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Moscow Summer School 2009
Economic Growth: Mathematical Dimensions
 Optimal Control Applications in Economics
     Prof. Thomas Weber, Stanford University, USA


Abstract

This course provides an overview of classical and nonclassical optimal control applications in economics. The approach is hierarchical. First we discuss single-person decision problems in which a firm or a social planner maximizes an objective function subject to certain constraints. Applications include dynamic pricing, investment, marketing, and the harvesting of renewable resources. Second we introduce games in which several decision makers interact, either in a leader-follower (Stackelberg) setting or in a situation where all players reach their decisions simultaneously. Applications include dynamic oligopolies with open and closed-loop equilibria, capital accumulation games, and the dynamic pricing with a strategic buyer. In the third part of the course, we look at problems, which involve the design of economic mechanisms for the interaction of different players. Applications include screening, market design, and dynamic auctions.

Part I – Optimal Control in Single-Person Decision Problems: Foundations (10 Sessions)

Review of Optimality Conditions & Standard Setups
Capital Accumulation
Dynamic Pricing
Exploitation of Nonrenewable Resources
Instantaneous Adjustments: Impulse Control Problems

Part II – Games (5 Sessions)

Differential Games and Equilibrium Concepts
Simple Duopoly Models
Capital Accumulation Games
Joint Exploitation of Nonrenewable Resources

Part III – Design of Mechanisms (5 Sessions)

Introduction to Asymmetric Information, Game Forms, and Mechanisms
The Screening Problem: Taxation, Regulation of Monopolies, and Nonlinear Pricing
Markets for Divisible Goods
Dynamic Mechanisms
Uncertainty and Robustness

A small 150-page monograph, written by the instructor for this occasion, will accompany the course.

Students are expected to complete a course project and several small exercises.


Prerequisites

The students should have some basic knowledge of linear and nonlinear dynamic systems, and ideally have had an introductory course in economics with elements of game theory. Students should also be familiar with elementary probability theory.


Literature

  1. P. Bolton, M. Dewatripont, Contract Theory, MIT Press, Cambridge, MA, 2005.
  2. E. Dockner, S. Jørgensen, N. Von Long, G. Sorger, Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, UK, 2000.
  3. A. A. Milyutin, N. P. Osmolovskii, Calculus of Variations and Optimal Control, American Mathematical Society, Providence, RI, 1998.
  4. T. R. Palfrey, S. Srivastava, Bayesian Implementation, Harwood Academic Publishers, Langhorne, PA, 1993.
  5. A. Seierstad, K. Sydsæter, Optimal Control Theory with Economic Applications, North-Holland, Amsterdam, NL, 1987.
  6. S. P. Sethi, G. L. Thompson, Optimal Control Theory: Applications to Management Science and Economics, 2nd ed., Springer, New York, NY, 2000.
  7. T. A. Weber, Applied Information Economics, Oxford University Press, Oxford, UK. [The complete manuscript is due with the publisher on March 15, and will be available as a draft in April 2009.]
  8. T. A. Weber, Optimal Control Theory with Applications in Economics, Moscow State University Press. [These course notes will be available on June 15, 2009.]

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