Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.8.2024.6.06

Volume 8, Issue 6, 1 December 2024, Pages 935-952

 

Abstract. Multicommodity trade enables the production, consumption, and flow of commodities across the globe from agricultural ones to precious metals. Mathematical formalisms to model, analyze, and solve such problems have advanced and are also relevant to policy and decision-making. In this paper, we construct a variational inequality trade network model in price and quantity variables, which captures possible losses on transportation routes, which can occur because of perishability of commodities, as in the case of agricultural ones, or outright thefts. The equilibrium conditions are stated and the variational inequality formulation derived. Qualitative properties of existence and uniqueness of the equilibrium supply price, commodity shipment, and demand price pattern are provided under reasonable conditions. Illustrative examples help to demonstrate the model. An algorithm that is proposed yields closed form expressions at each iteration and can also be interpreted as a discrete time adjustment process for the evolution of the economic variables. A spectrum of algorithmically solved numerical examples, with full input and output data provided, yields insights into the impacts of commodity losses, increased congestion, as well as enhanced marketing on producers as well as consumers. This new model expands the scope of spatial price equilibrium modeling under commodity losses.

 

How to Cite this Article:
A. Nagurney, I. Pour, S. Samadi, A variational inequality trade network model in prices and quantities under commodity losses, J. Nonlinear Var. Anal. 8 (2024), 935-952.