Accordingly a consumer has the choice of buying nothing or

Question

Problem Set

Instructions: Answer all questions and show your work.

Be sure to put all group members' names on the solution set for your study group.

A monopolist with constant marginal cost of 4 (MC ≡ 4) to just two consumer types, which are of equal size n. Members of group 1 have individual inverse demand curve given by p₁ (q) = 16 - ½q while members of group 2 have individual inverse demand given by p₂ (q) = 20 - ½q. (Because marginal cost is constant, you may assume each group has just one member.)

Resale of the good among consumers is impossible.

1. Suppose the monopolist offers just a single two-part tariff. Calculate the one that maximizes its profit. Calculate the associated profit.

2. Suppose the monopolist can not tell whether a person is in group 1 or group 2. So it offers a pair of two-part tariffs and lets each consumer buy according to the one he or she prefers. Calculate the profit-maximizing pair of two-part tariffs for the monopolist to offer. Calculate the associated profit.

3. Suppose the monopolist offers just a single package for sale, described as (q₀ , TE₀ ). Accordingly a consumer has the choice of buying nothing or buying exactly q₀ units for a total expediture (payment from that consumer) of T E₀ . Determine the profit-maximizing single package to offer. How does this profit compare with that in the two previous parts?

4. Suppose the monopolist offers two packages for sale, described as (q₁ , TE₁ ) and (q₂ , TE₂ ). Accordingly a consumer has the choice of buying nothing or buying exactly q₁ units for a total expediture of TE₁ or buying exactly q₂ units for a total expediture of TE₂ . (The monopolist envisions that those in group 1 will choose (q₁ , TE₁ ) and those in group 2 will choose (q₂ , TE₂ ).) Determine the profit-maximizing pair of packages to offer. Calculate the associated profit.