IssN 1880e2818

数理解析研究所講究録 1557

経済の数理解析.

京都大学数理解析研究所

2007 年 5 月

RIMS 1¡61tyOroku Z557

Mathematical Economics

May, 2007

Research institute for Mathematzcal SZ7iencesK)2oto University, Kyoto, .Lapan

This is a report of research done at Research Institute fbr MathematicalSciences, Kyoto University The papers contamed herem are m final form

and will not be subrmtted for publication elsewherePweface

This volume is a collecuon of papers presented at the symposium on mathematacaieconomios sponsored by the Research Instatute for Mathematacal Serences, Kyoto
Universitsc which was held dumg December 8 - 10, 2006.
On behalf of the programme committee, I would hke to extend my cord]al thanks to ali

the partzerpants of the symposium for therr smcere and constructive contnbutuons to ourproject.
Wke can safbly say that mathematieal reasonings have been playmg a mueh more
mdjspensable roles m economic theory than in any other djs(mp1ine of so( al s(iences.

There seems to be several reasons which have endowed economic theory with peculiar

mathematical characters.
1inrst of a]1, many economic phenomena pernnt expressions m terms of quantutat irve

laa Lguages.
We have a]so to take aocount of the fact that an economy conststs of a huge number ofsectx)rs whieh are entangled m a complex manner. Economic phenomena result from theinteracaons of these interdependent component sectx)rs. Inxeir mutual relation is socomphcated that an ordmary language and a casual way of thmkmg have only very 1]mited

abilities to deseribe and analyze economic phenomena. It is quite easy for anyone tormagme serious confUsions which would result if we had recourse exclusively to ordiriary

languages and casual reasonmgs. Although mathematacal reasonmgs may sometimes
seem too round’about for our purposes, sc certamly provrdes economtsta with sunple andeMctent analytlcal weapons.
Furthermore economusts have been suffemmg from the difficulty of controlled
expemments m therr researches. That us exactly why much ]mportance has been attachedto ngorous speculatave expemments m econormc theory. So called ”axiomatic method”
developed m Vienna durmg the mter”war penod should be regarded as being promoted bythe same view and recognitaon under the mfluence ofD. H]lbert.

I would be pleased very much rf our symposium could contnbute to widerung anddeepening of the mathematical foundations m economic theory
7bruMaruyama

経済の数理解析

Mathematical Economics
RIMS 研究集会報告集
˜
2006 年 12 月 8 日{}12月 10 日

研究代表者 丸山 徹 (Toru Maruyama)
目次 (*speaker)

1 Dynamic Macro-economic Theory
1 Economic Growth and Unemployment 一一一 Theoretical Foundations of Okun s Law 一 一一 1
流通科学大・情報 (UMarketmg and Distnbution Sc1》
足立 英之 (Hldeyukl Adackm》

2 A High-Dimensioma1 Keynesian Macrodynamic Model wnh and wnhout
TIMe Delay Of Pohcy Response 一一一・一・一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 一一一一一一一一一一一一一一一一 一 14
中央大・経済 (Chuo U》 浅田 統・・
・…A 郎 (Tolchlro Asada》

3 HOMOgeneous Epldemlc Systems m the S table P(rpulation 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 28
東大・数理科学 (UTokyo) 稲葉 寿 (Hisashi lnaba》

4 lnsecure Property R」ghts and Long-Run Growth under lncreasmg Returns 一一一一一一一一一一一一一一一一 45
北大・経済学 (Hokkaldo U) 板谷 淳一 (Jun-1chl Itaya》
阪大・経済学 (Osaka U) 三野 和雄 (Kazuo・Mmo》*

5 History versus Expectations m Economic Geography Reconsidered 一一一一一一一一一一一一一一一一一一一一一一一一一 58
一橋大・経済学 (Hltotsubashl U) 尾山 大輔 (Dalsuke Oyama》

il Decision Theory

6 Repre sentation of Preference Orderings on LP-spaces by Integra 1 Functionals
MyOPIa, COntMurty and TAS Utlllty 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 59

法政大・経済 (Hosel U》 佐柄 信純 (Nobusuml Sagara)
7 A Note on Certamty Effect and Self-Control 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 e 一一 一一一一一一一一一一一一 71
立命館大・経済 (Rltsumelkan・U) 武岡 則男 (Norio Takeoka)

8 Axiomatic Re-examination of the Maxirmn Principle in Arrow-Dasgupta Economy 一一一一一 93
早大・政経 (Waseda U) 須賀 晃一 (Kolchl Suga)
早大・経済学 (Waseda U) 宇田川 大輔 (Daisuke Udagawa)*
F mance
皿 9 Mathematical
Super-repllcatlon cost for a smgle large mvestor 一一一一一一一・・一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 107
福島医大 (Fukushlma Medical U) 安達 隆 (Takashl Adach1》

10Nondegeneracy condltlon of order q ln dlscrete t11 皿 e…。…・・。・一一・n 一・h 一一』一一・一一…一一一一 pe-e…。118
慶慮大・経済 (Kelo U) 新井 拓児 (TakxxJ1 Arai)

一 1 一一

1 1 On a dynamic fund protection option for a B ayesian growth optimal portfolio 一一一一一一一一一一 123
京大・経済研 (Kyoto U) 関根順 (Jun Sckme)

1 2 OPTIMAL STOPPING OF A RISK PROCESS WHEN CLAIMS ARE COVEREDIMMEDIATELY . 一一.e 一. 一. 一一一 d 一一.. 一一一. 一一一 e.... 一.e 一一 eee 一 ・. 一一一一一一..e. 一 ee 一一... 一一一. 一一一一一. 一 e-eee.. 一.. 一一. 一.pve 一 132

Wroclaw U. Tech. Bogdan K Muciek,i K rzysztof J SzaJ owski*

IV. Game, C ontract and lndustnal Organization
1 3 On the Strategic B ehavior of lnformation S ervice Company 一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一 140
東京国際大・経済 (Tokyo lnternational U》 古川 徹也 (Tetsuya Furukawa)
1 4 An lnterpretation of the (ireatest Hits 一 1ike Behavior 一一一一一一一一一一一一一一一一一一一一一・・一一一一一・一一一一一一一一一一一 152

賢慮大・経済学 (Keio U) 細矢 声誉 (Yuhkl Hosoya》
1 5 Pnce and Quantity Competition m an Oligopoly with Discrete Choices 一一一一一一一一一一一一一一一一一 162
名大・経済学 (Nagoya U) 河合 伸 (Shln Kawa1)*〃 皆川 正 (Tadash1 Mlnagawa》

1 6 Reconsideration of the Defimtion of C ommitment-Proof Agreements 一一一一一一一一一一一一一一一一一一一一一 173
大阪経済大・経済 (Osaka U Economlcs》 増澤 拓也 (Takuya Masuzawa)
1 7 Bayesian Communication Leadmg to a N ash Equilibnum in Belief 一一一一一一一一一一一一一一一一一一一一 179
茨城工業高専 (lbaraki・Nat Coll Tech) 松久 隆 (Takashi Matsuhlsa)*

Samt-Petersburg State U P avel S trokan
1 8 Electnclty markets analysls and deslgn 一一一一一一一一一一 q 一一一一一一一一一一一一一一一一 ・一・・一一一一一一一一一一一一一一一 b 一一一一一一一一 187
Lomonosov Moscow State U/ New Econ Sch Alexander Vasm*

Dorodnicyn C omputmg Center of the RAS Polma Vasima

V. Histoncal Perspectives
1 9 Vilfredo Pareto and the lntegrability Problem of Demand Functions 一一一一一一一一一一一一一一一一一一一一一一 211
慶鷹大・経済 (Kelo U》 須田 伸一 (Shlmchl Suda)

一 11 一