Suppose that demand for cruise ship vacations is given by P = 1200 - 5Q, where Q is the total number of passengers when the market price is P.
a) The market initially consists of only three sellers, Alpha Travel, Beta Worldwide, and Chi Cruiseline. Each seller has the same marginal cost of $300 per passenger. Find the symmetric Cournot equilibrium price and output for each seller.
b) Now suppose that Beta Worldwide and Chi Cruiseline announce their intention to merge into a single firm. They claim that their merger will allow them to achieve cost savings so that their marginal cost is less than $300 per passenger. Supposing that the merged firm, BetaChi, has a marginal cost of c < $300, while Alpha Travel's marginal cost remains at $300, for what values of c would the merger raise consumer surplus relative to part (a)?