Local Determinacy of Prices in an Overlapping Generations Model with Continuous Trading

d'Albis, Hippolyte and Augeraud-Véron, Emmanuelle and Hupkes, Herman Jan (2014): Local Determinacy of Prices in an Overlapping Generations Model with Continuous Trading.

Abstract

We characterize the determinacy properties of the intertemporal equilibrium for a continuous-time, pure-exchange, overlapping generations economy with logarithmic preferences. Using recent advances in the theory of functional differential equations, we show that the equilibrium is locally unique and that prices converge to a balanced growth path and are determined.

• Item Type: MPRA Paper
• Language: English
• Keywords: Overlapping generations models ⋅ Local dynamics ⋅ Existence ⋅ Determinacy ⋅ Functional differential equations
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling

References

H. d'Albis and E. Augeraud-Véron (2007), Balanced Cycles in an OLG Model with a Continuum of Finitely-lived Individuals. Economic Theory 30, 181-186

H. d'Albis and E. Augeraud-Véron (2009), Competitive Growth in a Life-cycle Model: Existence and Dynamics. International Economic Review 50, 459-484

H. d'Albis and E. Augeraud-Véron (2013), Frequency of Trade and the Determinacy of Equilibrium in Economies of Overlapping Generations. International Journal of Economic Theory 9, 85-100

H. d'Albis, E. Augeraud-Véron and H. J. Hupkes (2012), Discontinuous Initial Value Problems for Functional Differential-Algebraic Equations of Mixed-Type. Journal of Differential Equations 253, 1959-2024

H. d'Albis, E. Augeraud-Véron and H. J. Hupkes (2014), Stability and Determinacy Conditions for Mixed-type Functional Differential Equations. Journal of Mathematical Economics 53, 119-129

M. Allais (1947), "Économie et Intérêt". Imprimerie Nationale, Paris

Y. Balasko, D. Cass, K. Shell (1980), Existence of Competitive Equilibrium in a General Overlapping-generations Model. Journal of Economic Theory 23, 307-322

Y. Balasko and K. Shell (1980), The Overlapping-generations Model, I: The Case of Pure Exchange without Money. Journal of Economic Theory 23, 281-306

R. Boucekkine, D. de la Croix and O. Licandro (2002), Vintage Human Capital, Demographic Trends and Endogenous Growth. Journal of Economic Theory 104, 340-375.

P. Brito and R. Dilão (2010), Equilibrium Price Dynamics in an Overlapping-generations Exchange Economy. Journal of Mathematical Economics 46, 343-355

J. L. Burke (1996), Equilibrium for Overlapping Generations in Continuous Time. Journal of Economic Theory 70, 364-390

D. Cass and M. E. Yaari (1967), Individual Saving, Aggregate Capital Accumulation, and Efficient Growth. In K. Shell (Ed.) "Essays on the Theory of Optimal Economic Growth", 233-268, MIT Press: Cambridge MA

S. Demichelis (2002), Solution of Two Equations Arising in the Overlapping Generations Model. Mathematical Models and Methods in Applied Sciences 12, 1269-1280

S. Demichelis and H. M. Polemarchakis (2007), The Determinacy of Equilibrium in Economies of Overlapping Generations. Economic Theory 32, 461-475

C. Edmond (2008), An Integral Equation Representation for Overlapping Generations in Continuous Time. Journal of Economic Theory 143, 596-609

D. Gale (1973), Pure Exchange Equilibrium of Dynamic Economic Models. Journal of Economic Theory 6, 12-36

J. M. Geanakoplos (2008), Overlapping Generations Model of General Equilibrium. In S. N. Durlauf and L. E. Blume (Eds.) "The New Palgrave Dictionary of Economics", Palgrave Macmillan

J. M. Geanakoplos and H. M. Polemarchakis (1991), Overlapping Generations. In W. Hildenbrand and H. Werner (Eds.) "Handbook of Mathematical Economics", vol. 4, chap. 35, 1899--1960, Elsevier

C. Ghiglino and M. Tvede (2004), Dynamics in OG Economies. Journal of Difference Equations and Applications 10, 463-472

H. J. Hupkes (2008), Invariant Manifolds and Applications for Functional Differential Equations of Mixed Type. Ph.D. Thesis. University of Leiden

H. J. Hupkes and E. Augeraud-Véron (2011), Well-Posedness of Initial Value Problems for Functional Differential and Algebraic Equations of Mixed Type. Discrete and Continuous Dynamical Systems A 30, 737-765

H. J. Hupkes and S. M. Verduyn Lunel (2008), Invariant Manifolds for Periodic Functional Differential Equations of Mixed Type. Journal of Differential Equations 245, 1526-1565

T. Kehoe and D. Levine (1985), Comparative Statics and Perfect Foresight in Infinite Horizon Economies. Econometrica 53, 433-453

T. Kehoe and D. Levine (1990), The Economics of Indeterminacy in Overlapping Generations Models. Journal of Public Economics 42, 219-243

T. Kehoe, D. Levine, A. Mas-Colell and M. Woodford (1991), Gross Substitutability in Large-square Economies. Journal of Economic Theory 54, 1-25

T. Kehoe, D. Levine, A. Mas-Colell and W. R. Zame (1989), Determinacy of Equilibrium in Large-scale Economies. Journal of Mathematical Economics 18, 231-262

J. Mallet-Paret and S. M. Verduyn Lunel (2001), Exponential Dichotomies and Wiener-Hopf Factorizations for Mixed-Type Functional Differential Equations. Journal of Differential Equations, forthcoming

J.-F. Mertens and A. Rubinchik (2012), Regularity and Stability of Equilibria in an Overlapping Generations Model with Exogenous Growth. Mimeo

J.-F. Mertens and A. Rubinchik (2013), Equilibria in an Overlapping Generations Model with Transfer Policies and Exogenous Growth. Economic Theory 54, 537-595

J. O. Mierau and S. J. Turnovsky (2014), Capital Accumulation and the Sources of Demographic Change. Journal of Population Economics 27, 857-894

J. O. Mierau and S. J. Turnovsky (2014), Demography, Growth and Inequality. Economic Theory 55, 29-68

P. A. Samuelson (1958), An Exact Consumption-loan Model of Interest with or without the Social Contrivance of Money. Journal of Political Economy 66, 467-482

K. Shell (1971), Notes on the Economics of Infinity. Journal of Political Economy 79, 1002-1011

J. Tobin (1967), Life Cycle Saving and Balanced Growth. In "Ten Economic Studies in the Tradition of Irving Fischer", John Wiley & Sons, New York

M. Yaari (1965), Uncertain Lifetime, Life Insurance, and the Theory of the Consumer. Review of Economic Studies 32, 137-160