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Imagine an amusement park with a sole attraction: a roller coaster. For simplicity, the cost of providing a ride is zero. There is a single consumer with demand for rides on the roller coaster given by P(Q)=1 - Q. Let the park not only charge a price p per ride but also an access fee F at the entrance.
(a) What is the pro?t maximising combination of p and F? Illustrate graphically. [Hint: ?rst, for a given price per ride p, how much is the consumer willing to pay to access the roller coaster - you know a measure for that, and this will be the optimal ?xed fee for any given p,say F(p). Looking at the corresponding pro?ts, you will see what the optimal p is.]
(b) What kind of price discrimination is this (?rst, second or third degree)?
(c) Is there still an ineffciency?
(d) Do your answers change if there are instead many, say e. g. 100, identical consumers with the given demand?
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