Spatial Monopolist Research Articles

Effects of a customer gradient in a spatial monopoly

Traditional location theory analyzes the behavior of a monopolist selling a good (service) in a spatial market having identical customers distributed at uniform density. However, customers in highly urbanized societies rarely exhibit uniform (flat) densities. Consequently, location theory has lost some of its relevance for clarifying how firms should behave in densely populated spatial markets. This paper uses a downward-sloping function, centered on the point of sales, to represent the type of customer gradient that is now common in urban settings. Therefore, the location-specific demand density for a low-order retail good is determined by the interaction between a (single-good) linear pricing system and a linear customer gradient. The spatial monopolist must adjust its price to both exogenous factors when seeking to maximize profit in the market. Under a mill (f.o.b.) price system, a steeper customer density induces the monopolist to raise its price higher to maintain its profit.

SO 2 policy and input substitution under spatial monopoly

Following the U.S. Clean Air Act Amendments of 1990, electric utilities dramatically increased their utilization of low-sulfur coal from the Powder River Basin (PRB). Recent studies indicate that railroads hauling PRB coal exercise a substantial degree of market power and that relative price changes in the mining and transportation sectors were contributing factors to the observed pattern of input substitution. This paper asks the related question: To what extent does more stringent SO 2 policy stimulate input substitution from high-sulfur coal to low-sulfur coal when railroads hauling low-sulfur coal exercise spatial monopoly power? The question underpins the effectiveness of incentive-based environmental policies given the essential role of market performance in input, output, and abatement markets in determining the social cost of regulation. Our analysis indicates that environmental regulation leads to negligible input substitution effects when clean and dirty inputs are highly substitutable and the clean input market is mediated by a spatial monopolist.

An application of the Beckmann-Ingene argument to a monopsonist's spatial pricing problem

The purpose of this note is to show that an analogue of the Beckmann-Ingene proposition on price policies of a spatial monopolist applies to a properly formulated profit maximization problem for a spatial monopsonist. The proof of this fact uses the same linear transformation employed in the Beckmann-Ingene argument.

An application of the Beckmann‐Ingene argument to a monopsonist's spatial pricing problem

Abstract. The purpose of this note is to show that an analogue of the Beckmann‐Ingene proposition on price policies of a spatial monopolist applies to a properly formulated profit maximization problem for a spatial monopsonist. The proof of this fact uses the same linear transformation employed in the Beckmann‐Ingene argument.

How to tax a spatial monopolist

This paper models the interaction of a government that maximizes tax revenue and a spatial monopolist that maximizes profit. The government has two tax instruments, a per unit output tax and a transport tax, and the monopolist can strategically alter its location and the mode of transport. If allowed only one tax instrument, then the government chooses the output tax, which generates inefficient strategic choices by the monopolist in order to avoid profit losses. Since the inefficiency is greater than with the transport tax, this isolates a new tradeoff between government tax revenue and economic efficiency.

GENERAL EQUILIBRIUM OF SPATIAL PRODUCT AND LABOR MARKETS*

ABSTRACT A simple general equilibrium model relates spatial product markets and spatial labor markets. The firm is treated as being a spatial monopolist or as a Löschian competitor in the output market and as a spatial monopsonist in the labor market. Derived free spatial demand and free regional labor supply are defined, and their properties examined. The model provides the framework for analyzing the impact of a technological improvement in labor productivity on the structure of the spatial markets. The impact of entry on spatial labor supply is an important determinant of whether or not entry lowers wages and raises output prices. Unlike the spaceless competitive paradigm, zero‐profit long‐run equilibrium can occur in a space economy under conditions of increasing returns to scale.

THE SPATIAL MONOPSONY: A THEORETICAL ANALYSIS*

ABSTRACT. In this paper some of the most important properties of the behavior of a spatial monopsonist are derived. Many results are mirror images of corresponding results for the spatial monopolist. A few results are, however, genuinely new. A lot of effort is spent in comparing the properties of the profit function under three different pricing policies, f.o.b. (mill)‐pricing, uniform delivered pricing, and spatial price discrimination. It is shown, for example, how the profitability and welfare consequences of the different policies are related to the shapes of the supply and demand functions. It is argued that the theory may have important applications in economic analyses of renewable natural resources such as forests, where total transportation costs are nonnegligible.

Spatial monopoly and the U.S. electrical energy industry

We examine the effectiveness of regulation in the electrical energy industry in the U.S. On the whole, the industry is not allowed to act as a spatial monopolist. It is not justifiable, however, to conclude that monopolistic tendencies are absent. In particular, the pricing structure departs from the competitive criterion, which requires price to equal the marginal cost of supplying electrical energy to a given consumer.

The level of average production cost chosen by a multiplant spatial monopolist

Multiplant monopoly models generally assume that firm demand is unaffected by the number of plants established. This assumption is inappropriate when transportation costs are significant. Because of this, a multiplant spatial monopolist may choose to operate on the downsloping, constant, or upsloping segment of plant average production cost curves, depending upon the impact of additional plants on cost levels. However, such a monopolist will choose a long-run firm size which is associated with increasing firm level average costs as long as economic profits are available. Long-run average costs are minimized if the monopolist just breaks even.

The Price Effects of Spatial Competition

A recent paper by Capozza and Van Order (CVO) (1977) proposed a generalization of the Greenhut-Hwang-Ohta (GHO) (1975) analysis of pricing under three alternative types of spatial competition. The GHO analysis was based on a short-run model in which the locations of firms are assumed to be fixed. CVO accordingly proposed relaxation of this rigid assumption to examine if the GHO results also apply to the long-run zero-profit industry equilibrium. They confirmed the GHO results, which, however, they also contended, require certain particular modifications as well in the light of their own models. The CVO contribution lies in their simple model analysis of long-run industry equilibrium conditions-a generalization of the GHO analysis. However, they failed to recognize that the GHO analysis is based on another restrictive assumption regarding the form of the demand function. Moreover, they assumed even more restrictive demand conditions and misled themselves to a conclusion that L6schian competition never results in a lower price than spatial monopoly. Their conclusion is invalid since Loschian competition can be shown to result in a lower (not higher) mill price if only the demand function is assumed to be sufficiently convex to the origin (Ohta (1980)). This calls for a more general examination of conditions under which the firm's f.o.b. mill price may rise or fall due to spatial entry of rival firms. The present paper presents selected results of such examination. Section 2 briefly reviews the theory of spatial monopoly. Initially some fundamental assumptions are set forth. This is followed by derivation of the market demand function for the spatial monopolist. The market demand in turn is shown to be more or less elastic than the assumed basic demand function depending on the curvature of the latter curve. We also comment on the so-called paradox of spatial monopoly, which we claim is a misnomer. The analytical framework of Section 2 is employed in Section 3 as we generalize previous analyses and present a concise cataloguing of comparative static results of spatial competition.1 Again the basic demand characteristics, in combination with alternative types of spatial competition, are shown to play an important role in yielding the distinct elasticity results, and for that matter competitive equilibrium prices. In the process a counter-example to CVO's aforementioned argument on L6schian pricing is presented. Also discussed is the conceptual distinction between perceived and realized elasticities of demand under spatial competition, which CVO also failed to recognize. As a result, they erred in speculating that equilibrium mill prices would be the same under alternative types of spatial competition, given the size of the market area. We will show that they in fact are not. Section 4 concludes the paper by summarizing the basic results of our analysis.

Spatial Competition and Spatial Price Discrimination

Presents information on a study which analyzed the link between spatial monopoly and spatial competition. Impact of the degree of price discrimination on the degree of competition; Spatial analogue of the conventional, spaceless, monopoly/perfect competition comparison. (From Ebsco)

Pricing under Spatial Competition and Spatial Monopoly: Reply

IN A RECENT PAPER D. R. Capozza and R. Van Order (C.V.) [1] claim to show that there exist conditions under which a competitive firm in industry equilibrium in a spatial environment will charge a higher mill price than a spatial monopolist. This conclusion seems contrary to our intuition and consequently the conditions under which it arises should be made very clear. This paper argues that the C.V. result is not necessarily correct. In particular, there is an apparent error in the three sentences following equation (27). The positive roots of equation (27) are both possible candidates for equilibrium price.2 The difficulty is that there are no grounds for choosing between the two roots within the structure of the model. Capozza has argued, in correspondence, that the smaller root is inappropriate because demand is negative. However, demand is only negative at the border of the market area and one could equally well argue that this is a case of natural monopoly, induced by the cost structure. These remarks are made within the assumptions that C.V. makq in their paper. We can, however, shed further light on the matter by introducing some new elements. In particular, (i) we explicitly impose some simple dynamics on the system, and (ii) we use consumer surplus as a measure cf welfare. (i) Let us suppose that firms are price setters and assume a zero conjectural variation. Under these conditions it is not difficult to show that the larger positive root is stable and the smaller is unstable. (ii) The total of consumer surplus at price m and market radius Do is given by

The effectiveness of regulation in the electrical energy industry

There is a gap between what federal and state regulatory commissions are authorized to do and what they are doing to regulate the electrical energy industry. It has been argued that a pricing scheme in the industry has evolved akin to the pricing scheme a discriminating monopolist might employ for different classes of consumers that are spatially diffuse. The attention of the paper is focused on the effectiveness of regulation in the industry, given the characteristics of it. The method of analysis chosen is to construct two models which are polar opposites and compare the results with what was actually the situation in 1973. The conclusion indicates that it is justifiable to argue that the electrical energy industry on the whole is not allowed to behave as a spatial monopolist. It is not correct to conclude that monopolistic tendencies are absent. Specifically, the pricing structure does depart from the competitive criterion which requires price to equal marginal cost for each consumer sector and all regions. Further, little electrical energy is transmitted interregionally.

Spatial Price Discrimination, Competition and Locational Effects

Spatial price theory has typically assumed homogeneous gross demand curves among buyers who are dispersed over an economic landscape. Subtracting varying costs of distance to their locations yields a set of heterogeneous net demand curves. Any spatial monopolist subject to these conditions faces separable markets which are characterized by different effective demands. As a result price discrimination is feasible, and in theory straight-lined delivered price schedules of less than unit slope per unit cost of distance are customarily derived. But do spatial competitors ever discriminate (or appear to discriminate) over economic space? And if they do, what is the form of their delivered price schedules? Would their schedules also be linear given the same demand conditions that generate linear schedules for a discriminating monopolist? Without answering questions such as those raised above anti-trust regulations dealing with unfair price practices and, in particular, the determination of what is legal or illegal, ethical or not, cannot be readily accepted by economists. The present paper is designed to provide a basis for answering such questions by uncovering selected properties of spatial price discrimination under conditions of varying intensities of competition over an economic space. More generally, the paper is designed to determine the effect on prices of rival locations and the intensity of their competition. Sharp contrasts between spaceless and spatial price theory will thus be drawn, with competitive differences over the seller's trading area being revealed to generate differential discriminatory prices over the landscape. [Авторский текст]

Derivation of Optimal Spatial Prices

The price of a good prevailing at some local market point may or may not be identical to the price of that same good at another market point. Price differentials over regions depend in part upon the number and locations of firms which sell to these regions, and on the demand curves of buyers. The present paper evaluates the price policy of a firm selling over a set of linearly extended buying points. It derives the optimal spatial prices under alternative assumptions of consumer behavior and demand. It demonstrates mathematically as well as graphically that a spatial monopolist maximizes profits by subdividing his market into economic submarkets, utilizing fob mill prices for some submarkets, and optimal discriminatory prices for the remaining ones. Thus it explains the use of fob pricing over selected distances in a firm's market area notwithstanding the apparently greater profitability of a discriminatory price policy throughout a firm's market space.