Implementing Arrow-Debreu Equilibria by Trading Infinitely-Lived Securities

By Kevin X.D. Huang and Jan Werner
December 2002 
RWP 02-08
Research Division 
Federal Reserve Bank of Kansas City 

Abstract

      We show that Arrow-Debreu equilibria with countably additive prices in infinite-time economy under uncertainty can be implemented by trading infinitely-lived securities in complete sequential markets under two different portfolio feasibility constraints: wealth constraint, and essentially bounded portfolios. Sequential equilibria with no price bubbles implement Arrow-Debreu equilibria, while those with price bubbles implement Arrow-Debreu equilibria with transfers. Transfers are equal to price bubbles on initial portfolio holdings. Price bubbles arise in sequential equilibrium under the wealth constraint if some securities are in zero supply or negative prices are permitted, but cannot arise with essentially bounded portfolios.

Keywords: Arrow-Debreu equilibrium; security markets equilibrium; price bubbles; transfers

JEL Codes: D50, G12, E44

Kevin X.D. Huang is a senior economist at the Federal Reserve Bank of Kansas City. Jan Werner is a professor of economics at the University of Minnesota. The authors acknowledge helpful discussions with Roko Aliprantis, Subir Chattopaydhyay, Steve LeRoy, Manuel Santos, and seminar participants at Brown University, University of Pennsylvania, NBER Workshop in General Equilibrium Theory, SITE 2000, and the 2000 World Congress of the Econometric Society. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Kansas City or the Federal Reserve System.

Huang e-mail:  kevin.huang@kc.frb.org
Werner e-mail:  jwerner@atlas.socsci.umn.edu