You own the only fitness center in town. You are contemplating your pricing strategy for annual memberships to the center. You suspect that the demand you face for memberships is substantially different for senior citizens (over 60 years of age) than for younger potential members. You do some survey work and estimate the following (inverse) demand curves per year for these distinct markets:
Where P refers to prices charged to each group and Q refers to quantities demanded by each group. The total costs of your annual operation are given by:
a. If you decide to offer annual memberships for sale to everyone at a single price, at what price will seniors be priced out of the market?
b. What is the market demand function if you decide to offer memberships for sale to everyone at a single price?
c. If you decide to offer memberships for sale to all at a single price, what price will you charge and how many memberships will you sell? How many of the memberships will be bought by individuals in each group?
d. If you decide to offer memberships for sale to each group at different prices (i.e., engage in third-degree price discrimination), what price will you charge each group and how many memberships will each group buy?