Econ 160 hw

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 − 1 q while members of

2

group 2 have individual inverse demand given by p2(q) = 20 − 1 q. (Because marginal cost is constant, you may 2

assume each group has just one member.)
Resale of the good among consumers is impossible.

1. (3 points) Suppose the monopolist offers just a single two-part tariff. Calculate the one that maximizes its profit. Calculate the associated profit.

2. (3 points) 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. (3 points) 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 TE0. Determine the profit-maximizing single package to offer. How does this profit compare with that in the two previous parts?

4. (3 points) 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, T E1) and those in group 2 will choose (q2, T E2).) Determine the profit-maximizing pair of packages to offer. Calculate the associated profit.