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姓名 林雲雀(Yun-Chieh Lin)  查詢紙本館藏   畢業系所 產業經濟研究所
論文名稱 不對稱Cournot寡占三篇論文集
(Three Essays on Asymmetric Cournot Duopoly)
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摘要(中) 本論文以不對稱的產品作為討論的主軸,以Cournot 競爭討論雙占下的產量排序、社會福利等相關的議題分析。內容共分為三部分-前兩部分分別以代替品與互補品分開分析,第三部分則以第一部分的代替品加以應用,討論在此模型架構下,加入技術進步後的三種授權模式(包括:固定費用授權、最適授權金以及合併三種模式)下的分析。
第二章討論代替品的分析中,當完全競爭和獨占都是內解時,則Cournot 解也是內解;反之未必成立。因此討論兩種狀況:(1)當三者都是內解時,當產品的不對稱性低時,產量與社會福利的排序都是正常;當產品的不對稱性高時,有效率的產品在獨佔下比Cournot 下的產量高,在Cournot 的產業產量比在獨佔下低。
(2)當Cournot 為內解,而獨占為角解時,則出現產量和社會福利的不正常排序情形,即Cournot 競爭下的社會福利比獨占下的社會福利低。另,Cournot 下的價格比獨占下的價格低,因此出現低價格未必伴隨著高福利的情形。
第三章在互補品的分析中,如果Cournot 競爭下為內解(active),則獨占下亦然;然獨占下為內解時,反之未必成立。在獨佔下則出現交叉補貼的情形。這有兩個意涵,一為當存在有輔助品時,產量降低有助於提高社會福利。因此,Cournot下的社會福利不一定比獨占下的社會福利低。二為當兩個產品都是基礎品時,Cournot 下的社會福利比獨占下的社會福利低。為了證明社會福利排序是否出現
逆轉的結果,我們證明出:獨佔下的產品價格低於Cournot 競爭下的產品價格,而且低價的產品產生的社會福利較高,也就是獨占下創造出的社會福利較高。
最後在兩階段的技術授權部分,我們以三種方式比較出兩階段的技術授權:不管是福利或是產量排序都與需求不對稱的程度有重要的關係。
摘要(英) This dissertation concludes three parts analyzes goods with asymmetric Cournot duopoly. First, it’s demonstrated for two differentiated goods that if one of the perfectly competitive equilibrium and monopoly solution is interior, then Cournot equilibrium is interior; and the converse is not true. Consider two cases. One is that both Cournot equilibrium and monopoly solution are interior and if the asymmetry between goods is weak enough, then everything is normal. Otherwise, the more efficient good’’s Cournot output is lower than its monopoly output, and industry output may be lower in Cournot equilibrium than in monopoly solution. Nonetheless, the welfare ranking is normal. The other is that Cournot equilibrium is interior, whereas monopoly solution is corner. The abnormal rankings regarding outputs are able to reverse the welfare ranking: Cournot equilibrium yields lower welfare than monopoly
solution if and only if the asymmetry between is strong enough. We establish that each Cournot price falls below its corresponding monopoly price regardless of whether monopoly solution is interior or not. Unfortunately, it is known that lower prices are not necessarily better in welfare terms.
Second, it is demonstrated in two complementary goods if a good is active in Cournot equilibrium, then it is active in monopoly solution; but, the converse is not true. We
establish that if and only if a good is supplemental, then, in monopoly solution, it should be cross-subsidized. When there exists a supplemental good, lower quantities
are not necessarily worse in welfare terms, and hence Cournot equilibrium is not necessarily less welfare-efficient than monopoly solution. The other is that if each
good is a base good, then Cournot equilibrium indeed is less welfare-efficient than monopoly solution. We demonstrate that prices are lower in monopoly solution, and
that lower prices are better in the welfare terms. These two results imply that welfare is higher in monopoly solution, no matter the solutions are interior or not.
Finally, we apply in licensing by means of a two-part tariff in a Cournot duopoly where one of the firms is the patentee of a cost-reducing technology created by an
innovation. We compare the two-part tariff licensing by three alternative means for the transfer of technological knowledge: the fixed-fee licensing, the royalty licensing
and the merger. We demonstrate that the results are sensitive to the degree of demand asymmetry.
關鍵字(中) ★ 技術授權
★ 產量結構.寡占.獨占
關鍵字(英) ★ Cournot Duopoly
★ output structure
★ monopoly
★ technology licensing
論文目次 Contents
Contents i
List of Figures iii
1 Introduction 1
2 Comparing Cournot Duopoly with Monopoly in Asymmetric Differentiated Goods 3
2.1 introduction . . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Basic properties of the three solutions . . . . . . . . . . . . . . . . . . . . . 8
2.4.1 The basic lemma for welfare comparison . . . . . . . . . . . . . . . 8
2.4.2 The linear demand model . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 The Quantity Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5.1 Product selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5.2 Individual outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.3 Output level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.4 Output structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.5 Welfare analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Individual Price Rankings . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Comparing Cournot Duopoly with Monopoly in Asymmetric Comple-
ments Goods 23
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Reaction curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 The basic lemma for welfare comparison . . . . . . . . . . . . . . . . . . . 29
3.6 The Rankings Regarding Outputs, Prices and Welfare . . . . . . . . . . . . 30
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Comparing Two-part Tariff Licensing in a Cournot Duopoly in Differ-
entiated Goods 34
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 The Model and the Game . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 The Second Stage Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 A Preliminary Analysis of the First Stage . . . . . . . . . . . . . . . . . . . 41
i
4.5 The Solution for the Preplay Stage . . . . . . . . . . . . . . . . . . . . . . 44
4.6 Ramsey output vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.7 Three Outcomes Compared . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.8 Two Traditional Results Revisited . . . . . . . . . . . . . . . . . . . . . . . 52
4.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5 Conclusions 60
References 64
A Appendix of Ch2 66
A.1 The proof of (2.17) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
A.2 The proof of Proposition 2.5.5 . . . . . . . . . . . . . . . . . . . . . . . . . 66
A.3 The proof of Proposition 2.5.9 . . . . . . . . . . . . . . . . . . . . . . . . . 67
A.4 The proof of Fact 2.6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
A.5 The proof of Lemma 2.6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
B Appendix of Ch4 70
B.1 The proof of Proposition 4.4.2 . . . . . . . . . . . . . . . . . . . . . . . . 70
B.2 The proof of Fact 4.5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
B.3 The proof of Lemma 4.5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
B.4 The proof of Fact 4.5.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
B.5 The proof of Fact 4.6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
B.6 The proof of Proposition 4.7.2 . . . . . . . . . . . . . . . . . . . . . . . . 71
B.7 The proof of Proposition 4.7.5 . . . . . . . . . . . . . . . . . . . . . . . . 71
B.8 The proof of Lemma 4.8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
B.9 The proof of Lemma 4.8.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
ii
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指導教授 張明宗(Ming Chung Chang) 審核日期 2012-7-16
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