新產品剛進入市場時，群眾對該新產品的資訊是不知曉的，新產品廠商必須運用行銷策略，才能讓群眾開始知曉產品的存在，成為新產品的潛在消費者。但擴散過程中，各時間點知曉新產品資訊的群眾皆不同，因而即使在同一價格下，各時間點新產品之銷售率亦皆相異。為了能闡述並具體分析這種問題的特殊狀況，本文定義需求機會函數如下：獲悉新產品資訊之群眾，在價格水準p之下，願意購買此產品之機率為f(P)，0<=f(p)<=1且f'(p)<=0。透過此需求機會函數的表達，及新產品資訊隨時間的擴散之微分方程式，本文將「如何透過售價0)('≤pf影響新產品各時點之銷售資訊及其利潤回收」，製作成可具體討論的數學模式，數學模式最佳解的性質，及最佳解對模式各參數的敏感度分析，據以解釋其經營管理意涵，幫助廠商有效率的使用行銷資源，則為本研究的主要內容。 When a new product is launched by a product innovating firm, the firm must make great efforts to adopt marketing strategies in order to create awareness of the product in the market. But in the diffusion process of the new product, people who perceive the new product and purchase it in various time points are different. In order to elaborate and specifically analyze the special status of the problem mentioned above, the Demand Function f(p) is introduced in this study to illustrate the opportunity that people who perceive new products and purchase them under price p. Through the f(p) and the differential equation of the diffusion of new product information over time, a mathematical model is formulated in this paper to discuss “how price p affects the selling information of new products at each time point and its profit return”. The characteristic of the optimal price p* in the model and the sensitivity analysis of p* to every parameter in the model will assist firms that utilize marketing resources efficiently.
