The structure of the pseudo-equilibrium manifold in economies with incomplete markets
研究了不完全市场下金融创新对社会福利的影响，通过全局分析证明增加资产种类平均而言能提高帕累托效率，且效率提升程度与代理人数量相关。
This paper addresses the classical question: Is financial innovation beneficial to a society when markets are incomplete? The general answer given here is, ‘on average, yes’. The approach we employ is global analysis. To be precise, we consider the standard two-period exchange economy with uncertainty over S states of nature in the second period. There are l agents and J real assets, where J<S. It is shown that the set of Pareto pseudo-equilibria Φp forms a submanifold (a subvector bundle) of the pseudo-equilibrium manifold Φ (vector bundle), whose codimension in Φ is (S − J)(l − 1). A simple economic intuition captured by this result is that, from a global point of view, more assets are beneficial to a society in the sense that more assets reduce the codimension of the set of Pareto equilibria and therefore enlarge its relative size in Φ. Therefore, ‘on average’, there is a greater chance of efficiency if we open new markets. Furthermore, the presence of the term (l − 1) indicates that the inefficiency cost of market incompleteness increases as the number of agents increases.