Abstract
The paper reviews results on indeterminateness of equilibria in two extensions of the standard (Arrow-Debreu) model of general equilibrium. These extensions, motivated by macroeconomic interpretations, concern money and price rigidities. In a natural extension to money (held for transaction purposes), if monetary policy fixes either nominal interest rates or money supply (but not both), the variability of inflation rates is unrestricted, at equilibrium. In the absence of initial nominal asset positions, the indeterminateness of inflation rates is harmless, in the complete-markets framework of Arrow-Debreu. When some relative prices are predetermined, there exists generically a continuum of real equilibria, indexed by the overall degree of rationing. In a model combining money and nominal price rigidities, the fixed nominal prices limit the indeterminateness of inflation rates, but the real indeterminateness subsits. When one introduces in addition a tâtonnement process of nominal price formation, incorporating some downward nominal rigidities, both the nominal and the real indeterminateness may be eliminated (through the initial conditions), in the complete-markets framework. It is argued that macroeconomic interpretations call for an incomplete-markets framework, hence for expectations, another source of indeterminateness. A concluding section offers some heuristic remarks on the open problems associated with market incompleteness.
The author thanks Jean-Jacques Herings and David de la Croix for stimulating discussions on the contents of this paper.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arrow K.J. and G. Debreu (1954) “Existence of an equilibrium for a competitive economy”Econometrica 22 265–290.
Baumol, W. J. (1952): “The transactions demand for cash: an inventory theoretic approach”Quarterly Journal of Economics66, 545–556.
Blanchard, O. and S. Fisher (1989)Lectures on MacroeconomicsMIT Press, Cambridge (Mass).
Bloise, G., Drèze, J.H. and H. Polemarchakis (2001), “Monetary Equilibria over an Infinite Horizon”, mimeo, CORE, Louvain-la-Neuve.
Browder, F.E. (1960), “On Continuity of Fixed Points under Deformations of Continuous Mappings”Summa Brasiliensis Mathematicae 4183–91.
.Citanna, A., H. Crs, J.H. Drèze, P.J.J. Herings and A. Villanacci (2001), “Continua of Underemployment Equilibria Reflecting Coordination Failures, Also at Walrasian Prices”, forthcoming inJournal of Mathematical Economics.
Clarida, R., Gali, J. and M. Gertler (1999), “The Science of Monetary Policy: A New Keynesian Perspective”Journal of Economic Literature XXXVII 41161–1707.
Clower, R. (1967), “A Reconsideration of the Microfoundations of Monetary Theory”Western Economic Journal 6 1-8.
Dehez P. and J.H. Drèze (1984) “On Supply-Constrained Equilibria”Journal of Economic Theory 33 1172–182.
Drèze, J.H. (1997), “Walras-Keynes Equilibria, Coordination and Macroeconomics”European Economic Review 411735–1762.
Drèze, J.H. (1999a), “On the Dynamics of Supply-constrained Equilibria” in P.J.J. Herings, G. van der Laan and A.J.J. Talman, EdsTheory of Marketspp. 7–25, North-Holland, Amsterdam.
Drèze, J.H. (1999b), “The Formulation of Uncertainty: Prices and States”, Chap. 3 in G. Chichilnisky, Ed.Markets Information and UncertaintyEssays in Economic Theory in Honor of K.J. Arrow, Cambridge University Press, Cambridge, UK.
Drèze J.H. (2001) “On the Macroeconomics of Uncertainty and Incomplete Markets”Recherches Economiques de Louvain 67 13–28; Chap. 3 in J.H. Drèze, Ed.Advances in MacroeconomicsPalgrave, London.
Drèze, J.H. and H.M. Polemarchakis (1999), “Money and Monetary Policy in General Equilibrium” in: L.-A. Gérard-Varet, A. P. Kirman and M. Ruggiero, EdsEconomics the Next Ten YearsOxford University Press, Oxford.
Drèze, J.H. and H.M. Polemarchakis (2001a), “Intertemporal General Equilibrium and Monetary Theory”, Chap. 2 in A. Leijonhufvud, Ed.Monetary Policy as a Basis for Monetary PolicyPalgrave, London.
Drèze, J.H. and H.M. Polemarchakis (2001b), “Monetary Equilibria”, Chap. 5 in G. Debreu, W. Neuefeind and W. Trockel, EdsEconomics Essays A Festschrift for Werner HildenbrandSpringer, Berlin-Heidelberg.
Grandmont, J.M. (1982) “Temporary General Equilibrium Theory”, Chap.19 in K.J. Arrow and M.D. Intriligator, EdsHandbook of Mathematical EconomicsNorth-Holland, Amsterdam.
Hahn, F. and R. Solow (1995), ACritical Essay on Modern Macroeconomic TheoryMIT Press, Cambridge (Mass).
Herings, P.J.J. (1996)Static and Dynamic Aspects of General Disequilibrium TheoryKluwer, Boston.
Herings, P.J.J. and J.H. Drèze (1998), “Continua of Underemployment Equilibria”, CenTER DP 9805, Tilburg and CORE DP 9845, Louvain-La-Neuve.
Keynes, J.M. (1936)The General Theory of Employment Interest and MoneyMacmillan, London.
Leijonhufvud, A. (1968)On Keynesian Economics and the Economics of KeynesOxford University Press, Oxford.
Lucas, R. and N. Stokey (1987), “Money and Rates of Interest in a Cash-inAdvance Economy”Econometrica55, 491–513.
Magill, M and W. Shafer (1991), “Incomplete Markets”, Chap. 30 in K. Arrow and M. Intriligator, EdsHandbook of Mathematical EconomicsNorth-Holland, Amsterdam.
Mas-Colell, A. (1974), “A Note on a Theorem of F. Browder”Mathematical Programming 6229–33.
Radner, R. (1979), “Rational Expectations Equilbrium: Generic Existence and the Information Revealed by PricesEconometrica44, 655–78.
Sargent, T.N. and N. Wallace (1975), “Rational Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule”Jounral of Political Economy83 241–254.
Sims, C.A. (1994), “A Simple Model of the Determination of the Price Level and the Interaction of Monetary and Fiscal Policy”Economic Theory4, 381399.
Tobin, J. (1956): “The interest-elasticity of transactions demand for cash”Review of Economics and Statistics38, 241–247.
Tobin, J. (1972), “Inflation and Unemployment”American Economic Review62, 1, 1–18.
Van der Laan, G. (1984), “Supply-Constrained Fixed Price Equilibria in Monetary Economies”Journal of Mathematical Economics13, 2, 171–187.
Walras, L. (1902) (4th Edition)Elements d’Economie Politique PureF. Rouge.
Weddepohl, C. (1996), “A Simulation Study of Disequilibrium Price Dynamics”, Chap 15 in W.A. Barnett, G. Gandolfo and C. Hillinger, EdsDynamic Disequilibrium ModellingCambridge University Press, Cambridge, UK.
Woodford, M. (1994), “Monetary Policy and Price Level Determinacy in a Cash-in Advance Economy”Economic Theory4, 345–380.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Drèze, J.H. (2002). Indeterminateness of Equilibria and Macroeconomics. In: Hommes, C.H., Ramer, R., Withagen, C.A. (eds) Equilibrium, Markets and Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56131-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-56131-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62820-7
Online ISBN: 978-3-642-56131-3
eBook Packages: Springer Book Archive