## ES10095: Mathematical economics

[Page last updated: 20 April 2021]

Owning Department/School: Department of Economics
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 2
Assessment Summary: CW 50%, EX 50%
Supplementary Assessment:
ES10095 Resit Exam (where allowed by programme regulations)
Requisites:
Aims: To present methods of optimization commonly used in economics; to explain their theoretical basis and give a solid understanding of the wide variety of applications in economics and game theory that these optimization techniques are applicable to.

Learning Outcomes: On completing this unit, students should be able to:
* Recognise economic and practical problems where static and dynamic optimization methods can be applied fruitfully.
* Solve optimization problems analytically and, where appropriate, numerically by means of appropriate software (such as Mathematica).
* Implement appropriate solution algorithms, and understand their procedures.
* Recognise economic and practical problems in which game theory tools can be used effectively.
* Understand and apply the main solutions concepts from game theory, such as equilibrium in dominant strategies, Nash Equilibrium, etc.

Skills: Problem solving, abstraction, modelling of real-world optimisation problems, recognising different types of optimisation problems, using mathematical software.

Content: I. The Mathematical Programming Problem: Unconstrained Optimization; The Method of Lagrange Multipliers; The Interpretation of Lagrange Multipliers.
II. Nonlinear Programming: The Case of No Inequality Constraints; The Kuhn-Tucker Conditions; The Kuhn-Tucker Theorem; The Interpretation of the Lagrange Multipliers; Solution Algorithms.
III. Dynamic Optimization: Formal Statement of the Problem; Costate Variables, Hamiltonians, and the Maximum Principle; Interpretation of the Costate Variables. Applications of Dynamic Optimization.
IV. Game Theory: Basic concepts of strategic games, two-person zero sum games, two-person non-zero sum games. Applications.

Programme availability: