I’d like some help on this microeconomics question.
There are 5 competing petrol stations over a 100 mile stretch of road (Shell, BP, Texaco, Esso and Gulf), each setting their price for unleaded petrol daily. The managers of these stations consider tacitly colluding to set a higher price for unleaded petrol. As the quality of the unleaded petrol is identical, they know that any station that undercuts will win the market.
The stations estimate that the daily demand for petrol on this road is Q = 50,000 – 25,000P, where P denotes the price per litre of unleaded petrol and Q is liters of unleaded petrol. The marginal cost of providing petrol is £1 per litre for all firms.
(a) If the stations were to interact only once (compete on one day only), what price would you expect to prevail for unleaded petrol along the stretch of road? Explain your answer.
(b) Compute the price that would be charged for unleaded petrol if the market were a monopoly. How many litres of petrol would the monopolist sell daily and what profits would he make?
(c) Now suppose stations interact indefinitely. They wish to collude to price unleaded petrol at the monopoly level. Suppose station managers have a discount factor of δ = 0.7. There is an understanding that if any petrol station undercuts, the rest will punish by reverting to the price set in (a) forever. Is collusion sustainable amongst the 5 stations? What is the maximum number of stations that could sustain collusion?