本論文研究兩家各生產兩種商品的多產品廠商如何分配產品研發的投資組合，以及產品研發對社會的影響。其中，本論文的商品同時具有水平與垂直差異，而且兩家廠商也存在著廠商間的研發外溢效果。廠商在第一階段決定投入多少研發，並且在第二階段數量競爭。有別於將多產品產商與成本研發相結合的文獻，我們發現到在產品研發上，只要邊際成本夠小且水平產品差異度夠大，廠商就會更傾向於投資較多研發在低品質商品上。廠商是否會集中研發取決於(1) 邊際成本、(2)水平差異度、(3)廠商間外溢效果、(4)高品質產品的初始品質，以及(5)低品質產品的初始品質。透過數值分析，我們發現到產品研發以及廠商間外溢效果對整個社會都有正面效果。

This essay sheds light on the R&D portfolio choices of multiproduct firms, and the effect of product R&D toward the society. Our model presents a
multiproduct duopoly which both firms produce two products, which own both horizontal and vertical differentiation, and both firms have inter-firm R&D spillover effect. Firms decide the amount of product R&D in the first stage, and conduct quantity competition in the second stage. Unlike the literature combined both multiproduct firms and process R&D, firms under product R&D tend to invent more on low-quality product if marginal cost is small enough and the degree of horizontal product differentiation is high enough. Whether firms will specialize their R&D depends one (1) marginal cost, (2) the degree of horizontal product differentiation, (3) the degree of inter-firm R&D spillover. With numerical simulation, we show that the product R&D and inter-firm R&D spillover have positive effect toward the whole society.

圖形目錄 vi

表格目錄 vii

第一章 緒論 1

1 研究動機 1

2 文獻回顧 3

第二章 模型設定 6

1 第二階段 7

第三章 事件0：廠商無法進行研發 9

第四章 事件1：廠商可以進行研發，但沒有研發外溢效果 10

1 三個效果 10

2 反應函數與均衡研發投入 13

2.1 情況1.1：(G2)成立，x_H>x_L 16

2.2 情況1.2：(G2)不成立，x_H
3 對產量的影響 20

第五章 事件2：廠商可以進行研發，也存在廠商間的研發外溢效果 22

1 三個效果 22

2 反應函數與均衡研發投入 24

2.1 情況2.1：(G4)成立，x_H>x_L 27

2.2 情況2.2：(G4)不成立，x_H
3 對產量的影響 34

第六章 數值分析：事件比較 35

1 事件0和事件1的比較 35

2 事件0和事件2的比較 39

3 事件1和事件2的比較 49

第七章 結論 66

參考文獻 68

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