本文探討在雙頭壟斷市場中兩家使用相同原物料並製造具有替代性產品的製造商之間的定價問題。當原物料價格上漲之後，這兩家製造商必須根據原物料漲幅、對手價格決策以及雙方之間的競爭程度去決定新的價格以最大化自己的收益。我們計算出了一個最佳漲幅不但可使雙方各自收益最大化，還可令兩方的產品售價用最有效率的方式達到Nash equilibrium。然而，這兩家製造商在原料價格上漲之後未必皆會以最大化收益為目標，倘若其中一方因為目的不同而不以最佳漲幅為價格決策時，另一方就可以考慮使用臨界漲幅來刺激對手改變目的以及銷售價格。此外，我們也討論參數對我們價格模型的影響，例如最高可能銷售價格、起始銷售量、成本以及產品替代率。最後提出一些例題解釋我們得到的研究證明以及觀察結果。 A pricing decision in duopoly is considered in this paper. There are two major manufacturers using the same raw materials and their products are partially substitutable to each other. As raw materials prices increase, they have to decide how to change their selling prices accordingly with the consideration of their products substitutability, the increasing raw material’s prices and rival’s pricing strategies in order to maximize their profits. We calculate an optimal mark-up that will not only maximize the manufacturers’ profits but also make the selling prices reach to Nash equilibrium in a most efficient way. The optimal mark-up prices are determined for manufacturers respectively, however if they have different intentions, their mark-up pricing strategies might be varied. If one of the manufacturers decides not to change his selling prices which are based on optimal mark-up, the other can adopt the critical mark-up strategy to stimulate the rival changing his purpose and selling prices. In this paper, we discuss how the parameters such as highest feasible prices, initial sale quantities, costs and substitutability affect our model; we also provide examples to illustrate some propositions or observations at the end.
