You run a sport club that offers fitness guidance by the hour.
Your cost is $40 per hour and you have no other costs.
You serve 2 types of customers in equal number: 100 youngsters and 100 seniors.
The weekly demand by each youngster is: q = 6 - 0.05P where q is the number of hours per week and p is the price per hour.
Each senior customer is willing to pay no more than $50 per hour, for the first 3 hours, and zero thereafter.
a. Since you can distinguish between the customers, you have decided to set different prices to different customers. What price will you charge the seniors? How many hours will they buy? What price will you charge the youngsters? How many hours will they buy? What will your profit be in this case?
b. Now suppose that you have decided to change your pricing policy and to sell each customer a weekly card that indicates the maximum number of hours he/she can spend in the club, during the week. Since you can distinguish between the youngsters and the seniors, you can sell different customers different cards with a different number of hours and different prices. What price and how many hours will you set for a young client? What price and how many hours will you set for a senior client? What will your profit be in this case?
c. Instead, you have decided to use TPT for each group (charging an entry fee plus a price per hour). What prices should you set for each group? For how many hours will each customer use the club? What will your profit be in this case?
d. How would your answers to part c above change, if you could still use a TPT strategy but you could not discriminate between the customers?
e. Might your answers to part d above change had there been more seniors customers?