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Computing Equilibria in Finance Economies with Incomplete Markets and Transaction Costs

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  • P. Jean-Jacques Herings
  • Karl Schmedders

Abstract

Transaction costs in financial markets may have important consequences for volumes of trade, asset pricing and welfare. In the economic literature they are often given as one reason for the incompleteness of asset markets, which is a striking example of their potential impact on volumes of trade. We argue that analytical results on the impact of transaction costs are hard to obtain and a computational approach is needed. This paper introduces the first algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and linear transaction costs on the financial markets. The algorithm is based on the homotopy principle and is able to deal with the two major technical difficulties of the model, namely the existence of non-differentiabilities of agents'' asset demands as a function of the asset prices and the existence of locally non-unique equilibria. Several numerical examples give a first glimpse of the impact of transaction costs on the nature of the equilibria. We show that the consequences of transaction costs for volumes of trade and prices can be counterintuitive even for small economic models.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1318.

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Date of creation: Jun 2001
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Handle: RePEc:nwu:cmsems:1318

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  1. Schmedders, Karl, 1998. "Computing equilibria in the general equilibrium model with incomplete asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1375-1401, August.
  2. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
  3. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  4. Pradeep Dubey & John Geanakoplos & Martin Shubik, 1988. "Default and Efficiency in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 879R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1989.
  5. Herings, P.J.J., 1994. "A globally and universally stable price adjustment process," Discussion Paper 1994-52, Tilburg University, Center for Economic Research.
  6. John Heaton & Deborah Lucas, 1993. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," NBER Working Papers 4249, National Bureau of Economic Research, Inc.
  7. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
  8. Elul, Ronel, 1997. "Financial innovation, precautionary saving and the risk-free rate," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 113-131, February.
  9. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
  10. Demarzo, Peter M. & Eaves, B. Curtis, 1996. "Computing equilibria of GEI by relocalization on a Grassmann manifold," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 479-497.
  11. Hens,Thorsten, 1991. "Structure of general equilibrium models with incomplete markets and a single consumption good," Discussion Paper Serie A 353, University of Bonn, Germany.
  12. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
  13. Arrow, Kenneth J. & Hahn, Frank, 1999. "Notes on Sequence Economies, Transaction Costs, and Uncertainty," Journal of Economic Theory, Elsevier, vol. 86(2), pages 203-218, June.
  14. Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
  15. S Rao Aiyagari & Mark Gertler, 1997. "Asset Returns with transaction costs and uninsured individual risk," Levine's Working Paper Archive 648, David K. Levine.
  16. Geanakoplos, John, 1990. "An introduction to general equilibrium with incomplete asset markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 1-38.
  17. Prechac, Christophe, 1996. "Existence of equilibrium in incomplete markets with intermediation costs," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 373-380.
  18. S. Rao Aiyagari & Mark Gertler, 1990. "Asset Returns with Transactions Cost and Uninsured Risk: A Stage III Exercise," NBER Working Papers 3481, National Bureau of Economic Research, Inc.
  19. Laitenberger, Marta, 1996. "Existence of financial market equilibria with transaction costs," Ricerche Economiche, Elsevier, vol. 50(1), pages 69-77, March.
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Cited by:
  1. Marko Backovic & Zoran Popovic, 2012. "The Analysis Of Model Of General Economic Equilibrium And Financial Instability Of Economic System," Montenegrin Journal of Economics, Economic Laboratory for Transition Research (ELIT), vol. 8(1), pages 63-85.
  2. Carosi, Laura & Gori, Michele & Villanacci, Antonio, 2009. "Endogenous restricted participation in general financial equilibrium," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 787-806, December.
  3. V. Filipe MARTINS-DA-ROCHA & YIANNIS VAILAKIS, 2008. "Endogenous Transaction Costs," Discussion Papers 0810, Exeter University, Department of Economics.
  4. Gori, Michele & Pireddu, Marina & Villanacci, Antonio, 2013. "Regularity and Pareto improving on financial equilibria with price-dependent borrowing restrictions," Research in Economics, Elsevier, vol. 67(1), pages 100-110.
  5. V. Martins-da-Rocha & Yiannis Vailakis, 2010. "Financial markets with endogenous transaction costs," Economic Theory, Springer, vol. 45(1), pages 65-97, October.
  6. Michele Gori & Marina Pireddu & Antonio Villanacci, 2010. "Regularity and Pareto Improving on financial equilibria with endogenous borrowing restrictions," Working Papers - Mathematical Economics 2010-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa, revised Aug 2012.

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