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Programme & Unit Catalogues

## ES10095: Mathematical economics

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 100%
Assessment Detail:
• Coursework (CW 100%)
Supplementary Assessment:
ES10095 Resit Coursework (where allowed by programme regulations)
Requisites:
Description: 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:

#### ES10095 is Compulsory on the following programmes:

Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 1)
• UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 1)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 1)
• UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 1)

 Notes: This unit catalogue is applicable for the 2017/18 academic year only. Students continuing their studies into 2018/19 and beyond should not assume that this unit will be available in future years in the format displayed here for 2017/18. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.