有關廠商空間訂價行為的研究文獻，可以Capozza和Van Order 1978年以一完整的分析模型架構，分別針對不同廠商訂價行為的假設條件判斷其合理性，作為一代表性文章。Capozza 和Van Order認為，利用Loschian廠商行為假設條件，所求解出的最終結果，並不符合以一個不考慮空間因素的完全競爭市場裡，廠商對於生產成本變動而反應在商品訂價上的最終行為。 本研究內容主要是以非線性函數型式，來取代Capozza和Van Order的線性函數假設，並且利用Mathematica數學程式計算軟體來求解，廠商因成本改變，而反映在商品訂價上的行為。研究結果發現，(1)在Loschian模型假設條件下，Capozza 和Van Order以線性需求函數設定，所求解出的最終結果是成立的；(2)當生產邊際成本增加時，廠商亦會同時提高商品的訂價，二者間是呈一同向變動的正向關係；以及(3)在Benson所假設的消費需求數中，當對商品價格予以一階微分，再帶入v值等於 -1/2時，會出現需求函數違反一般需求法則的情形，即商品訂價愈高，消費者所購買的商品數量愈多。 Theoretical examination of Capozza and Van Order’s (1978) research of pricing behavior of firms competing in a spatial environment indicates that Loschian competition is inconsistent with the characteristics of perfect competition model.
The purpose of this paper is to replace Capozza and Van Order’s linear demand function assumption by nonlinear one. Moreover, we take advantage of Mathematica software as calculation tool and to see the firm’s reactions to the change of production costs. At last, we discover that (1) under nonlinear demand function, Capozza and Van Order conclusions of Loschian competition are correct; (2) the more marginal cost, the higher price of product; and (3) Benson’s assumption of demand function is against the Law of Demand when assuming v value is -1/2.
