Public Finance, 2nd Edition

entire output must be produced by a single Wrm. This is why decreasing cost

industries are referred to as ``natural monopolies'' and why they necessarily

violate the technological assumption of well-behaved production required for

a well-functioning competitive market system.

Chapter 9 explores the pareto-optimal conditions for eYcient production

with decreasing cost industries. It shows why the competitive market system

cannot achieve them and considers the pricing and investment rules implied

by the eYciency conditions. The pricing rules imitate standard competitive

principles and are therefore relatively straightforward. The investment rules

are far from standard, however. Investment in decreasing cost industries has

a lumpy, all-or-none quality to it that is absent in the usual marginal invest-

ment analysis applied to the small competitive Wrm. Also, proWtability is not

necessarily a reliable investment guideline for decreasing cost services, and

there may not be any other practicable criteria to determine whether an

investment in these services is worthwhile. As a result, investment decisions

for these industries are frequently among the more diYcult decisions the

government has to make, even under the simplifying assumptions of Wrst-

best theory.

The chapter concludes with a discussion of actual U.S. policy with

respect to the decreasing cost services. Governments in the United States

have not embraced the Wrst-best price and investment decision rules for

decreasing cost services. They tend to favor some form of average cost pricing

and the standard private-sector proWtability criteria for investment decisions,

neither of which is pareto optimal. The policy discussion speculates on the

popularity of these policies and analyzes their properties relative to the Wrst-

best decision rules.

DECREASING COST IN GENERAL EQUILIBRIUM ANALYSIS

The problems caused by a decreasing cost natural monopoly are directly

related to the particular form of its production function, nothing more.

Therefore, the general equilibrium model required to analyze decreasing cost

production can be extremely simple. There is no need to model explicitly the

interrelationships among consumers or producers, unlike in the analysis of

externalities. Also, the model can exploit the dual dichotomies of all Wrst-best

models. The demand side of the model can be adequately represented by a

single consumer. Were the model to include many consumers and a social

welfare function, the Wrst-order conditions would merely reproduce the inter-

personal equity conditions and the pareto-optimal consumption conditions of

the full model in Chapter 2. Assuming optimal redistributions implies a one-

consumer equivalent economy. Similarly, positing many ``well-behaved''

Wrms would reproduce the standard pareto-optimal production conditions

for those Wrms. Hence, a single producer is also suYcient so long as its

9. THE THEORY OF DECREASING COST PRODUCTION 273

production exhibits increasing returns to scale. Finally, there is no need to

specify N goods and factors. A one-good, one-factor economy is suYcient to

represent increasing returns/decreasing cost production. Consequently, a gen-

eral equilibrium model consisting of one person with one source of (decreasing

cost) production at which a single output is produced by means of a single

input is suYciently general to capture both the nature of the decreasing cost

problem and the decision rules necessary to ensure full pareto optimality.

Keeping the model this simple has the additional advantage of permitting a

two-dimensional geometric analysis, a welcome relief from the notational

complexities of the various externality models. Therefore, let us assume:

1. A single consumer with utility function:

U  UX, L (9:1)

where

X  the single output.

L  labor, the only factor of production.

By the usual convention, L enters Uwith a negative sign (leisure is the

good). The indiVerence curves corresponding to UX, L are represented in

Fig. 9.1.

2. A single Wrm produces X according to the production function:

X  fL (9:2)

0

L

X

2

I

0

I

1

I

FIGURE 9.1

274 DECREASING COST IN GENERAL EQUILIBRIUM ANALYSIS