統一交運價格廠商的訂價行為之理論分析

A Theoretical Model for Pricing Analysis of Firms Under Uniform Delivered Pricing

本研究提出一個二度空間下統一交運價格廠商的區位競爭模型，以探討不同猜測變量下廠商的行為差異。研究發現， Löschian 模型下的廠商間形同有聯合的行為，其均衡價格會較高但市場範圍則較小；而在Hotelling-Smithies competition 模型下，因極端的價格競爭，模型的均衡價格會較低而市場範圍則較大。若廠商間的市場範圍可以重疊時，則追求利潤極大化下的最適價格與最適銷售範圍會介於前兩個模型之間。由此推論出廠商在短期時最保守、最理性的策略是將距離設在H-S competition 模型的最適均衡距離上，而價格除非是在廠商間的猜測變量已知下，才能找到讓利潤達到最大的最適價格，否則只要訂在介於Löschian 模型與H-S competition 模型的利潤極大化價格間，日後再針對廠商間的猜測變量調整即可。

Mill pricing policy is that firms charge a mill price plus transportation cost to all consumers . Greenhut (1981) found that a third of the firms he had surveyed in the US used mill pricing policy (F.O.B.). Uniform delivered pricing (U.D.P.) policy is that firms set the same delivered price at all points in space. Under this policy the firms pay the transportation cost instead. Greenhut, Greenhut and Li (1980) and Greenhut (1981) have observed that about a quarter of the firms in the US charged uniform delivered price. In practice, the use of U.D.P. for final or intermediate products seems rather common in free-market economy. However, very few theoretical attempts have been made to present formally the possible free entry competitive equilibria under U.D.P. on spatial competition. Furthermore, although urban location of firms is better analyzed by two-dimensional space, it is usually examined by one-dimensional space in the literature on spatial competition due to mathematical tractability. The main interest of this research is to examine what happens if we relax space restriction in U.D.P. model and extend a market into two-dimensional one. Thus, the primary subject of this paper is to construct a two-dimensional spatial competition model of firms under U.D.P.. Equilibrium in spatial models invariably depends on firms’ conjectures about how competitors will react to their price changes. The potential equilibria, multiple price and spacing combinations, depend primarily on the conjectural variation assumption made by the firms. Three conjectural variation assumptions are taken into consideration. The first is the Löschian competition that each firm assumes its market area to be fixed, and sets prices like a monopolist within its market area. The second is the Hotelling-Smithies competition that each firm assumes the prices of competitors to be fixed. The third type involves shared market areas or overlapping markets in which the customers charging the same price by the firms in the disputed market area are assumed to randomly select the firm with which they do business. Therefore, this paper uses the standard spatial price model assumptions with free entry and competition to build a two-dimensional, U.D.P. spatial competition model to examine the competitive equilibria. The result shows that considering only equilibria involving equal spacing between firms, three different types of equilibria are found. The first involves a collusive market-sharing assumption, Löschian case, and yields an equilibrium with high prices and smaller market areas. The second involves extreme price competition, the Hotelling-Smithies competition case, and yields an equilibrium with large market areas and low prices. Finally, the third type of equilibrium involves shared market areas and the optimal price and spacing lies between the equilibria of the previous two models. These findings are consistent with the conclusions revealed by Greenberg and Meyer (1981) under the assumption of one-dimensional market. However, in this paper, our assumption of two-dimensional market is more realistic in the real world, but the algebra of our theoretical model is more complicated than in the one-dimensional model. Fortunately, by utilizing software Mathematica, we overcome this enormous complexity which accompanies computation of solution to the equilibrium and show the differences by simulation, especially for the models with overlapping markets. The simulation for the models makes the comparative analysis of competition equilibria easier and manifest. Finally, from the practical point of view, these findings also imply that the optimum strategy the firm should take is to locate at the equilibrium distance in the Hotelling-Smithies competition case, which is the most conservative and rational way because the location of the firm can not be relocated frequently. As to the optimum price, the firm may set the price lie between the equilibrium prices of the Löschian case and the Hotelling-Smithies competition case. After the first setting, the firm may adjust the price according to respective conjectural variations among the firms.