2. Alice is about to open her newest amusement park, Amuse World. Amuse World fe

Question

2. Alice is about to open her newest amusement park, Amuse World. Amuse World features a number of exciting attractions: you can ride the rapids in the Blue Suede Chutes, climb the Jailhouse Rock and eat dinner in the Heartburn Hotel. Alice figures that Amuse World will attract 2,000 people per day, and each person will take 50-25p rides, where p is the price of a ride. Everyone who visits Amuse World is pretty much the same and negative rides are not allowed. The marginal cost of a ride is essentially zero. (a) Write down Alice's profit maximizing problem (b) How many rides will be taken per day by a typical visitor? At what price? Calculate Alice's total profits. (c) If Alice decided to use a two-part tariff, what will an admission fee be? What about a price per ride? (d) Which one will Alice prefer between the single price and the two-part tariff? Explain

Explanation / Answer

a) Profit is given by = TR - TC

Here demand function is p = 2 - (1/25)x and so TR = 2x - (1/25)x^2. TC = 0 because MC = 0 and ther are no fixed cost

Then profit maximization implies MAX =  2x - (1/25)x^2

b) Since TR is maximzied when MR = 0, we have 2 - (2/25)x = 0

This gives x = 25 and p = $1. At this stage, profit = 2000 x 1 x 25 = $50,000

c) Two part tariff has only admission fee because MC = 0 so P = 0. This fee is the consumer surplus at P = 0. From demand function we see that when p = 0,x = 50. Hence admission fee = 0.5*(2 - 0)*50 = $50. This is the admission fee per person. Profits are $50 x 2000 = $100,000

d) Two-part tariffs as her profit is doubled using this strategy.

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