We investigated different ways that you can price the use of amusement park rides in a place like Disneyland. We now return to this example. Assume throughout that consumers are never at a corner solution.
A: Suppose again that you own an amusement park and assume that you have the only such amusement park in the area - i.e. suppose that you face no competition. You have calculated your cost curves for operating the park, and it turns out that your marginal cost curve is upward sloping throughout. You have also estimated the downward sloping (uncompensated) demand curve for your amusement park rides, and you have concluded that consumer tastes appear to be identical for all consumers and quasilinear in amusement park rides.
(a) Illustrate the price you would charge per ride if your aim was to maximize the overall surplus that your park provides to society.
(b) Now imagine that you were not concerned about social surplus and only about your own profit. Illustrate in your graph a price that is slightly higher than the one you indicated in part (a). Would your profit at that higher price be greater or less than it was in part (a)?
(c) True or False: In the absence of competition, you do not have an incentive to price amusement park rides in a way that maximizes social surplus.
(d) This is true (as already illustrated above). Social surplus falls from (a + b + c + d + e) under p∗ to (a + b + d) under
. Thus, while profit increases, social surplus falls because consumers lose more than the increase in profit.
(d) Next, suppose that you decide to charge the per-ride price you determined in part (a) but, in addition, you want to charge an entrance fee into the park. Thus, your customers will now pay that fee to get into the park - and then they will pay the per-ride price for every ride they take. What is the most that you could collect in entrance fees without affecting the number of rides consumed?
(e) Will the customers that come to your park change their decision on how many rides they take? In what sense is the concept of "sunk cost" relevant here?
(f) Suppose you collect the amount in entrance fees that you derived in part (d). Indicate in your graph the size of consumer surplus and profit assuming you face no fixed costs for running the park?
(g) If you do face a recurring fixed cost FC, how does your answer change?
(h) True or False: The ability to charge an entrance fee in addition to per-ride prices restores efficiency that would be lost if you could only charge a per-ride price.
(i) In the presence of fixed costs, might it be possible that you would shut down your park if you could not charge an entrance fee but you keep it open if you do?
B: Suppose, as in exercise 10.10, tastes for your consumers can be modeled by the utility function u(x1, x2) = 10x0.5 + x2 , where x1 represents amusement park rides and x2 represents dollars of other consumption. Suppose further that your marginal cost function is given by MC (x) = x/(250, 000).
(a) Suppose that you have 10,000 consumers on any given day. Calculate the (aggregate) demand function for amusement park rides.
(b) What price would you charge if your goal was to maximize total surplus? How many rides would be consumed?
(c) In the absence of fixed costs, what would your profit be at that price?
(d) Suppose you charged a price that was 25% higher. What would happen to your profit?
(e) Derive the expenditure function for your consumers.
(f) Use this expenditure function to calculate how much consumers would be willing to pay to keep you from raising the price from what you calculated in (b) to 25% more. Can you use this to argue that raising the price by 25% is inefficient even though it raises your profit?
(g) Next, determine the amount of an entrance fee that you could charge while continuing to charge the per-ride price you determined in (b) without changing how many rides are demanded.
(h) How much is your profit now? What happens to consumer surplus? Is this efficient?
(i) Suppose the recurring fixed cost of operating the park is $200,000. Would you operate it if you had to charge the efficient per-ride price but could not charge an entrance fee? What if you could charge an entrance fee?