Question 1: A monopolist provides service to two customers, 1 and 2. Their inverse demand curves are given by P(Q1) = 5 - Q1 and P(Q2) = 4 - Q2, respectively. The monopolist's marginal costs of production are zero, but it incurs fixed costs of F per period of operation.
a) What is the largest value of F such that it is socially worthwhile to provide this service?
b) Suppose the monopolist is limited to charging a non discriminatory uniform price. What is the largest value of F that can be covered by the revenues collected by the monopolist?
c) Suppose the monopolist can engage in 3rd Degree price discrimination.
That is, he can charge each customer a different uniform price. What is the largest value of F that can be covered by the revenues collected by the monopolist?
d) Now suppose the monopolist use a simple two part tariff. That is, each customer pays the same fixed fee e and usage charge p. What is the largest value of F that can be covered by the revenues collected by the monopolist?
e) Next, suppose the monopolist is allowed to offer discriminatory two part tariffs. That is, he can charge customer 1 the fixed fee and price combination (e1,p1) while charging customer 2 the combination (e2,p2). What is the largest value of F that can be covered by the revenues collected by the monopolist?
f) Suppose that the monopolist is allowed to offer a menu of two part tariffs. That is, he can offer each customer a choice between two tariffs, (e1,p1) and (e2,p2). However, the tariffs must be incentive compatible: i.e., each customer (at least weakly) prefers the tariff designed for him to the other tariff. What is the largest value of F that can be covered by the revenues collected by the monopolist?
g) Finally, assume that the monopolist can offer a general non linear tariff schedule. Since there are only two types of consumers, this just requires choosing two incentive compatible and individually rational outlay and quantity options (r1,Q1) and (r2,Q2). What is the largest value of F that can be covered by the revenues collected by the monopolist?
h) What is the largest value of F that allows the monopolist to cover its costs with a general non linear tariff and still achieve the 1st Best allocation?
Question 2: A regulated monopolist invests in a sunk asset that will provide services during period 1 and period 2, at which point the asset will become worthless. The purchase price of the asset is 4000. Once in place, the asset can provide unlimited quantity each period at a marginal cost of zero. The demand for the services provided by the asset are given by Q(p) = 120 - p. This demand curve is assumed to be the same in each period. For simplicity, assume that the interest rate (fair rate of return) is zero.
a) Find the prices p1 and p2 that will maximize the discounted present value (here, just the simple sum) of total surplus over the life of the asset subject to the condition that the firm recovers its investment cost.
b) What are the Economic Depreciation charges associated with those optimal prices? Now suppose that a new technology will allow entrants to serve the market at a constant unit operating cost of 10 without requiring any sunk costs. However, this technology will not be available until period 2.
c) Is it socially desirable for entrants to provide service during period 2?
Explain why or why not.
d) What are the optimal (surplus maximizing) prices that will prevent entry in period 2 yet allow the firm to recover its investment?
e) What are the Economic Depreciation charges associated with these optimal entry preventing prices?
f) Explain why it may sometimes be desirable to prohibit entry during the lifetime of sunk assets.
(Your explanation should include calculations of the total surplus obtainable with and without such entry prohibitions.)