Question 2.

Bulldog Gym is an up-market gym located near Imperial College London, that is frequented

both by students and members of the general public. It tends to be particularly busy during

certain hours (peak times) and less so at other times (off peak times). It has been estimated

that the demand for gym personal training sessions is as shown in the table below (P denotes

the price of a personal training session):

General public | Students

Off-peak 280 -2P| 240 -4P

Peak 680 - 2P | 200 - 4P

The marginal cost of an additional personal training session to the gym is zero. However, the

social distancing rules imposed during the Covid-19 pandemic have limited the capacity of the

gym to 280 personal training sessions in either time period. So no more than 280 person

training sessions can be booked at either peak or off peak times.

(a) Can Bulldog Gym charge a different price to different gym users? If yes, how? [6 marks]

(b) Find the profit maximizing prices for students and for the general public, both for peak

and off-peak times. [12 marks]

(c) Bulldog Gym has a contract with Stop Virus, a firm that deep cleans the gym according

to Covid-19 pandemic regulations. Stop Virus cleans at both off-peak and peak times.

The owner of Stop Virus argues it is more expensive to clean the gym when it is used by

more people. Bulldog Gym agrees to pay Stop Virus 1/4Q2 for cleaning at a given time,

where Q is the total number of gym users at that time (peak or off-peak).

What are the new profit maximising prices for students and for members of the general

public using the gym off-peak? Hint: find the optimal number of gym users at off-peak

times. [12 marks]