臺灣博碩士論文加值系統

Brouwer不動點定理是證明完全市場一般均衡存在性的關鍵。然而 [4] 指出在不完全市場下，一般均衡未必存在。本篇論文中我們綜合 [2]、[6] 的方法，利用Grassmannian流形的mod 2尤拉示性數不變的特性，得到類似的不動點定理，進而證明了不完全市場下，條件較弱的「假均衡」(Pseudo-equilibrium) 存在。論文最後討論一般均衡的普遍性，即一般均衡存在的經濟體是一稠密的開集合。

Brouwer’s fixed point theorem is critical to the existence of general equilibria in a complete market. However, [4] pointed out that in an incomplete market, a general equilibrium does not always exist. In this paper, following [2] and [6], we use the invariant property of mod 2 Euler number of Grassmannian manifold to derive a fixed-point-like theorem, and therefore, prove the existence of a weaker “pseudo-equilibrium”. At last, we discuss the genericity of general equilibria, that is, the economy in which the equilibria exist is an open and dense set.

口試委員審定書…………………………………………………………i
中文摘要………………………………………………………………ii
英文摘要………………………………………………………………iii
1.Introduction…………………………………………………………1
2.The Economic Structure……………………………………………3
3.Pseudo-equilibria……………………………………………………6
4.Existence of Equilibrium…………………………………………13
Appendix………………………………………………………………20
References……………………………………………………………24

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[2] Darrell Duffie and Wayne Shafer. Equilibrium in incomplete markets: A basic model of generic existence. Journal of Mathematical Economics, 14:285-300, 1985
[3] Victor Guillemin and Alan Pollack. Differential Topology. 1974
[4] Oliver D. Hart. On the optimality of equilibrium when the market structure is incomplete. Journal of Economic Theory, 11:418-443, 1975.
[5] M.W. Hirsch. Differential Topology. Springer-Verlage,1976.
[6] M.D. Hirsch, M. Magill and A. Mas-Collel. A geometric approach to a class of equilibrium existence theorems. Journal of Mathematical Economics, 19:95-106, 1990.
[7] S.Y. Husseini, J.M. Lasry and M.J.P. Magill. Existence of equilibrium with incomplete markets. Journal of Mathematical Economics, 19:39-67, 1990.
[8] Ryo Nagata. The Theory of Regular Economies. 2004.