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Optimization lies at the heart of economic modelling and analysis. A consumer’s consumption and savings decisions, a firm’s production decisions, a government’s design of a tax scheme; almost all models of economic decision making involve optimization. In this course, we’ll develop some of the fundamental tools of non-linear optimization and explore their applications to the analysis of models in both micro and macroeconomics. This course places special emphasis on developing techniques for optimization in dynamic settings and presenting the tools that will be used in the Research track MSc coursework.

This course is appropriate for any Bachelor's student interested in expanding their understanding of some of the mathematical tools and techniques used in economics. It is strongly encouraged that any student interested in the Research Track of the Master's program take this course.

  • Constrained Optimization
    • Equality Constraints (Lagrange Multipliers)
    • Inequality Constraints (Karush-Kuhn-Tucker Conditions)
    • Economic Application: The Consumer Problem
  • Concave Analysis
    • Concave functions
    • Quasi-concave functions
    • Separating Hyperplanes
    • Economic Application: Linear Production
    • Economic Application: Risk and Portfolio Choice
  • The Value Function
    • Continuity and other Properties of the Value Function
    • The Envelope Theorem
    • Economic Applications: Some Comparative Statics
    • Economic Application: Duality in the Consumer Problem
  • Dynamic Optimization: The Principle of Optimality
    • The Principle of Optimality
    • Bellman Equations
    • Dynamic Optimization with Uncertainty (in Discrete Time)
    • The HJB equation (without Uncertainty)
    • Economic Application: Search
    • Economic Application (time permitting): Bandit Problems and the Gittins Index
  • Dynamic Optimization: Pontryagin's Maximum Principle
    • Hamiltonians
    • A Discrete Time Maximum Principle
    • A Continuous Time Maximum Principle
    • Phase Diagrams
    • Economic Application: Consumption/Savings
    • Economic Application: Growth
    • Economic Application (time permitting): Independent Variables that aren’t Time
  • Completion method: contact teaching
  • Schedule: can be found in Sisu
  • Textbook: A.K. Dixit “Optimization in Economic Theory (Second Edition)” (Oxford University Press)
  • Study materials: can be found in MyCourses
    • Tips for enrolling in a MyCourses course area can be found here

Please register for the course in the Aalto Sisu with your Aalto username, further instructions can be found here.

    • Code: ECON-C1900
    • Target groups: BSc
    • Credit points: 6
    • Code: no equivalent code
    • Target groups: BSc
    • Credit points: 6
    • Credit transfer: apply for inclusion in Sisu
    • Code: no equivalent code
    • Target groups: BSc
    • Credit points: 6
    • Credit transfer: apply for inclusion in Sisu

This course is intended to aid the student in developing comfort and familiarity with the level of mathematics used in economics research. The course focuses on specifically on a careful treatment of optimization, with a focus on dynamic optimization methods, as applied to economic models.