A formulation of spatial price equilibrium model and its computation procedure

自从Samuelson(1952)指出在空间上分离的市场间存在最大化满足完全竞争均衡条件的目标函数以来，利用数学规划方法研究空间上的市场行为已经取得了显著的进展。到目前为止，许多著作一般都处理完全竞争模型或垄断模型，然而，人们自然而然地感觉到，大多数初级商品和制成品的市场的现实世界有点介于这两个极端之间，采取某种形式的寡头垄断。本研究的目的是第一。对格林霍特模型进行了扩展，以允许在某些区域之间不发生交易的商品市场中进行空间定价；第二，为在空间上分离的寡头垄断市场中寻找区域间均衡商品流提供了一种有效且易于实现的计算方法，即APPL…更适合于具有非线性边际生产成本的空间定价和变分等式的次优化规划。空间价格均衡模型的构建。本研究得出了三个主要结论。首先，基本定价方程本质上与交通均衡中使用的综合性能函数相同。然而，复合性能函数只是在给定需求函数和个体性能函数的情况下解释均衡过程的一种方便的工具，并没有被用于计算目的。可以说，G-G模型给出了一种关于如何在给定单个成本(或性能)函数的情况下将组合函数用于计算目的的想法。另一方面，交通均衡的方法论培育可能有助于从概念和数值上揭示一种特殊类型的空间寡头垄断均衡模型。其次，证明了在空间寡头垄断市场中，就像在无空间经济中一样，如果市场中存在过剩数量，就会提高市场价格，而如果市场处于均衡状态，那么过剩数量就会消失。这些结果表明，只要市场是试探性的，就存在试探性流动，一些企业因亏损而退出市场。因此，构造了一个计算程序来反映这些现象。就第三节所示的数值算例而言，本文提出的方法不仅能有效地收敛到平衡态，而且易于实现。第三，通过引入两阶段算法，本文提出的方法对于具有非线性边际生产成本的空间定价也可能是有效的。这可以大大节省在空间寡头垄断模型中寻找均衡流的计算时间。但是，对于可变边际成本问题的应用，还需要进一步的仔细检查和更详细的分析，以确认该方法的收敛。较少

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