Dynamic optimization and lab on Mathematica

Course description

This course focuses on intertemporal problems, which are a building block of many economic models, both in microeconomics (e.g. intertemporal consumer theory, life-cycle theories) and in macroeconomics (e.g. growth theory).

The first part of the course provides an introduction to dynamic optimization methods in continuous and discrete time (optimal control problems, Hamilton-Jacobi-Bellman equations and Bellman equations).

The second part of the course teaches how to use the Mathematica software to solve dynamic optimization problems.

Slides and additional material:

Go to Drobox folder

Topics:

1. Intertemporal choice

• Assumptions of the discounted utility model and implications
• Discrete or continuous time modelling?

2. Optimal control, Hamilton-Jacobi-Bellman equations (continuous time), Bellman equations (discrete time)

• Optimality conditions
• Steady state and asymptotic stability
• Sufficient conditions and transversality conditions

3. Mathematica: an introduction

• Solution of equations
• Graphical representation, plot manipulation
• Matrices: determinant, trace, eigenvalues

4. Optimal control using Mathematica

• From your notes to a Mathematica sheet
• Explicit solutions of linear-quadratic models

Readings/Bibliography:

• A friendly introduction to optimal control theory is in Chiang, A. (1992): Elements of Dynamic Optimization. McGraw-Hill, New York: New York
• A harder-to-digest handbook on dynamic programming is N. L. Stokey, R. E. Lucas, Recursive Methods in Economic Dynamics. Harvard University Press, 1989.
• A useful package for solving systems of nonlinear ordinary differential equations, and for visualizing their solutions, is DynPac by Al Clark, available here

We will replicate the results contained in:

• Dragone, D. (2009). I am getting tired: effort and fatigue in intertemporal decision-making. Journal of Economic Psychology, 30(4), 552-562.
• Dragone, D. (2009). A rational eating model of binges, diets and obesity. Journal of Health Economics, 28(4), 799-804.
• Dragone, D., Savorelli, L. (2012). Thinness and obesity: a model of food consumption, health concerns and social pressure. Journal of Health Economics, 31(1), 243-256.