當廠商所制定的價目表中出現所選擇品質高低與價格不成同比例關係時，這樣的價目表稱之為品質線性價目表。當獨占廠商或雙占市場中的廠商面對保留私人偏好訊息的消費者時，廠商可使用品質非線性價目表使得消費者自我選擇不同品質產品進行消費。在過去關於競爭非線性定價的研究中皆假設廠商間的成本為完全相同的。與這些文獻不同的是我們針對成本不對稱如何影響非線性定價模型進行探討，特別是討論廠商產品線與不同成本廠商最適合約之間差異的影響。本文建立了一個雙占市場模型，其中兩品牌分別由兩個不同廠商所擁有，並且廠商間的生產函數具有不對稱的特性。模型的問題可以表示為一個二階段最適控制問題，利用最適控制的最適化條件可找出雙占市場中廠商利潤極大化下的性質。 我們發現當成本上升時，廠商將會縮短其產品線。其理由是低需求消費者給予廠商的利潤貢獻是較少的，因此廠商將會優先放棄設計給低需求消費者的低品質產品。另一個性質是具成本優勢廠商的產品線長度比高成本廠商來的長。此結果是由於成本優勢廠商較具有能力去生產低品質產品以服務利潤貢獻較少的低需求消費者。在模型中發現，具成本優勢的廠商使用非線性定價時，設計給特定類型消費者的價目表會收取較高的價格，但同時也提供較高的品質。此一性質將會導致雙占市場非線性定價廠商間競爭時出現了違反成本優勢廠商定低價以奪取市場份額這樣一般直覺之結果。 The generic term quality nonlinear pricing refers to any case in which the tariff is not strictly proportional to the quality purchased. When a monopolist or duopolist faces consumers who hold private information about their tastes, the firm may use a quality nonlinear price schedule induce different type of consumers to choose different quality product. Most of studies on competing nonlinear pricing have been done under symmetric cost setting. Unlike the previous literature, we studies how cost asymmetric affects nonlinear pricing, in particular the product line offered by firm and the differ of optimal contracts between two firms. We present a model with two horizontally differentiated brands owned and operated by two separate firms and exhibits asymmetric cost function. Our problem can be formulated as an two-phase optimal control problem. By the optimal condition of two-phase optimal control problem, we can find the property of duopoly nonlinear pricing model out. We find that when cost rise, firms will curtail product line form bottom. The reason is consumer with low type as low profit contribution to firm, and therefore firms will first abandon low quality product for low type consumer. Another positive is firm with cost advantage has longer product line then the high cost firm. Because of low cost firm as more ability to serve consumers with low profit contribution. Specifically, we find that nonlinear pricing firms’ profit maximization outcome exhibits low cost firm would provide higher price and higher quality for specific type of consumers. It will lead to a situation violate general rule is that cost advantage firm make use of lower price to get more market share in duopoly environment.
