Reference no: EM131256040
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.
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