Bordeaux route under threat of entry

Knowing the growing importance of Bordeaux's corporate sector and the city's growing influence in hosting expositions and conferences, we were the first airline to offer a direct flight from Dubai to Bordeaux. Having a monopoly over the direct route, we have enjoyed strong profits to date. As a monopoly, our inverse demand for the flight route is P=3,000-5Q and our cost associated with the flight is C(Q)=150,000+100Q. We are currently charging $1,400 on average for a seat in our main cabin and we typically sell around 320 tickets per flight. Profits generated per flight exceed $265,000.

For your first task, please check if we are currently optimizing our monopoly price for profits at $1,400. I wonder if there is more willingness to pay than we are extracting.

We are not the only ones focusing on profits, our competitors have taken notice and are potentially planning entry. Specifically we think that Etihad Airways will make a play on a similar route from Abu Dhabi to Bordeaux. If Etihad enters, we will have to change our strategy in pricing under the Cournot Duopoly. To avoid this route competition we have inquired about purchasing the route rights before our competitors, but it comes with a sizeable fee of $200,000 per flight. Let me know if you think the cost is worth it to protect our monopoly on the route.

Our accounting department tells me that Etihad's costs are predictably in line with our costs, so our best estimate is to assume that they have the same cost structure as ours. Furthermore, the underlying daily market demand that we are enjoying today as the sole provider will not be altered once Etihad enters, so keep the given inverse demand function constant in your analysis of the Cournot competition as well.

Give me a best estimate of how much our profits will suffer if Etihad enters the market, and that would give me a good idea of whether or not buying the route rights from Abu Dhabi would be worth it.