5. Water Hyperwonderland, a theme park that features dolphin shows, estimates th

Question

5. Water Hyperwonderland, a theme park that features dolphin shows, estimates that the typical customer who likes the shows enough to want a season discount card has an annual demand curve represented by the equation Q = 18-P, where P is the price charged per admission and Q is the number of times per year the person will visit the park. The park's marginal cost per visit for any type of client is $2. Based on the d curve, to maximize profit from discount-card customers, what should be (a) the price of a season discount card and (b) the per-visit ticket price for a discount card holder? Explain your answer. (10 points)

Explanation / Answer

Profit is maximized by equating Marginal revenue (MR) with MC.

Q = 18 - P

P = 18 - Q

(a)

Total revenue (TR) = P x Q = 18Q - Q2

MR = dTR / dQ = 18 - 2Q

Equating MR & MC,

18 - 2Q = 2

2Q = 16

Q = 8

(b) When Q = 8,

P = 18 - 8 = $10

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