History versus Expectations in Economic Geography Reconsidered

Oyama, Daisuke (2006): History versus Expectations in Economic Geography Reconsidered.

Abstract

This paper studies global stability of spatial configurations in a dynamic two-region model with quadratic adjustment costs where rational migrants make migration decisions so as to maximize their discounted future utilities. A global analysis is conducted to show that, except for knife-edge cases with symmetric regions, there exists a unique spatial configuration that is absorbing and globally accessible whenever the degree of friction is sufficiently small, and such a configuration is characterized as the unique maximizer of the potential function of the underlying static model.

• Item Type: MPRA Paper
• Language: English
• Keywords: economic geography; mutiple equilibria; forward-looking expectation; global stability; potential
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

References

Baldwin, R., R. Forslid, P. Martin, G. Ottaviano, and F. Robert-Nicoud (2003). Economic Geography and Public Policy, Princeton University Press, Princeton.

Baldwin, R. E. (2001). ``Core-Periphery Model with Forward-Looking Expectations,'' Regional Science and Urban Economics 31, 21-49.

Baum, R. F. (1976). ``Existence Theorems for Lagrange Control Problems with Unbounded Time Domain,'' Journal of Optimization Theory and Applications 19, 89-116.

Forslid, R. and G. I. P. Ottaviano (2003). ``An Analytically Solvable Core-Periphery Model,'' Journal of Economic Geography 3, 229-240.

Fujita, M., P. Krugman, and A. J. Venables (1999). The Spatial Economy: Cities, Regions, and International Trade, MIT Press, Cambridge.

Fukao, K. and R. Benabou (1993). ``History versus Expectations: A Comment,'' Quarterly Journal of Economics 108, 535-42.

Hartl, R. F., S. P. Sethi, and R. G. Vickson (1995). ``A Survey of the Maximum Principles for Optimal Control Problems with State Constraints,'' SIAM Review 37, 181-218.

Hofbauer, J. and G. Sorger (1999). ``Perfect Foresight and Equilibrium Selection in Symmetric Potential Games,'' Journal of Economic Theory 85, 1-23.

Hofbauer, J. and G. Sorger (2002). ``A Differential Game Approach to Evolutionary Equilibrium Selection,'' International Game Theory Review 4, 17-31.

Kaneda, M. (2003). ``Policy Designs in a Dynamic Model of Infant Industry Protection,'' Journal of Development Economics 72, 91-115.

Krugman, P. (1991a). ``Increasing Returns and Economic Geography,'' Journal of Political Economy 99, 483-499.

Krugman, P. (1991b). ``History versus Expectations,'' Quarterly Journal of Economics 106, 651-67.

Matsui, A. and K. Matsuyama (1995). ``An Approach to Equilibrium Selection,'' Journal of Economic Theory 65, 415-434.

Matsuyama, K. (1991). ``Increasing Returns, Industrialization, and Indeterminacy of Equilibrium,'' Quarterly Journal of Economics 106, 617-650.

Matsuyama, K. (1992). ``The Market Size, Entrepreneurship, and the Big Push,'' Journal of the Japanese and International Economies 6, 347-364.

Monderer, D. and L. Shapley (1996). ``Potential Games,'' Games and Economic Behavior 14, 124-143.

Ottaviano, G. I. P. (2001). ``Monopolistic Competition, Trade, and Endogenous Spatial Fluctuations,'' Regional Science and Urban Economics 31, 51-77.

Oyama, D. (2002). ``p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics,'' Journal of Economic Theory 107, 288-310.

Oyama, D. (2006). ``Agglomeration under Forward-Looking Expectations: Potentials and Global Stability,'' mimeo.

Oyama, D., S. Takahashi, and J. Hofbauer (2008). ``Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics,'' Theoretical Economics 3, 155-192.

Sandholm, W. H. (2001). ``Potential Games with Continuous Player Sets,'' Journal of Economic Theory 97, 81-108.

Seierstad, A. and K. Sydsaeter (1987). Optimal Control Theory with Economic Applications, North-Holland, Amsterdam.

Sethi, S. P. and G. L. Thompson (2000). Optimal Control Theory: Applications to Management Science and Economics, Second Edition, Springer, New York.