Rational Expectations in Urban Economics

Berliant, Marcus and Yu, Chia-Ming (2012): Rational Expectations in Urban Economics.

Abstract

Canonical analysis of the classical general equilibrium model demonstrates the existence of an open and dense subset of standard economies that possess fully-revealing rational expectations equilibria. This paper shows that the analogous result is not true in urban economies under appropriate modifications for this field. An open subset of economies where none of the modified rational expectations equilibria fully reveals private information is found. There are two important pieces. First, there can be information about a location known by a consumer who does not live in that location in equilibrium, and thus the equilibrium rent does not reflect this information. Second, if a consumer's utility depends only on information about their (endogenous) location of residence, perturbations of utility naturally do not incorporate information about other locations conditional on the consumer's location of residence. Existence of equilibrium is proved. Space can prevent housing prices from transmitting information from informed to uninformed households, resulting in an inefficient outcome.

• Item Type: MPRA Paper
• Language: English
• Keywords: Urban Economics; General Equilibrium; Private Information; Rational Expectations
• Subjects: R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R13 - General Equilibrium and Welfare Economic Analysis of Regional Economies; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies

References

Abdel-Rahman, H. M. (1996): "When Do Cities Specialize in Production?" Regional Science and Urban Economics, 26, 1-22.

Abdel-Rahman, H. M. (1998): "Income Disparity, Time Allocation and Social Welfare in a System of Cities," Journal of Regional Science, 38, 137-154.

Abdel-Rahman, H. M., and M. Fujita (1993): "Specialization and Diversification in a System of Cities," Journal of Urban Economics, 33, 189-222.

Abdel-Rahman, H. M., and P. Wang (1995): "Toward a General- Equilibrium Theory of a Core-Periphery System of Cities," Regional Science and Urban Economics, 25, 529-546.

Abdel-Rahman, H. M., and P.Wang (1997): "Social Welfare and Income Inequality in a System of Cities," Journal of Urban Economics, 41, 462-483.

Allen, B. (1981): "Generic Existence of Completely Revealing Equilibria for Economies with Uncertainty when Prices Convey Information," Econometrica, 49, 1173-1199.

Allen, B. (1984): "Equilibria in Which Prices Convey Information: The Finite Case," in Bayesian Models in Economic Theory, M. Boyer and R. Kihlstrom (eds), Amsterdam: North Holland, 63-92.

Allen, B., and J. S. Jordan (1998): "The Existence of Rational Expectations Equilibrium: A Retrospective," in Organizations with Incomplete Information, M. Majumdar (ed), Cambridge: Cambridge University Press, 42-60.

Alonso, W. (1964): Location and Land Use. Cambridge: Harvard University Press.

Anas, A. (1992): "On the Birth and Growth of Cities: Laissez-Faire and Planning Compared," Regional Science and Urban Economics, 22, 243-258.

Anas A. (2004): "Vanishing Cities: What Does the New Economic Geography Imply About the Efficiency of Urbanization?" Journal of Economic Geography, 4, 181-199.

Anas, A., and K. Xiong (2003): "Intercity Trade and the Industrial Diversication of Cities," Journal of Urban Economics, 54, 258-276.

Arrow, K. J. (1964): "The Role of Securities in the Optimal Allocation of Risk Bearing," Review of Economic Studies, 31, 91-96.

Aumann, R. J. (1976): "Agreeing to Disagree," The Annals of Statistics, 4, 1236-1239.

Ausubel L. M. (1990): "Partially-Revealing Rational Expectations Equilibrium in a Competitive Economy," Journal of Economic Theory, 50, 93-126.

Berliant, M., and M. Fujita (1992): "Alonso's Discrete Population Model of Land Use: Efficient Allocations and Competitive Equilibria," International Economic Review, 33, 535-566.

Berliant, M., and Y. Zenou (forthcoming): "Labor Differentiation and Agglomeration in General Equilibrium," International Regional Science Review.

Blomquist, G. C., M. C. Berger, and J. P. Hoehn (1988): "New Estimates of Quality of Life in Metropolitan Areas," American Economic Review, 78, 89-107.

Cronon, W. (1991): Nature's Metropolis: Chicago and the Great West. New York: W. W. Norton.

Debreu, G. (1959): Theory of Value, New Haven: Yale University Press.

Debreu, G. (1972): "Smooth Preferences," Econometrica, 40, 603-615.

Fujita, M. (1985): "Existence and Uniqueness of Equilibrium and Optimal Land Use," Regional Science and Urban Economics, 15, 295-324.

Fujita, M. (1989): Urban Economic Theory. Cambridge: Cambridge University Press.

Fujita, M., and T. E. Smith (1987): "Existence of Continuous Residential Land-Use Equilibria," Regional Science and Urban Economics, 17, 549-594.

Grossman, S. J., and J. E. Stiglitz (1976): "Information, and Competitive Price Systems," American Economic Review Papers and Proceedings, 66, 246-253.

Grossman, S. J., and J. E. Stiglitz (1980): "On the Impossibility of Informationally Efficient Markets," American Economic Review, 70, 393-408.

Henderson, J.V. (1974): "The Sizes and Types of Cities," American Economic Review, 64, 640-656.

Henderson, J.V., and H. M. Abdel-Rahman (1991): "Urban Diversity and Fiscal Decentralization," Regional Science and Urban Economics, 21, 491-510.

Henderson, J. V., and R. Becker (2000): "Political Economy of City Sizes and Formation," Journal of Urban Economics, 48, 453-484.

Hirshleifer, J. (1971): "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review, 61, 561-574.

Jordan, J. S. (1982): "The Generic Existence of Rational Expectations Equilibrium in the Higher Dimensional Case," Journal of Economic Theory, 26, 224-243.

Jordan, J. S., and R. Radner (1979): "The Nonexistence of Rational Expectations Equilibrium: A Robust Example," mimeo, Department of Economics, University of Minnesota, Minneapolis.

Kreps, D. M. (1977): "A Note on `Fullled Expectations' Equilibria," Journal of Economic Theory, 14, 32-43.

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

Pines, D. (2000): "On Alternative Urban Growth Patterns," Unpublished manuscript, The Eitan Berglas School of Economics, Tel-Aviv University.

Radner, R. (1979): "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, 47, 655-678.

Roback, J. (1982): "Wages, Rents, and the Quality of Life," Journal of Political Economy, 90, 257-278.

Rosen, S. (1979): "Wage-Based Indexes of Urban Quality of Life," in Current Issues in Urban Economics, P. Mieszkowski and M. Straszheim (eds), Baltimore: Johns Hopkins University Press, 74-104.