3. Pricing Strategy of a Monopoly (26%)

Planet Gym is the only gym in town. Providing a session of workout to a customer is at a marginal cost of $c$. This marginal cost is perfect information. The gym is large enough so that even in peak hours there is no externality between the customers.¹

Planet Gym has two forms of feasible pricing strategies. It can set a uniform price per session for all customers with free entrance, or it can set a two-part tariff with a membership fee and a price per session conditional on paying the membership fee.

The market demand of gym session at price $p$ per session is $q = \Delta - \delta \cdot p$. The market demand is perfect information. To guarantee existence of an equilibrium, assume that $\Delta > \delta \cdot c$.