Brito, Paulo and Dilao, Rui (2006): Equilibrium price dynamics in an overlappinggenerations exchange economy.

PDF
MPRA_paper_699.pdf Download (201kB)  Preview 
Abstract
We present a continuous time overlapping generations model for an endowment ArrowDebreu economy with an agestructured population. For an economy with a balanced growth path, we prove that ArrowDebreu equilibrium prices exist, and their dynamic properties are agedependent. Our model allows for an explicit dependence of prices on critical agespecific endowment parameters. We show that, if endowments are distributed earlier than some critical age, then speculative bubbles for prices do exist.
Item Type:  MPRA Paper 

Original Title:  Equilibrium price dynamics in an overlappinggenerations exchange economy 
Language:  English 
Keywords:  ArrowDebreu equilibrium; overlapping generations models; McKendrick model 
Subjects:  G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates D  Microeconomics > D5  General Equilibrium and Disequilibrium > D51  Exchange and Production Economies J  Labor and Demographic Economics > J1  Demographic Economics > J10  General 
Item ID:  699 
Depositing User:  Rui Dilao 
Date Deposited:  08. Nov 2006 
Last Modified:  26. Apr 2015 09:10 
References:  Azariadis, C., Bullard, J., and Ohanian, L. (2004). Trendreverting fluctuations in the lifecycle model. Journal of Economic Theory, 119: 334356. Balasko, Y. and Shell, K. (1980). The overlappinggenerations model, {I}: The case of pure exchange without money. Journal of Economic Theory, 23: 281306. Beaudry, P., Collard, F., and Green, D.A. (2005). Demographics and recent productivity performance: insights from crosscountry comparisons. Canadian Journal of Economics, 38(2): 309344. Blanchard, O.J. (1985). Debt, Deficits and Finite {H}orizons. Journal of Political Economy, 93(2): 22347. Bommier, A. and Lee, R. D. (2003). Overlapping Generations Models with Realistic Demography: Statics and Dynamics. Journal of Population Economics, 16: 13560. Boucekkine, R., de la Croix, D., and Licandro, O. (2002). Vintage human capital, demographic trends and endogenous growth. Journal of Economic Theory, 104: 34075. Cass, D. and Yaari, M.E. (1967). Individual saving, aggregate capital accumulation, and efficient growth. In Shell, K., editor, Essays on the Theory of Optimal Economic Growth}, pages 233268. MIT Press. Corless, R.M., Gonnet, G., Hare, D. E.~G., Jeffrey, D.J., and Knuth, D.E. (1996). On the Lambert ${W}$ Function. Advances in Computational Mathematics, 5: 32959. Cushing, J.M. (1998). An introduction to structured population dynamics. SIAM, Philadelphia. d'Albis, H. and AugeraudVeron, E. (2004). Competitive growth in a lifecycle model: existence and dynamics. ftp://mse.univparis1.fr/pub/mse/cahiers2004/V04016.pdf. Demichelis, S. and Polemarchakis, H.M. (2006). The determinacy of equilibrium in economies of overlapping generations. Economic Theory, forthcoming. Diamond, P.A. (1965). National Debt in a Neoclassical Growth Model. American Economic Review, 55(5): 11261150. Dilao, R. (2006). Mathematical models in population dynamics and ecology. In Misra, J.C., editor, Biomathematics: Modelling and Simulation. World Scientific. Fair, R.C. and Dominguez, K.M. (1991). Effect of Changing U.S. Age Distribution on Macroeconomic Equations. American Economic Review, 81(5): 12761294. Gale, D. (1973). Pure exchange equilibrium of dynamic economic models. J. Econ. Theory, 6: 1236. Galor, O. and Weil, D. (2000). Population, Technology, and Growth: From the Malthusian Regime to the Demographic Transition and Beyond. American Economic Review, 90(4): 806828. Geanakoplos, J., Magill, M., and Quinzii, M. (2004). Demography and the longrun predictability of the stock market. Brookings Papers on Economic Activity, 1, 241307. Geanakoplos, J.~D. and Polemarchakis, H.M. (1991). Overlapping generations. In Hildenbrand, W. and Sonnenschein, H., editors, Handbook of Mathematical Economics, volume IV, pages 18991960. North Holland. Lanczos, C. (1970). The variational principles of mechanics. University of Toronto Press, Toronto. LeRoy, S. F. (2004). Rational exuberance. Journal of Economic Literature, 42: 783804. Lindh, T. and Malmberg, B. (1999). Age Structure Effects and Growth in the OECD, 195090. Journal of Population Economics, 12: 43199. McKendrick, A.~G. (1926). Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society, 44: 98130. Poterba, J. M. (2001). Demographic structure and asset returns. Review of Economic and Statistics, 83: 565584. Radner, R. (1972). Existence of equilibrium of plans, prices, and price expectations in a sequence of markets, Econometrica, 40: 289303. Samuelson, P.A. (1958). An Exact ConsumptionLoan Model of Interest with or Without the Social Contrivance of Money. Journal of Political Economy, 66(6): 46782. Shell, K. (1971). Notes on the economics of infinity. Journal of Political Economy, 79: 10021011. Webb, G.F. (1985). Theory of Nonlinear AgeDependent Population Dynamics. Marcel Dekker Inc., New York. Yaari, M.E. (1965). Uncertain Lifetime, Life Insurance, and the Theory of Consumer. Review of Economic Studies, 32: 13750. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/699 