A monopolist with constant marginal cost of 4 (MC 4) to just two consumer types,

Question

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 2 q while members of group 2 have individual inverse demand given by p2(q) = 20 1 2 q. (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, T E0). 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, T E1) and (q2, T E2). Accordingly a consumer has the choice of buying nothing or buying exactly q1 units for a total expediture of T E1 or buying exactly q2 units for a total expediture of T E2. (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.

Explanation / Answer

Answer for Part 4)

Since the monopolist will want to maximise profits in both markets - he will equate MR = MC in both markets.

Hence the calulations are as follows:

1. TR in Market 1 = Price in Mkt 1 *Qty in Market 1 = 5 (solving for the equation MR = MC)

2. TC is assumed to 4*Q1 since MC is constant - hence each additional Quantity adds only 4 units to cost

therefore, Price in Market 1 = .5

Eqm in Market 1 = (p1,Q1)= (.5,5) and associated profit = .5

3. Similar working for market 2 shows that equillibrium is attained at (P2, Q2) at (12,2/3) and associated profit = 5.33

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