貝氏統計於時間序列模型下探討廠商價格政策—以台灣鮮乳產業為例

Abstract

本研究以臺灣鮮乳市場為研究主題，首先探討市場始於鮮乳廠商定價行為之間的對抗情形，並指出鮮乳廠商定價行為之異質性造成各別鮮乳廠商市場佔有率循環反覆地變化，說明價量關係對於臺灣鮮乳市場型塑明顯的負面回饋效果，並以此途徑動態地持續影響鮮乳消費者。 不同於過往研究多採似無相關迴歸模式，本研究嘗試透過貝氏統計方法所構建之時間變化橫斷面模型進行鮮乳消費者需求價格彈性的推論，並以2009年至2010年零售通路鮮乳產品之銷售資料為例，推導鮮乳廠商味全、光泉、佳格以及統一鮮乳產品消費者之需求價格彈性後驗分配。實證分析指出，所有鮮乳廠商之需求自我價格彈性於95%可信區間皆大於1，說明鮮乳廠商當前定價水準並未達至單元彈性。其中，平均而言味全之需求自我價格彈性以及需求交叉價格彈性皆為本次研究對象中最低者，相對地，統一上述兩者需求價格彈性中皆為最高者。 本研究接續以經濟領域中最適加成定價法，將模型中各別鮮乳廠商需求自我價格彈性後驗分配之平均數作為指標，代入最適加成定價公式，以此設定各別鮮乳廠商最適價格水準，並以統計模擬途徑，嘗試推論最適價格水準下鮮乳廠商之預期銷售乳量以及預期利潤。其中，味全於目標研究範圍中平均而言最適價格水準最高，相對地，統一於目標研究期範圍中平均而言最適價格水準最低。實證結果指出，於本研究所設定之最適價格水準下，所有鮮乳廠商預期銷售乳量之95%可信區間皆大於原始資料實際銷售乳量，而光泉、佳格以及統一預期利潤之95%可信區間大於原始資料推估利潤，說明於機率層面上，本研究所設定之最適價格水準確實有助於鮮乳廠商在銷售乳量的提升。

This study discusses the competition between milk enterprises in Taiwan, and indicates that how the enterprises apply price strategy, resulting in volatility of its market share. Researcher would explain that the prices would dynamically arise negative feedback effect in the milk market. Distinct from adoption seemingly unrelated regression model in previous research, this study utilizes Bayesian regression model to infer price sensitivity of the milk consumers. Researcher would take the sales data of milk products from 2009 to 2010 as example, and derive the posterior distribution of price sensitivity of the milk enterprises such as Wei Chuan Foods Corporation, Kuang Chuan Dairy Corporation Limited, Standard Food Corporation and Uni-President Enterprises Corporation. Empirical analysis shows that 95% of credible interval of self price elasticity of demand of each milk enterprises is above 1 percent. Self price elasticity of demand and cross price elasticity of demand of Wei Chuan Foods Corporation are the lowest among milk enterprises in the study. On the contrary, self price elasticity of demand and cross price elasticity of demand of Uni-President Enterprises Corporation are the highest. This study would employ the optimal mark-up pricing and take the posterior distribution of the self price elasticity of demand as the proxy in order to construct optimal price level. As empirical analysis shows, 95 % credible interval of expected sales of milk product of each milk enterprise with adoption of optimal price level is higher than realistic sales. Except for Wei Chuan Foods Corporation, 95 % credible intervals of expected profit of remaining milk enterprise are higher than their own realistic profits.