A formulation of spatial price equilibrium model and its computation procedure

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Since Samuelson (1952) pointed out that there exists an objective function where maximization satisfies the conditions of perfectly competitive equilibria among spatially separated markets, the use of mathematical programming approach to study market behavior over space has been significantly progressed in this field. Many works developed so far generally treat a perfectly competitive model or a monopoly model, however, it is natural feeling that a real world for markets of most primary commodities and manufactured goods lie somewhat between these two extremes,taking some forms of oligopoly. The purpose of this research is first. to extend the Greenhut model so as to permit spatial pricing in commodity market where it could happen that no trading takes place between some pairs of regions and second, to provide an efficient and easily implementable computational procedure for finding the inter-regional equilibrium commodity flow in spatially separated oligopolistic market, which is appl … More icable to spatial pricing with nonlinear marginal- production cost and the sub-optimization program of the variational equality. formulation of the spatial price equilibrium model.Three major conclusions were drawn from this research. First, the fundamental pricing equation is essentially the same as the composite performance function used in traffic equilibrium. However, the composite performance function is no more than convenient device of interpreting equilibrium processes given demand function and individual performance functions and has not been used for computational purposes. It can be said that G-G model gives an idea about how to make the composite function for computational purposes given individual cost (or performance) functions. On the other hand,methodology cultivate in traffic equilibrium may shed light on a special type of spatial oligopolistic equilibrium model, conceptually and numerically. Second, it was shown that in a spatial oligopolistic market, as like in spaceless economy, if there is excess quantity in market it makes to raise market price and that excess quantity vanish if the market is in equilibrium. These results imply that as long as market is tentative, there exists tentative flows and that some firms exit from the market because of suffering deficit. Thus, a computational procedure was structured so as to reflect such phenomena. As far as a numerical example demonstrated in section 3 is concerned, the procedure proposed in this paper seems not only to converge to the equilibrium state in an efficient ways, but also to be easily implementable. Third, the method developed in this paper is likely to be efficient in spatial pricing with nonlinear marginal-production cost as well by introducing double- stage algorithm. This may bring a drastic computational time saving in finding equilibrium flows in spatial oligopolistic model. But further careful examination and more detail analysis on application of the proposed method to variable marginal-cost problem will be required to confirm the convergency of the procedure. Less