Public Finance, 2nd Edition

The chapter concluded by pointing out that the United States tends to

favor average-cost pricing rather than marginal-cost pricing for the decreas-

ing-cost services. The public apparently views average-cost pricing as being

fully consistent with the beneWts-received principle of public pricing and

therefore more equitable. In contrast, mainstream public sector theory has

no use for the beneWts-received principle as an equity principle.

Chapter 21 extends the analysis of decreasing cost Wrms by considering a

common property of these Wrms that Chapter 9 ignored: They are often

multiproduct Wrms that oVer a variety of services to diVerent customers

(e.g., the U.S. Postal Service and most public utilities).

THE BOITEUX PROBLEM: THE MULTIPRODUCT DECREASING-

COST FIRM

We begin with an analysis of the multiproduct, decreasing-cost Wrm de-

veloped by Marcel Boiteux in the 1950s.

2

Boiteux's analysis is one of the

seminal contributions to second-best public expenditure theory. He is as

closely associated with the decreasing-cost Wrm as Paul Samuelson is with

the nonexclusive public good.

Boiteux considered the optimal pricing and investment rules for multi-

product decreasing-cost monopolies that are required to raise a given amount

of revenue. His model is particularly appropriate for the United States. When

faced with multiproduct decreasing-cost Wrms, the U.S. regulatory agencies

simply extend their average-cost pricing philosophy to them. They require

that the Wrm's total revenue equal its total cost across all the products in the

aggregate rather than for each product individually. The total cost includes

an allowable return to capital. Requiring that total revenue equal total cost

(or any other arbitrary amount as in the Boiteux model) renders the analysis

second best. The Wrm's total revenue would be less than its total cost in a Wrst-

best environment.

Chapter 9 would have had to add one other good to show this formally, but it was clear from the

previous analysis of externalities in Chapters 6±8 that marginal cost pricing of all other goods is

pareto optimal.

2

M. Boiteux, ``On the Management of Public Monopolies Subject to Budgetary Con-

straints,'' Journal of Economic Theory, September 1971 (translated from the original in French,

Econometrica, January 1956). Jacques Dreze presents a useful interpretation of Boiteux's results

in J. Dreze, ``Some Post-War Contributions of French Economists to Theory and Public Policy,''

American Economic Review, June 1964 (suppl.), pp. 27±34. Our analysis closely follows these

two papers. We would also recommend W. Baumol and D. Bradford, ``Optimal Departures

from Marginal Cost Pricing,'' American Economic Review, June 1970, for an excellent intuitive

discussion of the Boiteux problem, including its relationship to the optimal tax literature.

The article also presents a brief historical account of the early second-best price and tax

literature.

680 THE BOITEUX PROBLEM: THE MULTIPRODUCT DECREASING-COST FIRM