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Consider a linear city whose (adult) population of 1 million is uniformly distributed over the interval [0; 5]. There is a monopoly operator of cinemas. The cost of building and operating a cinema is 500,000e per year. Marginal costof an additional cinemagoer is zero. Each inhabitant watches 36 movies a year as long as the price of a single attendance is below her maximum willingnessto pay of 10e minus her transport or inconvenience cost of jx yj if she has to move from her home at location x to the cinema at location y to watch themovie.
(a) How many cinemas should the monopoly operate, what will be the entrancefee, and where should the cinemas be located (if it is free to choose the location)?
(b) What is the socially optimal number of cinemas?
(c) Would the monopoly serve the whole market if the only location at whichit could operate cinemas is the city center (location 2.5)? Which price would it charge?
(d) Would the monopoly serve the whole market if the only location at which it could operate cinemas is outside of the city at location 1? Which price wouldit charge?
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