Two-Part Pricing

The San Diego Tennis & Racquette Club has asked Rachel Green to devise a profit-maximizing pricing strategy. In doing so, Green knows that a typical player will want to play 15 hours per season if court time costs $25 per hour. On average, this demand falls by 21/2 hours for each $10 increase in the price of court time. These data suggest the following demand and marginal revenue relations:

P = $85 - $4Q

MR = DTR/DQ = $85 - $8Q

where P is the price of 1-hour court time on the club's indoor tennis court, and Q is the number of hours of court time an individual player of average talent would demand during the tennis season. For simplicity, assume that the marginal cost of 1 hour of court time is $5 and that fixed costs are nil. This gives the following total and marginal cost relations:

TC = $5Q

MC = DTC/DQ = $5

A. Calculate the profit-maximizing price, output, profit level, and consumers' surplus assum- ing a per-unit price is charged each customer.

B. Calculate the profit-maximizing price, output and profit level assuming a two-part pricing strategy is adopted for each customer.

C. Now assume that fixed costs of $500,000 are incurred, and 1,000 customers are attracted when an optimal two-part pricing strategy is adopted. Calculate total profits.