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"Equations on the Derivatives of an Initial Endowment-Competitive Equilibrium Mapping for an Exchange Economy"

Steven R. Williams

 

First Author :

Steven R. Williams
Economics
University of Illinois at Urbana-Champaign
1206 S. Sixth Street, M/C 706
Champaign, IL 61820
USA

swillia3@uiuc.edu

http://www.business.uiuc.edu/faculty/williams.html

 
 
Abstract :
 
Consider an exchange economy with n traders and k goods. Suppose that there exists C2 mappings p(·) and x (·) that specify for each initial endowment w of the k goods to the n traders a price vector p(w) and a vector of net trades x(w) that deŽne a competitive equilibrium. Three systems of determinant equations are derived that the derivatives of p(·) and x(·) necessarily satisfy regardless of the underlying preferences that determine these mappings. Each of the three systems of equations fundamentally reflects the interaction among traders in the competitive mechanism.
 
 
Footnotes & Acknowledgements :
 
I thank Wayne Shafer for bringing to my attention the relationship between some of my work on decentralized mechanisms and a research program of Don Brown and Rosa Matzkin, which led to this paper. I also thank Leonid Hurwicz, Felix Kubler, Bill Zame and other participants at the 2002 General Equilibrium Theory Conference for their comments.
 
 
Manuscript Received : 2002
Manuscript Published : 2002
 
 
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