Abstract
Since the early 1950’s, there has been much effort expended in modeling interregional commodity flows. Among them are linear programming transportation models (e.g., Henderson); the Enke-Samuelson-Takayama-Judge models; the Leontief-Strout gravity models; and other econometric models. However, the entropy model has so far eluded description especially when implemented empirically. In this paper, we implement the Maxwell-Boltzmann entropy maximization model to the Appalachian steam coal market. We then compare the solution of optimum coal shipments with that of the corresponding linear programming transportation and spatial equilibrium models. It is found that (1) the performance of the Maxwell- Boltzmann entropy model is comparable to that of the spatial equilibrium model and (2) the entropy has outperformed the linear programming transportation model in its simplest form in terms of predicting actual coal shipments.
Highlights
The modem era is witnessing tremendous advances in knowledge, especially in physics
To the best of our knowledge, has never been empirically implemented in the commodity marlcet, we employ the data of the Appalachian steam coal market (Yang, 1979) to solve for the "optimum" solution under the assumptions of (i) maximizing Maxwell-Boltzmann entropy, (ii) minimizing Hitchcock-Koopmans' transportation cost, i.e., traditional linear programming (LP) model, and (iii) maximizing "net social payoff' (NSP or sum of consumer's and producer's surpluses) of the spatial equilibrium model
It is to be noted that the maximization of the NSP and the entropy is quite different: the solution to the former is based on estimated demand and supply relations in a spatial economy while the solution to the latter is dependent upon the assumption that there is an inherent tendency for commodity shipments to move toward a state of maximum spatial diffusion
Summary
The modem era is witnessing tremendous advances in knowledge, especially in physics. The scope ofclassical mechanics has been greatly expanded by the introduction of both quantum mechanics and relativity. In order to overcome such limited defmition, we propose and implement the Maxwell-Boltzmann entropy model in which it is hypothesized that energy flows (e.g., shipment of steam coal) resemble the movement of particles in a closed physical system.
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