1997 Fiscal Year Final Research Report Summary
Alternative Analytical Languages and their Translation in Economics
| Project/Area Number |
08630005
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
経済理論
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| Research Institution | Chiba University |
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Principal Investigator |
NOMURA Yoshimasa Chiba University, Faculty of Law and Economics, Professor, 法経学部, 教授 (00218372)
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| Co-Investigator(Kenkyū-buntansha) |
KAKIHARA Kazuo Chiba University, Faculty of Law and Economics, Professor, 法経学部, 教授 (30110282)
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| Project Period (FY) |
1996 – 1997
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| Keywords | Nonstandard analysis / Loeb measure / general equilibrium / core / bargaining set / infinite dimensional commodity space / limit theorems / asymptotic interpretations |
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| Research Abstract |
For the Mas-Colell bargaining set, despite its well-known 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 large-square economy on a Loeb measure space of agents and with an infinite dimensional Banach space of commodities, we secure the desired Lyapunov-type convexity and Fatou-type upper semicontinuity for integrals of Borel-measurable correspondences expressing individual economic decisions. These enable us to extend Mas-Colell's equivalence theorem for the bargaining set into a large-square economy.
2.By an asymptotic interpretation of 1, we derive convergence of the Mas-Colell 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 Mag-Colell 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 Mas-Colell bargaining set incorporating error terms reciprocal to the population.
Directions for Future Research :
1.Evaluate the advantage of the Loeb measure idealization of large-square 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 non-replica 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 non-competitive nature of the markset better than the core.
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