Price expectations in neo-Walrasian equilibrium models: an overview

Fratini, Saverio M. and Levrero, Enrico Sergio and Ravagnani, Fabio (2016): Price expectations in neo-Walrasian equilibrium models: an overview.

Abstract

Since the late 1960s, the efforts of general equilibrium theorists have been directed towards overcoming the evident limitation of the Arrow-Debreu model, i.e. the assumption that the transactions associated with the future activities of agents are all regulated at the initial date on a complete system of forward markets. Research has thus focused on ‘sequential economies’, in which spot markets are active in each period, and has developed along two paths, both inspired by Hicks’s Value and Capital and stressing the dependence of agents’ choices on their expectations of future prices. The first is temporary equilibrium theory, in which expectations are assumed to be subjective. The second postulates that all agents exactly predict the future prices (sequential economies with perfect foresight). This paper examines the analytical problems that the inclusion of expectations among the determinants of equilibrium originates within each approach. In the light of the studies of the 1970s and 1980s, it first illustrates the difficulties that arise in temporary equilibrium theory due to the subjective nature of individual forecasts. Then it moves on to examine sequential economies with perfect foresight. After illustrating the equilibrium notion on which the analysis of those economies relies, i.e. the ‘equilibrium of plans, prices and price expectations’ introduced by Radner (1972), it indicates, on the basis of recent contributions, that for plausible configurations of the economy the perfect foresight associated with Radner equilibria proves not only unrealistic but also theoretically dubious.

• Item Type: MPRA Paper
• Language: English
• Keywords: expectations; temporary equilibrium; Radner equilibrium
• Subjects: B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B21 - Microeconomics; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D46 - Value Theory; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D84 - Expectations ; Speculations

References

Arrow, K. (1953). Le rôle des valeurs boursières pour la répartition la meilleure des risques. Cahiers du Séminaire d’Economètrie, 40, 41-48. Reprinted as: (1964) The Role of Securities in the Optimal Allocation of Riskbearing. Review of Economic Studies, 31, 91-96.

Arrow, K.J. and Hahn, F.H. (1971). General Competitive Analysis. S. Francisco: Holden Day.

Bliss, C.J. (1976). Capital theory in the short run. In: M. Brown, K. Sato and P. Zarembka (eds) Essays in Modern Capital Theory. Amsterdam: North Holland.

Bliss, C.J. (1983). Consistent temporary equilibrium. In: J.P. Fitoussi (ed.) Modern Macroeconomic Theory. Oxford: Basil Blackwell.

Borglin A. and Tvede M. (2006). Economic Dynamics and General Equilibrium. Time and Uncertainty. Verlag: Springer.

Cass, D. (1984). Competitive equilibrium with incomplete financial markets. CARESS Working Paper, University of Pennsylvania, 84-09.

Dorfman R., Samuelson P.A., Solow R.M. (1958). Linear Programming and Economic Analysis, New York: McGraw-Hill.

Drèze J.H. and Herings P.J.J. (2008). Sequentially complete markets remain incomplete. Economic Letters, 100: 445-447.

Duffie, D. and Shafer, W. (1985). Equilibrium in incomplete markets I: basic model of generic existence. Journal of Mathematical Economics, 14, 285-300.

Duffie, D. and Shafer, W. (1986). Equilibrium in incomplete markets II: generic existence in stochastic economies. Journal of Mathematical Economics, 15, 199-216.

Fratini, S.M. and Levrero, E.S. (2011). Sraffian indeterminacy: a critical discussion. Cambridge Journal of Economics, 35(6): 1127-49.

Geanakoplos, J. and Polemarchakis, H.M. (1986). Existence, regularity and constrained suboptimality of competitive allocations when the asset market is incomplete. In: W. Heller, R. Starr and D. Starrett (eds), Uncertainty, Information and Communication: Essays in Honor of K. J. Arrow, vol. III. Cambridge: Cambridge University Press

Geanakoplos, J., and Mas-Colell, A. (1989). Real indeterminacy with financial assets. Journal of Economic Theory, 47: 22-38.

Grandmont, J.M. (1977), Temporary general equilibrium theory. Econometrica, 45, 535-572.

Grandmont J.M. (1988). Temporary equilibrium: money, expectations and dynamics. Seminar Paper no 422, Institute for International Economic Studies.

Grandmont, J.M. and Laroque G. (1976), On temporary Keynesian equilibria. The Review of Economic Studies, 43, 53-67.

Green, J.R. (1973), Temporary general equilibrium in a sequential trading model with spot and future transactions. Econometrica, 41, 1103-23.

Grossman, S. J. and Hart, O. (1979), A theory of competitive equilibrium in stock market economies. Econometrica, 47, 293-330.

Guesnerie, R. (2006), General equilibrium, coordination and multiplicity on spot markets. PSE Working Papers n. 2006-05.

Guesnerie, R. and Jaffray J.Y. (1974), Optimality of Equilibria of Plans, Prices and Price Expectations. In: J. Drèze (ed.), Uncertainty, Equilibrium, Optimality. London: Macmillan.

Hayek, F.A. (1928). Das intertemporale gleichgewichtssystem der preise und die bewegungen des ‘geldwertes.’ Weltwirtschaftliches Archiv, N. 28, pp. 33-76. English translation (1984). Intertemporal price equilibrium and movements in the value of money. In: R. McCloughry (ed.) Money, Capital and Fluctuations: Early Essays. Chicago: The Chicago University Press.

Hellwig M. (1996), Rational expectations equilibria in sequential economies with symmetric information: The two period case, Journal of Mathematical Economics, 26, 9-49

Hicks, J.R. (1933). Gleichgewicht und konjunktur. Zeitschrift für Nationalökonomie, 4(4), 441-55. English translation (1982). Equilibrium and the trade cycle. In: Money, Interest and Wages: Collected Essays in economic Theory, vol. II. Oxford: Basil Blackwell.

Hicks J.R. (1946). Value and Capital, 2nd edition. Oxford: Clarendon Press.

Hicks J.R. (1965). Capital and Growth. Oxford: Clarendon Press.

Kehoe T.J. and Levine, D.K. (1990). The economics of indeterminacy in overlapping generations models. Journal of Public Economics, 42, 219-243.

Mandler M. (1995). Sequential indeterminacy in production economies. Journal of Economic Theory, 66: 406-436.

Mandler M. (1999). Sraffian indeterminacy in general equilibrium. The Review of Economic Studies, 66(3): 693-711.

Mandler M. (2008) Sraffian Economics (New Developments). In: L. Blume and S. Durlauf (eds), The New Palgrave Dictionary of Economics, 2nd edition. Basingstoke, Hampshire New York: Palgrave Macmillan.

Magill, M. and Shafer, W. (1991). Incomplete markets. In: W. Hildebrand and H. Sonnenschein (eds), Handbook of Mathematical Economics, vol. IV. Amsterdam: North-Holland.

Magill, M. and Quinzii, M. (1996). Theory of Incomplete Markets. Cambridge (MA): MIT Press.

Mas-Colell, A., Whinston, D. and J. Green, J. (1995). Microeconomic Theory. New York and Oxford: Oxford University Press.

McKenzie, L.W. (1989), General equilibrium, in J. Eatwell, M. Milgate and P. Newman (eds), The New Palgrave: General Equilibrium, Palgrave Macmillan

Milne, F. (1980). Short-selling, default risk and the existence of equilibrium in a securities model. International Economic Review, 21, 255-267.

Radner, R. (1972). Equilibrium of plans, prices and price expectations. Econometrica, 40: 289-303.

Radner, R. (1974). Market equilibrium and uncertainty: concepts and problems. In M.D. Intriligator and D.A. Kendrick (eds), Frontiers of Quantitative Economics, vol. II. Amsterdam: North-Holland.

Radner, R. (1982). Equilibrium under uncertainty. In K.J. Arrow and M.D. Intriligator (eds), Handbok of Mathematical Economics, vol. II. Amsterdam: North-Holland.

Radner R. (1989), Uncertainty and general equilibrium, in J. Eatwell, M. Milgate and P. Newman (eds), The New Palgrave: General Equilibrium, Palgrave Macmillan

Radner, R. (1991). Intertemporal general equilibrium. In L.W. McKenzie and S. Zamagni (eds), Value and Capital Fifty Years Later. London: Macmillan.

Sato, K. (1976). Comment on Bliss. In: M. Brown, K. Sato and P. Zarembka (eds), Essays in Modern Capital Theory. Amsterdam: North Holland.

Stahl, D.O. (1983). Bankruptcy anticipation in a bilateral trade model, unpublished.

Stahl, D.O. (1985). Bankruptcies in temporary equilibrium forward markets with and without institutional restrictions. Review of Economic Studies, 52: 459-471.

Stahl, D.O. (1995). Arbitrage and information in a sequential economy with many credit agencies. Mathematical Finance, 5, 33-54.

Werner, J. (1985). Equilibrium in economies with incomplete financial markets. Journal of Economic Theory, 36, 110-119.