Alternative Analytical Languages and their Translation in Economics
Project/Area Number  08630005 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
経済理論

Research Institution  Chiba University 
Principal Investigator 
NOMURA Yoshimasa Chiba University, Faculty of Law and Economics, Professor, 法経学部, 教授 (00218372)

CoInvestigator(Kenkyūbuntansha) 
KAKIHARA Kazuo Chiba University, Faculty of Law and Economics, Professor, 法経学部, 教授 (30110282)

Project Fiscal Year 
1996 – 1997

Project Status 
Completed(Fiscal Year 1997)

Budget Amount *help 
¥1,900,000 (Direct Cost : ¥1,900,000)
Fiscal Year 1997 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1996 : ¥1,100,000 (Direct Cost : ¥1,100,000)

Keywords  Nonstandard analysis / Loeb measure / general equilibrium / core / bargaining set / infinite dimensional commodity space / limit theorems / asymptotic interpretations / 超準解析 / ローブ測度 / 競争均衡 / コア / 交渉集合 / 無限次元財空間 / 極限定理 / 漸近解釈 / 市場均衡 / 経済コア 
Research Abstract 
For the MasColell bargaining set, despite its wellknown subtle convergence, the hyperfinite Loeb measure economy has the advantage over the Lebesgue measurable continuum economy by demonstrating its effectiveness in establishing the following major results intractable by the continuum idealization. 1.In a largesquare economy on a Loeb measure space of agents and with an infinite dimensional Banach space of commodities, we secure the desired Lyapunovtype convexity and Fatoutype upper semicontinuity for integrals of Borelmeasurable correspondences expressing individual economic decisions. These enable us to extend MasColell's equivalence theorem for the bargaining set into a largesquare economy. 2.By an asymptotic interpretation of 1, we derive convergence of the MasColell bargaining set along an increasing sequence of finite economies with infinitely many commodities. 3.By a standard proof patterned after that for 1, we establish equivalence for the MagColell bargaining set in a continuum economy with countably many commodities. 4.By eliminating all "external" entities from the proof 1, and suitably restricting to those commodity spaces that permit space specific arguments, we give "elementary" convergence theorems for the MasColell bargaining set incorporating error terms reciprocal to the population. Directions for Future Research : 1.Evaluate the advantage of the Loeb measure idealization of largesquare economies over the continuum idealization in deriving "generic" (non) convergence of several bargaining sets with subtle differences in their treatment of "(no) leader (s)" for objections, with an emphasis on robustness of these conclusions along nonreplica sequences of finite economies. 2.Represent mixed markets by hyperfinite Loeb measure spaces, rich enough to treat both atoms and an atomless sector in the same manner, to conclude convergence of bargaining sets which are known to distinguish the noncompetitive nature of the markset better than the core.

Report
(4results)
Research Output
(17results)