13.6 Conclusion
Time preference influences intertemporal allocations. Ramsey’s many agent model provides us with a framework for seeing how individual tastes can influence an economy’s development and the distribution of its produce. The ways in which it differs from the representative agent theory may, with further research, provide us with a foundation for macrodynamic models with many agents where there interactions influence the level of macroeconomic activity and the conduct of macroeconomic policy.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Charalambos D. Aliprantis and Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, 2nd Edition, Springer-Verlag, Berlin, 1999.
Charalambos D. Aliprantis, Kim C. Border, and Owen Burkinshaw, “New Proof of the Existence of Equilibrium in a Single-Sector Growth Model,” Macroeconomic Dynamics, 1 (1997), 669–679.
Costas Azariadis, Intertemporal Macroeconomics, Basil Blackwell Publishers, Cambridge, 1993.
Robert J. Barro and Xavier Sala-i-Martin, Economic Growth, 2nd Edition, The MIT Press, Cambridge, 2004.
Robert A. Becker, “On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households,” Quarterly Journal of Economics, 95 (1980), 375–382.
Robert A. Becker, “Cooperative Capital Accumulation Games and the Core,” in Economic Theory and International Trade: Essays in Memoriam J. Trout Rader (Wilhelm Neuefeind and Raymond G. Riezman, eds.), Springer-Verlag, 1992.
Robert A. Becker, “Stationary Strategic Ramsey Equilibrium,” Working Paper, Indiana University, 2003.
Robert A. Becker and John H. Boyd III, Capital Theory, Equilibrium Analysis and Recursive Utility, Basil Blackwell Publishers, Malden, MA, 1997.
Robert A. Becker, John H. Boyd III, and Ciprian Foias, “The Existence of Ramsey Equilibrium,” Econometrica, 59 (1991), 441–460.
Robert A. Becker and Subir K. Chakrabarti, “The Recursive Core,” Econometrica 63 (1995), 401–423.
Robert A. Becker and Baoline Chen, “Implicit Programming and Computing the Invariant Manifold for Dynamic Equilibrium Problems,” Indiana University Working Paper, February 2000.
Robert A. Becker and Ciprian Foias, “A Characterization of Ramsey Equilibrium,” Journal of Economic Theory, 41 (1987), 173–184.
Robert A. Becker and Ciprian Foias, “Convergent Ramsey Equilibria,” Libertas Mathematica, 10 (1990), 41–52.
Robert A. Becker and Ciprian Foias, “The Local Bifurcation of Ramsey Equilibrium,” Economic Theory, 4 (1994), 719–744.
Robert A. Becker and Ciprian Foias, “Implicit Programming and the Invariant Manifold for Ramsey Equilibria,” in Functional Analysis and Economic Theory (Yuri Abramovich, Evgenious Avgerinos, and Nicholas Yannelis, eds.), Springer-Verlag, 1998.
Robert A. Becker and Itzhak Zilcha, “Stationary Ramsey Equilibria Under Uncertainty,” Journal of Economic Theory, 75 (1997), 122–140.
Robert A. Becker and Eugene N. Tsyganov, “Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households,” Journal of Economic Theory, 105 (2002), 188–225.
Richard Bellman, Dynamic Programming, Princeton University Press, Princeton, N.J., 1957.
Michael Ben-Gad, “Balanced-Growth Consistent Recursive Utility and Heterogeneous Agents,” Journal of Economic Dynamics and Control, 23 (1999), 459–462.
Jess Benhabib, Saqib Jafarey, and Kazuo Nishimura, “The Dynamics of Efficient Intertemporal Allocations with Many Agents, Recursive Preferences and Production,” Journal of Economic Theory, 44 (1988), 301–320.
Ernst R. Berndt, “Reconciling Alternative Estimates of the Elasticity of Substitution,” Review of Economics and Statistics, 58 (1976), 59–68.
Claude Berge, Topological Spaces, Dover Publications, 1997.
Truman F. Bewley, “An Integration of Equilibrium Theory and Turnpike Theory,” Journal of Mathematical Economics, 10 (1982), 233–267.
Truman F. Bewley, “Dynamic Implications of the Form of the Budget Constraint,” in Models of Economic Dynamics (Hugo F. Sonnenschein, ed.), Springer-Verlag, Berlin, 1986.
Christopher J. Bliss, Capital Theory and the Distribution of Income, North-Holland, Amsterdam, 1975.
Christopher J. Bliss, “The Real Rate of Interest: A Theoretical Analysis,” Oxford Review of Economic Policy, 15 (1999), 46–58.
Christopher J. Bliss, “Koopmans Recursive Preferences and Income Convergence,” Journal of Economic Theory, 117 (2004), 124–139.
John H. Boyd III, Preferences, Technology and Dynamic Equilibria, Ph.D. Dissertation, Indiana University (Bloomington), 1986.
John H. Boyd III, “Dynamic Tax Incidence with Heterogeneous Agents,” Working Paper, University of Rochester, 1990.
John H. Boyd III, “Symmetries, Dynamic Equilibria, and the Value Function,” in Conservation Laws and Symmetry: Applications to Economics and Finance (R. Sato and R.V. Ramachandran, eds.), Kluwer Academic Publishers, 1990.
William A. Brock, Comments on Radner’s “Market Equilibrium under Uncertainty,” in Frontiers of Quantitative Economics (John J. McCall, ed.), North-Holland, 1974.
William A. Brock and Leonard Mirman, “Optimal Consumption Growth and Uncertainty: The Discounted Case,” Journal of Economic Theory, 4 (1972), 479–513.
Edwin Burmeister, Capital Theory and Dynamics, Cambridge University Press, Cambridge, 1980.
Edwin Burmeister and A. Rodney Dobell, Mathematical Theories of Economic Growth, MacMillan, New York, 1970.
Jeffrey L. Coles, “Equilibrium Turnpike Theory with Constant Returns to Scale and Possibly Heterogeneous Discount Factors,” International Economic Review, 26 (1985), 671–679.
Jeffrey L. Coles, “Equilibrium Turnpike Theory with Time-Separable Utility,” Journal of Economic Dynamics and Control, 10 (1986), 367–394.
Rose-Anne Dana and Cuong Le Van, “Structure of Pareto Optima in an Infinite-Horizon Economy Where Agents Have Recursive Preferences,” Journal of Optimization Theory and Applications, 64 (1990), 269–292.
Rose-Anne Dana and Cuong Le Van, “Equilibria of a Stationary Economy with Recursive Preferences,” Journal of Optimization Theory and Applications, 71 (1991), 289–313.
Rose-Anne Dana and Cuong Le Van, “Optimal Growth and Pareto Optimality,” Journal of Mathematical Economics, 20 (1991), 155–180.
James Davidson, Stochastic Limit Theory, Cambridge University Press, 1994.
David de la Croix and Phillipe Michel, A Theory of Economic Growth, Cambridge University Press, Cambridge, UK, 2002.
James F. Dolmas, “Balanced-growth Consistent Recursive Utility,” Journal of Economic Dynamics and Control, 20 (1996), 657–680.
Jorge Durán and Cuong Le Van, “Simple Proof of Existence of Equilibrium in a One-Sector Growth Model with Bounded or Unbounded Returns From Below,” Macroeconomic Dynamics, 7 (2003), 317–332.
Larry G. Epstein and J. Allan Hynes, “The Rate of Time Preference and Dynamic Economic Analysis,” Journal of Political Economy, 41 (1983), 611–635.
Roger E.A. Farmer, Macroeconomics of Self-Fulfilling Prophecies, second edition, The MIT Press, Cambridge, 1999.
Irving Fisher, The Rate of Interest, MacMillan Company, New York, 1907, reprinted by Garland Publishing, 1982.
Irving Fisher, Elementary Principles of Economics, MacMillan Company, New York, 1912.
Irving Fisher, Theory of Interest, MacMillan Company, New York, 1930, reprinted by Augustus M. Kelley, 1970.
Shane Frederick, George Lowenstein, and Ted O’Donoghue, “Time Discounting and Time Preference: A Critical Review,” Journal of Economic Literature, 40 (2002), 351–401.
David Gale, “Nonlinear Duality and Qualitative Properties of Optimal Growth,” in J. Abadie, ed., Integer and Nonlinear Programming, North-Holland, Amsterdam, Chapter 13, 309–319, 1970.
David Gale, Tracking the Automatic Ant and Other Mathematical Explorations, Springer-Verlag, New York, 1998.
John Galsworthy, “Indian Summer of a Forsyte,” originally published in 1917, compiled in: The Forsyte Saga, Scribner Paperback Fiction, Simon & Schuster, New York, 2002.
Christian Ghiglino, “Introduction to Economic Growth and General Equilibrium,” Journal of Economic Theory, 105 (2002), 1–17.
Christian Ghiglino, “Wealth Inequality and Dynamic Stability,” Journal of Economic Theory, forthcoming.
Christian Ghiglino and Marielle Olszak-Duquenne, “Inequalities and Fluctuations in a Dynamic General Equilibrium Model,” Economic Theory, 17 (2001), 1–24.
Roger Guesnerie and Michael Woodford, “Endogenous Fluctuations,” in Advances in Economic Theory Sixth World Congress, Volume II (Jean-Jacques Laffont, ed.), Cambridge University Press, 1992.
Ismail Hadji and Cuong Le Van, “Convergence of Equilibria in an Intertemporal General Equilibrium Model: A Dynamical System Approach,” Journal of Economic Dynamics and Control, 18 (1994), 381–396.
G.H. Hardy, Divergent Series, Oxford University Press, Oxford, 1949.
Alejandro Hernández D., “The Dynamics of Competitive Equilibrium Allocations with Borrowing Constraints,” Journal of Economic Theory, 55 (1991), 180–191.
Kenneth L. Judd, Numerical Methods in Economics, The MIT Press, Cambridge, 1998.
Timothy J. Kehoe, “Intertemporal General Equilibrium Models,” in Frank Hahn, Ed., The Economics of Missing Markets, Information, and Games, Clarendon Press, Oxford, 1989.
Timothy J. Kehoe, “Computation and Multiplicity of Equilibria,” in Handbook of Mathematical Economics, Volume IV (Werner Hildenbrand and Hugo Sonnenschein, eds.), North-Holland, Amsterdam, 1991.
Timothy J. Kehoe and David K. Levine, “Comparative Statics and Perfect Foresight in Infinite Horizon Economies,” Econometrica, 53 (1985), 433–454.
Timothy J. Kehoe, David K. Levine, and Paul M. Romer, “Steady States and Determinacy of Equilibria with Infinitely Lived Agents,” in Joan Robinson and Modern Economic Theory (George R. Feiwel, ed.), New York University Press, New York, 1989.
Timothy J. Kehoe, David K. Levine, and Paul M. Romer, “Determinacy of Equilibria in Dynamic Models with Finitely Many Consumers,” Journal of Economic Theory, 50 (1990), 1–21.
Timothy J. Kehoe, David K. Levine, and Paul M. Romer, “On Characterizing Equilibria of Economies with Externalities and Taxes as Solutions to Optimization Problems,” Economic Theory, 2 (1992), 43–68.
Ben P. Klotz, The Macroeconomics of Anticipated Events, 1stbooks.com, 2001.
Cuong Le Van and Yiannis Vailakis, “Existence of a Competitive Equilibrium in a One-Sector Growth Model with Heterogeneous Agents and Irreversible Investment,” Economic Theory, 22 (2003), 743–771.
Lars Ljungqvist and Thomas J. Sargent, Recursive Macroeconomic Theory, The MIT Press, Cambridge, MA.,2000.
Robert E. Lucas, Jr. and Nancy L. Stokey, “Optimal Growth with Many Consumers,” Journal of Economic Theory, 32 (1984), 139–171.
Michael J.P. Magill, “Some New Results on the Local Stability of the Process of Capital Accumulation,” Journal of Economic Theory, 15 (1977), 174–210.
N. Gregory Mankiw, “The Savers-Spenders Theory of Fiscal Policy,” American Economic Review Papers and Proceedings, 90 (2000), 120–125.
Rodolfo E. Manuelli and Thomas J. Sargent, Exercises in Dynamic Macroeconomic Theory, Harvard University Press, Cambridge, 1987.
Ramon Marimon, “Stochastic Turnpike Property and Stationary Equilibrium,” Journal of Economic Theory, 47 (1989), 282–306.
Frederick R. Marotto, “Snap-Back Repellers Imply Chaos in ℝn,” Journal of Mathematical Analysis and Its Applications, 63 (1978), 199–223.
Andreu Mas-Colell, The Theory of General Economic Equilibrium: A Differentiable Approach, Cambridge University Press, Cambridge, 1985.
Robert M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, and Oxford University Press, Oxford, UK, 2001 [Reprint of second edition, 1974].
Lionel W. McKenzie, “Optimal Economic Growth, Turnpike Theorems and Comparative Dynamics,” in Handbook of Mathematical Economics, Volume III, (Kenneth J. Arrow and Michael D. Intrilligator, eds.), North-Holland, Amsterdam, 1986.
Lionel W. McKenzie, Classical General Equilibrium Theory, The MIT Press, Cambridge, MA., 2002.
Leonard J. Mirman and Itzhak Zilcha, “On Optimal Growth under Uncertainty,” Journal of Economic Theory, 11 (1975), 329–339.
Leonard Mirman and Itzhak Zilcha, “On Optimal Growth Under Uncertainty,” Journal of Economic Theory, 11 (1975), 329–339.
Jacques Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, Inc., San Francisco, 1965.
Kazuo Nishimura and Makoto Yano, “Non-linearity and Business Cycles in a Two-Sector Equilibrium Model: An Example with Cobb-Douglas Production Functions,” in Nonlinear and Convex Analysis in Economic Theory (T. Maruyama and W. Takahashi, eds.), Springer-Verlag, New York, 1995.
Bezalel Peleg and Menachem E. Yaari, “Markets with Countably Many Commodities,” International Economic Review, 11 (1970), 369–377.
Trout Rader, The Economics of Feudalism, Gordon and Breach, New York, 1971.
Trout Rader, Theory of General Economic Equilibrium, Academic Press, New York, 972.
Trout Rader, “Utility Over Time: The Homothetic Case,” Journal of Economic Theory, 25 (1981), 219–236.
Roy Radner, “Optimal Stationary Consumption with Stochastic Production and Resources,” Journal of Economic Theory, 6 (1973), 68–90.
John Rae, Statement of Some New Principles of Political Economy, Hilliard, Gray, and Co., Boston, reprinted by Augustus M. Kelley Publishers, 1964.
Frank P. Ramsey, “A Mathematical Theory of Saving,” Economic Journal, 38 (1928), 543–559.
Frank P. Ramsey, Philosophical Papers (D.M. Mellor, ed.), Cambridge University Press, Cambridge, 1990.
Thomas J. Sargent, Dynamic Macroeconomic Theory, HarvardUniversity Press, Cambridge, 1987.
R. Tyrell Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.
Nils-Erik Sahlin, The Philosophy of F.P. Ramsey, Cambridge University Press, 1990.
Pierre-Daniel G. Sarte, “Progressive Taxation and Income Inequality in Dynamic Competitive Equilibrium,” Journal of Public Economics, 66 (1997), 145–171.
Robert M. Solow, “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics, 70 (1956), 65–94.
Gerhard Sorger, “On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots,” Economic Theory, 4 (1994), 745–764.
Gerhard Sorger, “Chaotic Ramsey Equilibrium,” International Journal of Bifurcation and Chaos, 5 (1995), 373–380.
Gerhard Sorger, “On the Long-Run Distribution of Capital in the Ramsey Model,” Journal of Economic Theory, 105 (2002), 226–243.
Michael L. Stern, personal communication, June 1, 1998.
Joseph E. Stiglitz, “Distribution of Income and Wealth Among Individuals,” Econometrica, 37 (1969), 382–397.
Eammanuel Thibault, “Existence and Specific Characters of Rentiers: A Savers-Spenders Theory Approach,” Economic Theory 25 (2005), 401–419.
Matatsugu Tsuji, “A Note on Professor Stiglitz’ ‘Distribution of Income and Wealth Among Individuals,’” Econometrica, 40 (1972), 947–949.
Henry Wan, Jr., “A Simultaneous Variational Model for International Capital Movements,” in Trade, Balance of Payments, and Growth (J. Bhagwati, et al., eds.), North-Holland, Amsterdam, 1971.
Michael Woodford, “Imperfect Financial Intermediation and Complex Dynamics,” in Economic Complexity, Chaos, Sunspots, Bubbles, and Nonlinearity (William A. Barnett, John Geweke, and Karl Shell, eds.), Cambridge University Press, 1989.
Makoto Yano, “Competitive Equilibria on Turnpikes in a McKenzie Economy, I: A Neighborhood Turnpike Theorem,” International Economic Review, 25 (1984), 695–718.
Makoto Yano, “Temporary Transfers in a Simple Dynamic General Equilibrium Model,” Journal of Economic Theory, 54 (1991), 372–388.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer Berlin · Heidelberg
About this chapter
Cite this chapter
Becker, R.A. (2006). Equilibrium Dynamics with Many Agents. In: Dana, RA., Le Van, C., Mitra, T., Nishimura, K. (eds) Handbook on Optimal Growth 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32310-4_13
Download citation
DOI: https://doi.org/10.1007/3-540-32310-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32308-2
Online ISBN: 978-3-540-32310-5
eBook Packages: Business and EconomicsEconomics and Finance (R0)
