Lotka-Volterra模型於台灣晶圓代工產業營收之應用分析

Abstract

半導體製造是一個眾所周知需要高度技術、資本和知識密集的產業。因此擁有晶圓製造產能的半導體企業，特別是晶圓代工廠，準確的預測模型是產業發展策略的重要工具。本研究係以Lotka-Volterra模型探討台灣晶圓代工產業的投資發展策略，比較台積電以及聯電的動態競合關係。以台積電與聯電之每月營收驗證台積電以及聯電是否存在著競爭或合作的關係，並且預測未來台積電以及聯電的月營收，是否存在著均衡關係。此外，除了以本研究所應用的Lotka-Volterra模型進行預測外，會再運用Bass模型進行預測，並比較兩模型何者較能精確的預測台灣晶圓雙雄的營收趨勢。 本研究結果顯示，台積電與聯電的營收競合模式為聯電的營收成長會對台積電的營收成長有幫助、台積電對聯電沒有影響的片利共生關係，其可能原因為聯電在先進製程技術上的發展時程上一直緊追著台積電，台積電必須全力衝刺先進製程技術的開發與持續擴大產能滿足客戶的需求，才能維持在晶圓代工市場的領導地位。因此聯電對於台積電產生了馬蠅效應 (Lincoln, 1860) 的效果，刺激台積電的製程技術開發與營收持續成長。在模型預測能力上，Lotka-Volterra模型的預測準確度優於Bass模型。其原因是Bass模型僅就個別公司做擴散成長預估分析，而Lotka-Volterra模型除了考量個別公司的擴散成長預估分析之外，更考慮了兩家公司之間的競爭合作關係，因此準確度較高。Lotka-Volterra模型相較於Bass模型，對台積電與聯電的月營收的樣本資料有較佳的配適準確度與整體解釋能力。在均衡分析方面，台積電的月營收在產能利用率接近滿載的情況下，各世代製程產能會交互阻礙。在未來長期的競合關係之下，會逐漸收斂到新台幣74,185百萬元。聯電的月營收在產能未滿載的情況下仍有成長的空間。在未來長期的競合關係之下，會逐漸成長並收斂到新台幣13,105百萬元。此結果也說明台積電和聯電在長期競合下，將會達到穩定均衡的狀態。

This study employs Lotka-Volterra Model to investigate the investment and development strategies for IC foundry industry in Taiwan by comparing the dynamic competitive relation between Taiwan Semiconductor Manufacturing Company (TSMC) and United Microelectronics Corporation (UMC). We explore whether TSMC and UMC compete or cooperate each other through analyzing TSMC’s and UMC’s monthly revenue. In addition, we conduct equilibrium analysis as well. This study also implements Bass Model to verify the accuracy of prediction for TSMC’s and UMC’s revenue trend with Lotka-Volterra Model. The result shows the relation between TSMC and UMC is Commensalism. UMC’s revenue growth benefits TSMC, while TSMC has no effect on UMC. The possible reason is that TSMC pursues the development of advanced technologies and improves capacity to fulfill customers’ demand. As a competitive follower, UMC triggers TSMC’s advancement, having the horse flies effect as proposed by Lincoln (1860) on TSMC. Our results also conclude that Lotka-Volterra model has better prediction ability and better fit on data samples than Bass model since the competitive and cooperative relation between TSMC and UMC is considered in Lotka-Volterra model. In the equilibrium analysis, under the circumstances of fully capacity utilization, production from different generations may have negative interaction among each other in TSMC. As a result, based on future self-competitive relation, TSMC’s revenue will be convergent to NT$ 74,185 million, and UMC is NT$ 13,105 million per month. This result tells the relation between TSMC and UMC will be stable equilibrium in long-term competition.