Question:

A typical tennis player in West L.A. has the following demand for tennis lessons:

Q=200.5P

where Q is the number of overall lessons per month and P is the price for each lesson. A local tennis club is contemplating how to optimally charge for their lessons. The rent for the local courts is free. Assume that the only relevant cost to the club is the salary of coaches, which is $20 per hour. Each lesson takes one hour.

1. The tennis club is contemplating a monthly membership fee, plus (possibly) a charge per lesson for members. How should they design their profit-maximizing membership / charge-per-lesson package?
2. After a while, it becomes clear that there are really two types of tennis players: Those with regular jobs (Customer type 1) who will only book lessons after 5pm and 'freelancers' (Customer type 2) who book lessons all throughout the day and value the flexibility of being able to play any time. One of the tennis coaches, who is getting an MBA at UCLA, has estimated the following demand curves:

Type 1: Q1=150.4P1

Type 2: Q2=40P2

Assume that the club can directly distinguish between the two types and now wants to have separate offers for each type of player. What is the optimal membership / price-per-lesson package for players of type 1 and 2?

3. If the club cannot directly distinguish the two types, which problem could arise when offering the two pricing packages? Assume that freelancers value their flexibility to schedule tennis lessons any time during the day at $150 per month. Then, in practice, which policy could the tennis club implement to solve this problem and distinguish the two types of players?