Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-17T16:34:44.309Z Has data issue: false hasContentIssue false
  • English
  • Français

NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION

Published online by Cambridge University Press:  14 October 2014

A. Kerem Coşar  and
Edward J. Green
A. Kerem Coşar*
Affiliation:
University of Chicago
Edward J. Green
Affiliation:
The Pennsylvania State University
*
Address correspondence to: A. Kerem Coşar, University of Chicago, Booth School of Business, 5807 South Woodlawn Avenue, Chicago, IL 60637, USA; e-mail: kerem.cosar@chicagobooth.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

Keywords

Dynamic OptimizationTransversality Condition
Type
Articles
Information
Macroeconomic Dynamics , Volume 20 , Issue 3 , April 2016 , pp. 667 - 684
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aliprantis, Charalambros D. and Burkinshaw, Owen (2003) Locally Solid Riesz Spaces with Applications to Economics, 2nd ed.Providence, RI: American Mathematical Society.Google Scholar
Benveniste, L. M. and Scheinkman, J. A.. (1982) Duality theory for dynamic optimization models of economics: The continuous time case. Journal of Economic Theory 27, 1–19.Google Scholar
Bewley, Truman F. (1972) Existence of competitive equilibria in economies with infinitely many commodities. Journal of Economic Theory 4 (3), 514–540.Google Scholar
Gale, David (1967) On optimal development in a multi-sector economy. Review of Economic Studies 34 (1), 1–18.Google Scholar
Kamihigashi, Takashi (2001) Necessity of transversality conditions for infinite horizon problems. Econometrica 69 (4), 995–1012.Google Scholar
Kamihigashi, Takashi (2003) Necessity of transversality conditions for stochastic problems. Journal of Economic Theory 109 (1), 140–149.Google Scholar
Luenberger, David (1969) Optimization by Vector Space Methods. New York: Wiley.Google Scholar
Mas-Colell, Andreu and Richard, Scott F. (1991) A new approach to the existence of equilibria in vector lattices. Journal of Economic Theory 53 (1), 1–11.Google Scholar
McKenzie, Lionel W. (1974) Turnpike theorems with technology and welfare function variable. In Los, Jerzy and Los, Maria W. (eds.), Mathematical Models in Economics, pp. 271–288. Amsterdam: North Holland.Google Scholar
McKenzie, Lionel W. (1976) Turnpike theory. Econometrica 44 (5), 841–865.Google Scholar
Michel, Philippe (1990) Some clarifications on the transversality condition. Econometrica 58 (3), 705–723.Google Scholar
Peleg, Bezalel and Ryder, Harl (1972) On optimal consumption plans in a multi-sector economy. Review of Economic Studies 39 (9), 159–169.Google Scholar
Sims, Christopher A. (1994) A simple model for study of the determination of the price level and the interaction of monetary and fiscal policy. Economic Theory 4 (3), 381–399.Google Scholar
Stokey, Nancy and Lucas, Robert E. Jr., (1989) Recursive Methods in Economic Dynamics. Cambridge, MA: Harvard University Press.Google Scholar
Weitzman, Martin (1973) Duality theory for infinite horizon convex models. Management Science 19 (7), 783–789.Google Scholar