Time—Dependent Spatial Price Equilibrium Problem: Existence and Stability Results for the Quantity Formulation Model

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

SPATIAL PRICE EQUILIBRIUM AS A FOUNDATION TO UNIFIED SPATIAL COMMODITY MODELING

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.

Disequilibrium and variational inequalities

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

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 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.

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.

Equilibrium is a concept central to the analysis of economic phenomena. Methodologies that have been applied to the formulation, qualitative analysis, and computation of economic equilibria have included systems of equations, optimization theory, complementarity theory, as well as fixed point theory. In this chapter the foundations for the theory of variational inequalities are established and the relationship of this methodology to other existing equilibrium analysis tools identified. Variational inequality theory will be utilized throughout the book as the fundamental methodology in synthesizing network economic equilibrium models operating under a spectrum of behavioral mechanisms and ranging from spatial price equilibrium problems and imperfectly competitive oligopolistic market equilibrium problems to general financial equilibrium problems.KeywordsVariational InequalityEquilibrium ProblemComplementarity ProblemVariational Inequality ProblemMonotonicity ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Utilization of the peat bogs of Canada

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.

To investigate the trade and welfare consequences of specific market policies and economic developments in the European market for apples and pears, a spatial price equilibrium model is formulated and applied. For the evaluation of the welfare consequences of certain policies, the concept of economic surplus is used. The empirical analysis shows that there are still severe data deficiencies which limit the application of such models for decision-making. Nevertheless, it appears to be appropriate to conclude from our calculations that withdrawals of apples and pears can be considered as a valuable instrument, if only used as a temporary measure, to stabilize markets. Further results suggest that the extension of the EEC is not only of advantage to consumers in the newly integrated countries but that it also leads to substantially increasing incomes in the main production areas for apples and pears in Europe.

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.

A dynamic disequilibrium interregional commodity flow model

A stochastic fractional differential variational inequality with Lévy jump and its application