Consider a perfectly competitive market with many homogenous exercise gyms. Exercise gyms have learned that customers tend to use the gym less often than the customer anticipated when she signed up. Specifically, if the marginal price per gym visit is set equal to p, suppose that consumers anticipate they will use the gym 2(1 - p) times, when in fact they will end up using it only 1 - p times. Each gym?s marginal cost per visit is c < 1. Competition between gyms means that a gym will offer the two-part tariff, with marginal price p and fixed membership charge A, which maximizes a consumer?s anticipated net surplus, subject to the gym breaking even.

(a) Assuming that negative prices are not feasible, show that a gym will set p = 0 and A = c so that there is no marginal charge for a visit.

(b) What two-part tari¤ would be o¤ered if all consumers accurately forecast their demand?