We suggested in the text that there may be technological reasons for the barriers to entry required for the existence of monopoly. In this exercise, we consider two examples.
A: Microsoft and your local utilities company have one thing in common: They both have high fixed costs and low variable costs. In the case of Microsoft, the fixed cost involves producing software which, once produced, can be reproduced cheaply. In the case of your local utility company, the fixed cost involves maintaining the infrastructure that distributes electricity to homes, with the actual delivery of that electricity costing relatively little if the infrastructure is in good shape.
(a) Let’s begin with Microsoft. Draw a graph with low constant marginal costs and a downward sloping demand curve. Add Microsoft’s marginal revenue curve and indicate which point on the demand curve Microsoft will choose (assuming, until later chapters, that it is not worried about potential competitors). Then draw a second and similar graph for your local utilities company.
(b) There is one stark difference between Microsoft and your local utilities company: Microsoft has not asked the government for help to allow it to operate but has instead been under strict scrutiny by governments around the world for potential abuse of its market power. Utility companies, on the other hand, have often asked for government aid in regulating prices in such a way that the companies can earn a reasonable profit. What is missing from your two graphs that can explain this difference?
(c) Put into words the “problem” in the two cases from a government’s perspective (assuming the government cares about efficiency)?
(d) In the case of Microsoft, how can the granting of a copyright on the software explain the existence of “the problem”? How much is Microsoft willing to pay for this copyright?
(e) Now consider the “problem” in the utilities industry. How would setting a two-part tariff allow the utilities company to produce at zero profit? If properly structured, might its output level be efficient?
(f) Explain how the alternative of having the government lay and maintain the infrastructure on which electricity is delivered could address the same “problem”.
(g)What would be the analogous government intervention in the software industry— and why might you think that this was not a very good idea there? Could you think of a way to offer a similar criticism regarding the proposal of having the government provide the infrastructure for electricity delivery?
B: We did not develop the basic mathematics of natural monopolies in the text and therefore use the remainder of this exercise to do so. Suppose demand for x is characterized by the demand curve p(x) = A –α x. Suppose further that x is produced by a monopolist whose cost function is c(x) = B +β x.
(a) Derive the monopolist’s profit maximizing supply point—i.e. the price and quantity (pM ,xM)under the implicit assumption of no price discrimination.
(b) At the output level xM, what is the average cost paid by the monopolist?
(c) How high can fixed costs be and still permit the monopolist to make non-negative profit by choosing the supply point you calculated in (a)?
(d) How much is Microsoft willing to pay its lawyers to get copyright protection?
(e) Suppose both Microsoft and your local utility company share the same demand function.
They also share the same cost function except for the fixed cost B. Given our description of the “problem” faced by Microsoft versus your utility company, whose B is higher?
(f) Suppose B for the utility company is such that it cannot make a profit by behaving as you derived in (a) and suppose there are N households. Suggest a two-part tariff that will allow the utility company to earn a zero profit while getting it to produce the efficient amount of electricity.
(g) Suppose the government were to build and maintain the infrastructure needed to deliver electricity to people’s homes. It furthermore allows any electricity firm to use the infrastructure for a fee δ (per unit of electricity that is shipped). Can the electricity industry be competitive in this case? What has to be true about the fee for using the infrastructure in order for this industry to produce the efficient level of electricity?