A spatial price network equilibrium paradox

ABSTRACTUrea fertilizer is widely used in the United States, however, urea is not publicly traded and formula pricing is common. This article studies spatial transmission and efficiency of urea prices in the Arkansas River‐New Orleans urea markets and the New Orleans‐Middle East urea markets. A vector error correction model (VECM) and Baulch's (1997) parity bound model (PBM) are estimated. A threshold VECM is considered, but no threshold effects are found so threshold effects are not included in the final VECM. The estimated VECM shows that violations of spatial price equilibrium are corrected faster between Arkansas River‐New Orleans prices than New Orleans‐Middle East prices. The long term adjustments to deviations from spatial equilibrium in the New Orleans‐Middle East price relationship are made through adjustments in the New Orleans price. The PBM shows that New Orleans‐Middle East price spreads are greater than transportation costs about 23% of the time. [EconLit citations: C32, Q13, R32].

We consider the multicriteria spatial price network equilibrium model in which consumers are allowed to weight both the transportation cost and the transportation time associated with the shipment of a given commodity. In particular, we assume that weights are not deterministic but subject to random fluctuations. Therefore, we formulate the problem as a random variational inequality and prove that under natural assumptions the associated random operator satisfies a uniform monotonicity property. The subsequent analysis is carried out in the framework of the theory of random variational inequalities.

In this chapter, we consider models for facility sizing and location under oligopolistic market equilibrium conditions on a spatial network. As in Chapter 6, we employ the paradigm of a large firm locating facilities on a defined network. To solve facility sizing/location models in oligopolistic competition, sensitivity based bilevel algorithms are developed. We will observe that there exist both significant similarities and differences between the algorithms developed in this chapter and those presented in Chapter 6 where a spatial price equilibrium characterized the economic conditions under which the firm of interest made its locational decisions.

In this paper, we develop a spatial price network equilibrium model with marketable pollution permits using the theory of variational inequalities. The model has the distinctive feature that it allows for the imposition of environmental quality standards for both the producers at the supply markets as well as on the transportation links. The permits are distinct and recognize that producers may emit pollutants that are different from those that are emitted during transportation. We provide qualitative properties of the equilibrium supply, shipment, demand, marginal cost of emission abatement, license, and license price pattern as well as a numerical scheme for the computation of the equilibrium pattern. We conclude with several numerical examples for illustrative purposes.

Equilibrium networks; Generalized monotonicity: Applications to variational inequalities and equilibrium problems; Oligopolistic market equilibrium; Spatial price equilibrium; Traffic network equilibrium; Walrasian price equilibriumEquilibrium networks; Generalized monotonicity: Applications to variational inequalities and equilibrium problems; Oligopolistic market equilibrium; Spatial price equilibrium; Traffic network equilibrium; Walrasian price equilibriumFINANCIAL EQUILIBRIUM

In this paper, we prove that the equilibrium of predator-prey networks is, in fact, a spatial price equilibrium. This result demonstrates the underlying economics of predator-prey relationships and interactions and provides a foundation for the formulation and analysis of complex food webs, which are nature's supply chains, through the formalism of network equilibrium. Moreover, it rigorously links the equilibrium conditions of commodity networks in which a product is produced, transported, and consumed, with those of ecological networks in which prey are consumed by predators.

ABSTRACT. Conditions for spatial price equilibrium are derived for a set of firms in oligopolistic spatial competition, distributed at fixed locations in a heterogeneous region where consumer purchasing patterns are a probabilistic function of the price distribution rather than a deterministic function of proximity to firms. The resulting prices vary with accessibility to consumers or with the degree of local spatial monopoly, and result in non‐zero profits for firms. Conditions describing the existence and stability properties of this spatial price equilibrium are defined, and are shown to be equivalent for two different hypotheses concerning disequilibrium pricing behavior: a partial price adjustment model and a Bertrand game. For two different profit goals, total profit maximization and profit rate maximization, it is shown that a spatial price equilibrium exists and is at least locally quasi‐stable.

In this paper we explicitly incorporate competitive markets for transportation services into the framework of spatial price equilibrium modeling. These markets can be purely local, purely global, or a combination thereof. We show that the existence of markets for transportation services is equivalent to the existence of congestion in a spatial price equilibrium model. In addition, we give general suggestions regarding the application of these models.

The concept of a spatial price equilibrium has dominated the network-based models of spatial competition ever since Samuelson's (1952) formulation of this concept as a mathematical program. In practice, however, this model has often been a poor predictor of interregional flows and regional commodity prices. In this paper an extension of the spatial price equilibrium model is presented, in which attempts are made to overcome the poor predictive capabilities of this model by imbedding it within a gravity model representation of interregional flows. After the conceptual framework of this model is stated, a variational inequality formulation is presented and this formulation is then used to derive a convex mathematical programming statement of this model. Solution algorithms and sensitivity analysis of the equilibrium solution are discussed, and in the conclusion to the paper a discussion of the extensions of this model are presented which incorporate multiple commodities and imperfect competition in the regional commodity markets.

This paper describes a method for selecting a grid size for the piece wise‐linear approximation of a separable quadratic program. It describes and demonstrates application of the procedure to a spatial price equilibrium model. The method is based on an a priori bound relating the amount of objective function approximation error to the suboptimality induced in the solution of the actual optimization problem.

Measuring the influence of Canadian carbon stabilization programs on natural gas exports to the United States via a ‘bottom-up’ intertemporal spatial price equilibrium model

This paper concerns with the study of the time–dependent variational inequality associated to the spatial price equilibrium model related to the quantity formulation. In particular existence the -orems of the solution to the associated variational inequality and a stability analysis of the equilibrium pattern is reported.

A dynamic disequilibrium interregional commodity flow model

SPATIAL PRICE EQUILIBRIUM AS A FOUNDATION TO UNIFIED SPATIAL COMMODITY MODELING

This paper considers equilibria among multiple firms that are competing non-cooperatively against each other to sell electric power and buy resources needed to produce that power. Examples of such resources include fuels, power plant sites, and emissions allowances. The electric power market is a spatial market on a network in which flows are constrained by Kirchhoff’s current and voltage laws. Arbitragers in the power market erase spatial price differences that are non-cost based. Power producers can compete in power markets a la Cournot (game in quantities), or in a generalization of the Cournot game (termed the conjectured supply function game) in which they anticipate that rivals will respond to price changes. In input markets, producers either compete a la Bertrand (price-taking behavior) or they can conjecture that price will increase with consumption of the resource. The simultaneous competition in power and input markets presents opportunities for strategic price behavior that cannot be analyzed using models of power markets alone. Depending on whether the producers treat the arbitrager endogenously or exogenously, we derive two mixed nonlinear complementarity formulations of the oligopolistic problem. We establish the existence and uniqueness of solutions as well as connections among the solutions to the model formulations. A numerical example is provided for illustrative purposes.