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ES10095: Mathematical economics

[Page last updated: 20 April 2021]

Academic Year: 2021/2
Owning Department/School: Department of Economics
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Semester 2
Assessment Summary: CW 50%, EX 50%
Supplementary Assessment:
ES10095 Resit Exam (where allowed by programme regulations)
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:
NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2021

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)


  • This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22.
  • 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.
  • Find out more about these and other important University terms and conditions here.