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# Dynamic Programming

2022/2023
Academic Year
ENG
Instruction in English
3
ECTS credits
Course type:
Elective course
When:
1 year, 4 module

### Course Syllabus

#### Abstract

The main aim of the "Dynamic Programming and Applications" course is to provide students with an overview of the standard methods for the solution of problems with intertemporal trade-offs. The problems with intertemporal trade-offs, which require to weight the costs of the current decisions against the benefits of the future outcomes, have extremely wide applicability in various disciplines of the economic science. In this course we will go over the basics of the dynamic programming, a method of solving problems with intertemporal trade-offs, will see how it can be applied to a wide range of real-life situations, and then move to some of the most popular (macro)economic applications of the method. There are no prerequisites to this course, although some very basic knowledge of calculus and basic macro is welcome.

#### Learning Objectives

• By the end of the course, students will understand the basics of the dynamic programming, will be able to define and solve problems with intertemporal trade-offs.

#### Expected Learning Outcomes

• • To apply financial economic theory to investment problems
• Introduction to the concept of DP, scope of application
• Motivational examples: inventory control, deterministic scheduling problem
• More of motivational examples: machine replacement, chess match strategy
• Definition of the basic problem of DP in discrete time
• The DP algorithm, principle of optimality
• Applying the DP algorithm on the deterministic scheduling example
• The DP algorithm with inventory control
• Linear quadratic problem
• Indirect utility: firms and consumers
• Cake-eating problem: direct attack vs. DP approach
• Cake-eating problem with infinite horizon
• Example of analytical solution for the DP problem
• Taste shocks and discrete choice
• Consumption problem: two-period problem, stochastic income, infinite horizon, endogenous labor supply
• Consumption problem: two-period problem, stochastic income, infinite
• Value function iteration: general principle and illustration on cake-eating problem
• Policy function iteration: principle and advantages over the value function iteration
• Definition of the simplest problem in continuous time
• Hamiltonian function and the maximum principle
• Application to the problem of energy use and environmental quality
• Dynamics of employment adjustment
• Price setting problem
• McCall labor search model
• Inflation and unemployment: Phillips tradeoff

#### Course Contents

• Introduction to Dynamic Programming, Part 1.
• Introduction to Dynamic Programming, Part 2.
• DP in (Macro)Economics, Part 1.
• DP in (Macro)Economics, Part 2.
• Numerical Methods
• Introduction to the problem of optimal control.
• DP Applications.

#### Assessment Elements

• Homework Tasks
• Class Participation
• Midterm
• Final Exam

#### Interim Assessment

• 2022/2023 4th module
0.25 * Midterm + 0.1 * Class Participation + 0.15 * Homework Tasks + 0.5 * Final Exam

#### Recommended Core Bibliography

• Dynamic economics : quantitative methods and applications, Adda, J., 2003
• Elements of Dynamic Optimization, 327 p., Chiang, A. C., 1992
• Numerical methods in economics, Judd, K. L., 1998

#### Recommended Additional Bibliography

• Elements of dynamic optimization, Chiang, A. C., 1992
• Numerical methods in economics, Judd, K.L., 1998