Nathan sells gourmet hot dogs. His customers have identical inverse demands, given by P = 5 − .25Q. Nathan can produce hot dogs at a constant marginal and average cost of $1.
a. If Nathan operates as a single-price monopolist, what price should he set? How many units will he sell? What will his profits be?
b. Suppose Nathan decides to create a hot dog club where members pay an annual enrollment fee and are then entitled to buy as many hot dogs as they wish at a fixed price. If Nathan chooses a fixed price of $2.00 per hot dog, what is the maximum membership fee he will be able to charge his customers? How much profit will Nathan earn from each customer? (Hint: Add Nathan's profits from selling hot dogs to the membership fee.) How do Nathan's profits compare to what he earned in (a)?
c. If Nathan chooses a fixed price of $1.00, what membership fee will he be able to charge his customers? What will his overall profits be?
d. Can Nathan increase his profits by charging a super-high admission fee and giving away hot dogs to members for free?
e. Generalize a rule about the per-unit price and membership fee that will maximize profits for a seller implementing a two-part tariff.