Voting, Spatial Monopoly, and Spatial Price Regulation

Economic Inquiry, Jan, 1992, 29-39

MH Ye and M. J. Yezer

Presentation Date: 06/Jan/14

Abstract

Regulation often require that local public utilities engage in high rates of freight absorption

These regulations are shown to arise logically as a consequence of self-interest voting behavior

Consumer may change their delivered price by voting to require a rate of freight absorption

Voting outcomes under a median voter model predict the high rate of freight absorption often observed in practice

I Introduction

While literature on spatial monopoly and regulated firms are large, very little attention has been given to the study of regulations affecting the spatial monopolist

Regulated spatial monopolies could include either public or private production of many services

Indeed the analysis could be adapted to mass transportation systems providing access to a center

It is common to see that regulations on the spatial monopolist require uniform delivered pricing in which the firm must absorb most or all transportation costs

Motivation

It appears that regulated freight absorption by the spatial monopolist is one of those cases that everyone knows but which no one has bothered to analyze in detail

An Economic Analysis of Regulated Freight Absorption Requires

The reaction of a spatial monopolist to the full range of requirements for freight absorption, from zero to full absorption, be available

But no such treatment in the literature yet

The First Objective of This Paper

To fill the gap by analyzing the effects of continuous variation in freight absorption on price, output, profits, consumers’ surplus and total welfare

The Results Obtained Are Rather Surprising

The unregulated profit-maximizing spatial monopolist is found to be a knife-edge case in which second-order conditions are not satisfied

Welfare maximization is achieved by regulating the rate of freight absorption so that it lies between zero and the rate practiced by an unregulated firm

Construct a Voting Model

Having determined the effects of alternative freight absorption regulations on the firm, this paper then construct a voting model in which spatially distributed consumer-voters choose the rate of regulated freight absorption

The spatial distribution of consumer surplus is used to generate voter preferences regarding the regulated level of freight absorption

Spatial Surplus Surface Analysis

This analytical approach shows that the median voter prefers a high level of freight absorption

The regulatory outcome most often observed

Consumer Voters Choose

These voters choose freight absorption regulations with higher required rates of freight absorption than practiced by an unregulated spatial monopolist engaged in spatial price discrimination

The Voting Outcome

This outcome lowers both total welfare and total consumers’ surplus below the levels obtained under unregulated spatial monopoly

II Model of the Spatial Monopolist: Assumptions

A given linear market characterized by location along X

A single plant located at point 0 Producing and distributing a homogenous

product, q, to consumers distributed at uniform density across the market

Resale is not possible

Demand side

Total quantity demanded at distance r is given by

P(r) is the delivered price, P(r) = P(0)+etr

Cost side

The voting behavior

The voting behavior of consumers is motivated by an attempt to maximize their personal consumer surplus

III standard results on the behavior of the spatial monopolist

First consider the production and pricing decision of the unregulated spatial monopolist maximizing profit

The monopolist chooses a market radius R, selects P(0) and determines e

Producer surplus

Consumer surplus

Well-known result

For linear demand, the level of e which maximizes profit is 0.5

Welfare maximization implies maximization of +S, which has been shown to required e =1

Other well-understood results involve the case of e = 0, which is often prompted by regulation

IV regulating freight absorption by the spatial monopolist

The major object of this study is the effect of regulations controlling the level of transportation cost absorption

Given that welfare is maximized at e=1,and firm profit is maximized at e=0.5, it is curious that regulations commonly require that the monopolist set e=0.

Our analysis is designed to determine if voter self-interest and knowledge of the effects of e on consumer surplus can lead to regulations requiring low values of e

To determine the effect of variation in e

Treat e as a parameter and use standard maximizing techniques

For purposes of comparison with results already in the literature, outcomes obtained for specific values of e=0.5, e=1, and e=0 will be noted using subscripts 0.5, 1, and 0 respectively and w will indicate a result that maximizes welfare

Proposition1

A single-plant spatial monopolist under transportation cost absorption regulation will charge the choke price at r = R if regulated e is relatively large; otherwise it will charge a price less than the choke price at r = R if regulated e is relatively small

Proposition 2

Regarding the maximum market radius of the single-plant spatial monopolist under transportation cost absorption regulation

Figure 1

Proposition 3

Concerning total output,

Proposition 4

Total consumer surplus generated by the single-plant spatial monopolist under alternative transportation cost regulations follows

Figure 2

Proposition 5

Profit of the single-plant spatial monopolist under alternative transportation cost regulations ranges from

Proposition 6

Welfare associated with the regulated single-plant spatial monopolist varies as

Figure 3

V consumer voting and regulated transportation cost absorption

Mueller(1989), if consumer welfare can be reduced to a single metric, voting outcomes on regulation are determined by the median voter

The spatial distribution of consumer’s surplus for different values of transportation cost absorption is given by s( r, e ), displayed in Figure 4

Figure 4

Consumer-voters

Voting behavior of consumers located at a particular r is motivated by an attempt to maximize surplus generated by different rate of transportation cost absorption

Finding e*( r ),which maximizes consumer surplus for voters at a given r

Conceptually, slicing the spatial surplus surface along a given r and determining the level of e

Median voter

The median voter preference is for e = 0.33 While voters consider only their own self

interest, the final outcome appears to have an obvious element of cross-subsidy.

Voters living from 0 to 0.357 are forced to subsidize those living past 0.357

Figure 5

Surprising voting outcome

The high rate of freight absorption selected by the median voter is inconsistent with a maximum of profit, welfare, or consumers’ surplus

Indeed consumers’ surplus is lower at the e = 0.33 level selected by voters than when the unregulated profit-maximizing firm engages in spatial price discrimination and sets e =0.5

The median voter selects such high freight absorption that consumers near the maximum market radius are cut off from service

VI Summary and Conclusions

It is common to find a regulatory requirement that spatial monopolists absorb most transportation cost, i.e. that they engage in uniform delivered pricing

Given this is a clear departure from marginal cost pricing, the conclusion that it is not consistent with welfare maximization follows easily

contribution

The results presented here extend in several ways and provided a voting model which explains the political pressure for uniform pricing schemes

Merging theoretical models of the spatial firm with regulatory and voting analysis in a manner not previously reported in the literature, this paper obtain a variety of original and interesting results

Results

Analysis of the effect of varying e over the entire choice set shows that uniform pricing minimize both firm profits and total consumer surplus

Internal welfare maximization is achieved with fairly low levels of transportation cost absorption

The spatial distribution of consumer surplus generated by alternative levels of transportation cost absorption is such that the median voter prefers regulations requiring very high levels of absorption

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