Question

Suppose a firm owns a gym and is trying to determine the best pricing structure to use. The gym’s cost structure is C(Q) = 10, 000 + 15Q. There are two types of users: Heavy Gym users and Light Gym users. The individual demand curve for a Heavy user is qDH(P) = 400?10P and the individual demand for a Light user is qDL(P) = 125?5P. Suppose in the market there are 10 Heavy users and 5 Light users.

(a) Suppose the firm cannot tell the two types apart and offers a single price. What quantity will be offered and at what price? Would the gym have both types attending? Graph the solution. (b) How would this change if the gym decided to offer a two-part pricing strategy (assuming the gym cannot distinguish between the two groups)? Would the gym have both types attending (i.e. does the gym make higher profits excluding one group)? Would the gym prefer the pricing structure here or in part (a)?

(c) Suppose the gym can tell the two types apart. What would be the price and profits from group discrimination? Does the gym prefer this outcome to the previous parts? Why? (d) Show the two-part pricing solution when the gym can distinguish between the two types. How do profits compare with part (b) and part (c)?

Answer 1