Microeconomics: price discrimination or not?

Question Description

I need help with this question in my assignment for Microeconomics as I am simply not sure where to start.. I’m not expecting anyone to solve the question for me, but I would appreciate guidance on where to start and how to think 🙂

Bulldog Gym is an up-market gym located near X 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 ¼Q² 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]

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