Readings listed under References are provided for students seeking further information on topics, but are not required reading.

Stokey, Nancy L., and Robert E. Lucas, Jr., with Edward C. Prescott. Recursive Methods in Economic Dynamics. Cambridge, MA: Harvard University Press, 1989.


Euler Equations and Transversality: Sufficiency and Necessity

Weitzman, M. L. “Duality Theory for Infinite Horizon Convex Models.” Management Science 19, no. 7 (March 1973): 783-789.

Benveniste, L. M., and J. A. Scheinkman. “Duality Theory for Dynamic Optimization Models of Economics: The Continuous Time Case.” Journal of Economic Theory 27, no. 1 (1982): 1-19.

Kamihigashi, Takashi. “Necessity of Transversality Conditions for Infinite Horizon Problems.” Econometrica 69, no. 4 (July 2001): 995-1012.

Kamihigashi, Takashi. “A Simple Proof of the Necessity of the Transversality Condition.” Economic Theory 20, no. 2 (September 2002): 427-433.

Araujo, A., and J. A. Scheinkman. “Maximum Principle and Transversality Condition for Concave Infinite Horizon Economic Models.” Journal of Economic Theory 30, no. 1 (June 1983): 1-16.

Michel, Philippe. “On the Transversality Condition in Infinite Horizon Optimal Problems.” Econometrica 50, no. 4 (July 1982): 975-985.

Michel, Philippe. “Some Clarifications on the Transversality Condition.” Econometrica 58, no. 3 (May 1990): 705-723.

Leung, Siu Fai. “Transversality Condition and Optimality in a Class of Infinite Horizon Continuous Time Economic Models.” Journal of Economic Theory 54, no. 1 (June 1991): 224-233.

Differentiability of the Value Function

Milgrom, Paul, and Ilya Segal. “Envelope Theorems for Arbitrary Choice Sets”, Econometrica 70, no. 2 (March 2002): 583-601.

Differentiability of the Policy Function

Araujo, A. “The Once but Not Twice Differentiability of the Policy Function.” Econometrica 59, no. 5 (September 1991): 1383-1393.

Araujo, A., and J. A. Scheinkman  “Smoothness, Comparative Dynamics, and the Turnpike Property.” Econometrica 45, no. 3 (April 1977): 601-620.

Santos, Manuel S. “Smoothness of the Policy Function in Discrete Time Economic Models.” Econometrica 59, no. 5 (September 1991): 1365-1382.

Homogenous Dynamic Programming

Alvarez, Fernando, and Nancy L. Stokey. “Dynamic Programming with Homogenous Functions.” Journal of Economic Theory 82, no. 1 (September 1998): 167-189.

Complicated Dynamics from Dynamic Optimization Problems

Boldrin, Michele, and Luigi Montrucchio. “On the Indeterminacy of Capital Accumulation Paths.” Journal of Economic Theory 40, no. 1 (1986): 26-29.

Mitra, Tapan. “On the Relationship between Discounting and Complicated Behavior in Dynamic Optimization Models.” Journal of Economic Behavior and Organizations 33, nos. 3-4 (January 1998): 421-434.

Repeated Games and Dynamic Contracts

Abreu, Dilip, David Pearce, and Ennio Stachetti. “Towards a Theory of Infinitely Repeated Games with Discounting.” Econometrica 58, no. 5 (1990): 1041-1063.

Ljungqvist, Lars, and Thomas Sargent. Recursive Macroeconomic Theory. Cambridge, Mass.: MIT Press, 2000, chap. 16.

Phelan, Christopher, and Ennio Stacchetti. “Sequential Equilibria in a Ramsey Tax Model.” Econometrica 69, no. 6 (November 2001): 1491-1518.

Athey, Susan, Andrew Atkeson, and Patrick J. Kehoe. “On the optimality of transparent monetary policy.” Federal Reserve Bank of Minneapolis (2001), Working Paper Number 613.

Athey, Susan, Kyle Bagwell, and Chris Sanchirico. “Collusion and Price Rigidity.” Manuscript (2002).

Jonathan Levin. “Relational Incentive Contracts.” Manuscript. Stanford University (2002).

Continuous-Time Dynamic Programming

Fleming, Wendell Helms, and H. Mete Soner. Controlled Markov Processes and Viscosity Solutions. Applications of Mathematics, vol. 25. Berlin: Springer-Verlag, 1993, chap. 1.