Centre for Financial & Management Studies (CeFiMS) - University of London

Individual Professional Courses – IPC  

Mathematics & Statistics for Economists [EP104]

Introduction

Mathematics and Statistics for Economists covers topics including differential calculus, maximisation subject to constraints, frequency distributions, probability theory and hypothesis testing. These techniques are taught with reference to their applications to economic principles. Because the key to success in understanding mathematical techniques is practice, the course provides a wide range of problems for solution, as well as the theoretical foundations of their uses in economics, and includes computer-based exercises.

Aims & Objectives

This course aims to provide students with the necessary background for advanced study in market economics and econometrics. It should also enable them to use basic mathematical and statistical techniques for economic analysis.

Resources

Students receive a looseleaf binder containing eight ‘course units’; these texts are carefully structured to provide the main teaching and are equivalent to traditional course lectures, defining and exploring the main concepts and issues, locating these within current economics debate and introducing and linking the further assigned readings. Two assignments (which are counted towards the final course grade) marked by your CeFiMS tutors, and a specimen examination paper are also included within the student pack, along with the following:

Textbooks:

Mike Rosser, Basic Mathematics for Economists, First Published 1993 , Routledge, London, ISBN0415084253.

T.H. Wonnacott and R.J. Wonnacott, Introductory Statistics for Business and Economics, Fourth edition, 1990 , John Wiley & Sons, New York, ISBN047161517X.

Readings:

A compilation of further readings: recently published articles or seminal writings which augment and illustrate the main text.

Video Cassette:

The video lecture is intended to review and reinforce the teaching in the unit texts by discussing the same issues through a different medium.

Course Timetable:

This shows the linkage between the various components of the course and indicates the schedule for reading the texts, watching the video lecture, submitting assignments, etc.

Course Content

Unit 1 Introduction to Mathematics and Statistics for Economists

This unit provides an introduction to both the course and to the uses of mathematics in the context of economics thinking. The reasons for studying mathematics and statistics are explained and guidance on how to do so is provided. The study of mathematics is introduced through an analysis of functions and functional forms. The uses and drawing of graphs is explained and, importantly for economics analysis, the unit focuses on how to calculate the slope of a line and a curve and demonstrates their relevance to economics modelling. Finally, the unit discusses simultaneous equations and the methods used to solve them.

Unit 2 Mathematics of Growth

The different ways in which growth rates can be evaluated are demonstrated here. First, the unit introduces natural logarithms and exponentials, which are mathematical tools used in analysing problems about growth. Then it covers the techniques for calculating simple and compound interest, present value, net present value and the internal rate of return and their applications to finance and investment issues. The unit also introduces the concepts of arithmetic and geometric series. It discusses index numbers — the different types, how they are constructed and used and, specifically, the distinction between a Laspeyres and a Paasche index.

Unit 3 Introduction to Calculus and Unconstrained Optimisation

In its introduction to differential calculus, this unit explains the relationship between the derivative of a function and its slope. It also discusses how differentiation is used in economics and its relationship to changes at the ‘margin’ such as marginal revenue, marginal cost and marginal product. The unit then applies differentiation to unconstrained optimisation problems, such as how to determine the level of output at which a firm maximises its product, or minimises the use of inputs in its production process. In doing so, it introduces the first and second order conditions necessary for optimisation, and how these are applied in economics; demonstrates how to distinguish between a maximum, minimum and point of inflection, and how to differentiate using the chain, product and quotient rules.

Unit 4 Partial Derivatives and Constrained Optimisation

Unit 4 introduces partial differentiation, which is used when The University has functions with more than one variable. It then goes on to discuss how partial differentiation is used to solve optimisation problems. The unit also investigates the methods for solving optimisation problems when there are restrictions on some of the variables — for example, maximising consumer satisfaction subject to given goods prices. The concepts of total differentiation and total derivatives are also covered. The last section of the unit is about simple integration and how it is used in economics. The techniques taught include how partial differentiation is applied in economics; the first- and second-order conditions for determining maximum and minimum points; how to solve constrained optimisation problems; the nature of the Lagrangian function and multiplier and how it is used; the distinction between total differentiation and the total derivative; and how to do simple integration.

Unit 5 Descriptive Statistics

The techniques and uses of statistics are taught in the second half of the course, and this unit introduces the main notions and concepts used in descriptive statistics. It presents the main methods of analysing data, defines the centre and spread of a statistical distribution and, finally, the unit shows some of the most commonly used graphical representations of data. Topics covered include the distinction between descriptive and inferential statistics; why random sampling is important in statistical inference; the nature of frequency tables, histograms, box-and-whisker plots; the mode, median and mean of a statistical distribution; the range, inter-quartile range, mean absolute deviation, mean squared deviation, variance and standard deviation of a statistical distribution; and how to perform a linear transformation on a statistical variable.

Unit 6 Probability Theory

In explaining what is meant by probability, this unit introduces the main rules in probability theory. It shows how probabilities can be up-dated as new information emerges. The unit also introduces the notion of random variables, and describes expectations and variances of random variables. It examines the nature of conditional probabilities; how statistical independence is defined; how to use the multiplication rule for statistically independent events; Bayes’ theorem; the frequentist and subjective definitions of probability; what is meant by expectation and variance of a random variable; and the nature of binomial and normal distributions.

Unit 7 Statistical Inference I

Sampling and Point Estimation

Unit 7 deals with some of the most important concepts in statistical inference: random sampling, point estimation and the statistical properties of estimators. Its main objective is to show how to use the information contained in a random sample in order to make inferences about the characteristics of a more general population, from which the sample is drawn. The unit covers the expectation and the variance of the statistical distribution of the sample mean; the shape of the distribution of the sample mean where the sample size is large; the nature of statistical and unbiased estimators, and their relative efficiency; and what is meant by consistency and asymptotic unbiasedness of an estimator.

Unit 8 Statistical Inference II

Confidence Intervals and Hypothesis Testing

This final unit of this course explains what is meant by interval estimation and why it is important in statistics, and it discusses the logic behind statistical hypothesis testing. The concept of the confidence interval is introduced and applied to inferences regarding means and proportions; its use in testing statistical hypotheses is also demonstrated. The teaching includes how to compute confidence intervals using the tables of the normal distribution; how to determine the sample size to obtain a desired precision in our estimates; how to compute confidence intervals for small samples, for the difference between two means, for proportions, and when two samples are matched; the nature of a statistical hypothesis and how to test it using confidence intervals; what is meant by the p-value; the difference between a type-I and a type-II error; how we can measure the power of a statistical test; and what is meant by one-sided and two-sided alternative hypotheses.

Tuition & Assessment

Mathematics and Statistics for Economists is assessed by two assignments, which are counted towards the final grade, and by a three-hour examination held in the autumn. Each assignment consists of compulsory questions and problems to be solved. The pass mark for each assignment is 40%; 70% or above is the equivalent of a distinction. Assignments count for 30% of the overall grade for this course, while the examination is worth 70% of the final assessment.