EC206-Intermediate Mathematics for Economics

Module Provider: School of Politics, Economics and International Relations
Number of credits: 20 [10 ECTS credits]
Level:5
Terms in which taught: Spring term module
Pre-requisites: EC121 Introductory Mathematics for Economics 2 or EC116 Introductory Mathematics for Economics 1 and MA1FM Foundations of Mathematics
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2022/3

Module Convenor: Dr Christos Mavrodimitrakis
Email: c.mavrodimitrakis@reading.ac.uk

Type of module:

Summary module description:

This module complements the corresponding Part 2 intermediate modules on micro- and macroeconomics, along with econometrics, by developing the necessary mathematical tools used to describe economic phenomena; and econometric techniques. It does so by building on Part 1 introductory mathematics modules, EC116 and EC121, respectively. In particular, you need to be familiar with and adapt in the use of techniques in the areas of differentiation of functions of a single variable and of several variables, optimisation, integration, and elementary matrix algebra.

Aims:

Students will become familiar with the idea that mathematics can be used to describe and extend economics in a rigorous fashion. The precision of this approach and the breadth of application to economics of the different mathematical techniques will be emphasised throughout.

Assessable learning outcomes:

At the end of the module students should be able to understand economic theory formulated in mathematical models, to solve these economic models using various mathematical techniques, such as matrix algebra and/or optimisation under constraints, and to operate a comparative-static analysis. Moreover, students Ìýshould obtain the tools necessary to master the material of Part 3 compulsory or optional courses that are more mathematical in content.

Additional outcomes:
Students will have a better-developed sense of the precision involved in formulating economic models rigorously. Weaknesses in their numeracy and mathematical skills should have been eliminated through practice with class exercises.

Outline content:

The module concentrates on Ìýthe following main topics: (i) Linear algebra – static or equilibrium analysis; (ii) calculus and applications – comparative static analysis; and (iii) optimisation problems. The first topic provides a method for handling large linear-equation systems; in particular, for testing the existence of a solution and finding that solution. We will be concerned with the representation of economic models in matrix form. The concepts and techniques that will be discussed include matrix multiplication, determinants, matrix inversion, Cramer’s rule, characteristic roots and vectors, and sign definiteness. The second topic considers both partial and total differentiation and their economic interpretation. Comparative-static analysis investigates the adjustment process; i.e., shifts of the equilibrium state in response to exogenous changes. The concepts and techniques that will be discussed include partial derivatives, the gradient vector, totaldifferentials and total derivatives, the Jacobian determinant and the implicit-function theorem, and higher-order derivatives. The third topic deals with the study of goal equilibrium, in which the equilibrium state is defined as the optimum position for a given economic unit; the latter is deliberately striving for attainment of that equilibrium. The concepts and techniques that will be discussed include unconstrained optimisation and second-order conditions in relation to concavity and convexity, optimisation subject to equality constraints using the Lagrangian method, and optimisation subject to inequality constraints using the Kuhn-Tucker conditions.

Brief description of teaching and learning methods:

The lectures are a formal presentation of mathematical techniques and their economic applications. Handouts are distributed to assist students, and lecture slides are available in advance. Classes review a series of exercises and economic applications of the material.Ìý These must be attempted beforehand. The class tutor and lecturers are available in their feedback and consultation hours to provide further assistance.

Contact hours:

Ìý	Autumn	Spring	Summer
Lectures		20	2
Tutorials		9
Guided independent study:		154	15
Ìý	Ìý	Ìý	Ìý
Total hours by term		183	17
Ìý	Ìý	Ìý	Ìý
Total hours for module	200

Summative Assessment Methods:

Method	Percentage
Written exam	80
Class test administered by School	20

Summative assessment- Examinations:

One 3-hour unseen written paper.Ìý This will account of 80% of the overall module mark.

Part 2 examinations are held in the Summer term.

The examination for this module will require a narrowly defined time window and is likely to be held in a dedicated exam venue.

Summative assessment- Coursework and in-class tests:

There will be one in-class test held near the end of the term in which the module is taught (20% of overall mark).

Formative assessment methods:

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/cqsd-old-site-documents/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:
A minimum overall mark of 40%.

Reassessment arrangements:

Re-examination for all modules takes place in August/September of the same year.

Re-assessment is by examination only; the in-class test is not included at the second attempt.

Additional Costs (specified where applicable):

1) Required text books:ÌýÌý

2) Specialist equipment or materials:ÌýÌý

3) Specialist clothing, footwear or headgear:ÌýÌý

4) Printing and binding:Ìý There may be optional costs associated with photocopying or printing sources listed on the reading list relating to this module. Please note that the Library charges approximately 5p per photocopy.Ìý

5) Computers and devices with a particular specification:ÌýÌý

6) Travel, accommodation and subsistence:ÌýÌý

Last updated: 22 September 2022