburgh after passengers disembark. Initially, Flying Scotsman pays Scottish Shine a fixed fee for their services. Upon renewal of the contract, the owner of Scottish Shine argues it is more expensive to clean trains with more passengers. You agree to pay Scottish Shine Q² for cleaning, where Q is the total number of passengers who travelled on the train.

What are the new profit maximising prices for Seniors and for the general public travelling off-peak? Hint: find the optimal number of passengers in an off-peak train.