Module outline
This module teaches the necessary mathematical techniques required for a modern degree in Economics. It focuses on economic examples so that students learn important mathematical skills and also how to apply those skills to problems of economic interest. The module starts at a basic level, but progresses quickly so that by the end of the module students have the tools to solve relatively sophisticated economics problems.
Module aims
The aims of this module are to:
- provide students with a strong grasp of fundamental mathematical concepts
- enable students to use a range of mathematic methods to express economic reasoning.
- enable students to acquire knowledge of the mathematical methods needed to comprehend economic principles.
- enable students to carry out mathematical operations on economic models and interpret the economic meaning of the relevant mathematical concepts.
- provide students with a firm foundation for further studies in economics.
Learning outcomes
On successful completion of the module a student will demonstrate:
- knowledge of the fundamental principles of economic analysis.
- the ability to use a range of mathematical techniques correctly and to apply them to the analysis of economic problems.
- the ability to apply a rigorous, analytical and numerate approach to a problem.
- the ability to effectively communicate mathematical arguments and interpret the results of analysis in an economics context.
- the ability to identify, evaluate and find effective solutions to problems.
- the use of mathematical analysis to gain a more sophisticated understanding of economic principles.
Syllabus
The content will cover the following topics:
- Linear economic models: linear equations and functions; slope and intercept; simultaneous linear equations and existence of solutions; application of linear equations to microeconomic and macroeconomic applications; comparative static analysis.
- Non-linear functions: quadratic functions; exponential and logarithmic functions.
- Quadratic equations: algebraic and graphical solutions; economic applications including total cost and total revenue functions; Cournot game.
- Matrix algebra: rules of matrix algebra, using matrix algebra to solve systems of linear equations.
- Functions with more than one variable: graphs of functions with two variables; level curves; economics applications including Cobb-Douglas functions, Leontief functions; homogeneity.
- Economics and finance: single and compounded interests; net present values; discrete and continuous growth; using exponential and logarithmic functions to model continuous growth.
- Differentiation: interpretation of derivatives and rules of differentiation; first and second derivatives; maximum and minimum, points of inflexion, convex and concave functions, necessary and sufficient conditions for optimality.
- Applications of differentiation: interpretation of marginal quantities (e.g. cost, revenue, utility) as derivatives; elasticity of demand and supply; profit maximisation of monopolists and competitive firms.
- Partial differentiation: graphical and economic interpretation; marginal rate of substitution and marginal rate of transformation; homothetic functions; cross partials and Young's Theorem.
- Optimisation with more than one variable: maximum, minimum and saddle points; economic applications e.g. profit maximisation for multi-product firms; Cournot and Stackelberg models in a duopoly.
- Total differentiation: intuition and basic theory; Chain rule; applications and examples.
- Constrained optimization: objective functions and constraints; substitution method; total differentiation method; Lagrangean approach; Economic applications and examples including cost minimization subject to a production function constraint, theory of consumer behaviour
Learning and teaching methods
There are six contact hours per week; this includes a two-hour lecture and two classes of two hours each where students apply the techniques taught in lectures by attempting exercises alone and in groups with support from teachers.
Weekly tutorials will also be provided offering students the opportunity to ask the module teacher further questions regarding the material covered in lectures and classes
Assessment
In order to pass this module, students must pass the final exam with at least 40% and the aggregate module mark with at least 40%. The coursework weighting is 50% and the exam weighting is 50%.
Coursework consists of:
- One in-class test in week 9 (50%)
- One in-class test in week 23 (50%)
Final Exam:
- One 3 hour exam undertaken in weeks 40, 41.
This module teaches the necessary mathematical techniques required for a modern degree in Economics. It focuses on economic examples so that students learn important mathematical skills and also how to apply those skills to problems of economic interest. The module starts at a basic level, but progresses quickly so that by the end of the module students have the tools to solve relatively sophisticated economics problems.
Module aims
The aims of this module are to:
- provide students with a strong grasp of fundamental mathematical concepts
- enable students to use a range of mathematic methods to express economic reasoning.
- enable students to acquire knowledge of the mathematical methods needed to comprehend economic principles.
- enable students to carry out mathematical operations on economic models and interpret the economic meaning of the relevant mathematical concepts.
- provide students with a firm foundation for further studies in economics.
Learning outcomes
On successful completion of the module a student will demonstrate:
- knowledge of the fundamental principles of economic analysis.
- the ability to use a range of mathematical techniques correctly and to apply them to the analysis of economic problems.
- the ability to apply a rigorous, analytical and numerate approach to a problem.
- the ability to effectively communicate mathematical arguments and interpret the results of analysis in an economics context.
- the ability to identify, evaluate and find effective solutions to problems.
- the use of mathematical analysis to gain a more sophisticated understanding of economic principles.
Syllabus
The content will cover the following topics:
- Linear economic models: linear equations and functions; slope and intercept; simultaneous linear equations and existence of solutions; application of linear equations to microeconomic and macroeconomic applications; comparative static analysis.
- Non-linear functions: quadratic functions; exponential and logarithmic functions.
- Quadratic equations: algebraic and graphical solutions; economic applications including total cost and total revenue functions; Cournot game.
- Matrix algebra: rules of matrix algebra, using matrix algebra to solve systems of linear equations.
- Functions with more than one variable: graphs of functions with two variables; level curves; economics applications including Cobb-Douglas functions, Leontief functions; homogeneity.
- Economics and finance: single and compounded interests; net present values; discrete and continuous growth; using exponential and logarithmic functions to model continuous growth.
- Differentiation: interpretation of derivatives and rules of differentiation; first and second derivatives; maximum and minimum, points of inflexion, convex and concave functions, necessary and sufficient conditions for optimality.
- Applications of differentiation: interpretation of marginal quantities (e.g. cost, revenue, utility) as derivatives; elasticity of demand and supply; profit maximisation of monopolists and competitive firms.
- Partial differentiation: graphical and economic interpretation; marginal rate of substitution and marginal rate of transformation; homothetic functions; cross partials and Young's Theorem.
- Optimisation with more than one variable: maximum, minimum and saddle points; economic applications e.g. profit maximisation for multi-product firms; Cournot and Stackelberg models in a duopoly.
- Total differentiation: intuition and basic theory; Chain rule; applications and examples.
- Constrained optimization: objective functions and constraints; substitution method; total differentiation method; Lagrangean approach; Economic applications and examples including cost minimization subject to a production function constraint, theory of consumer behaviour
Learning and teaching methods
There are six contact hours per week; this includes a two-hour lecture and two classes of two hours each where students apply the techniques taught in lectures by attempting exercises alone and in groups with support from teachers.
Weekly tutorials will also be provided offering students the opportunity to ask the module teacher further questions regarding the material covered in lectures and classes
Assessment
In order to pass this module, students must pass the final exam with at least 40% and the aggregate module mark with at least 40%. The coursework weighting is 50% and the exam weighting is 50%.
Coursework consists of:
- One in-class test in week 9 (50%)
- One in-class test in week 23 (50%)
Final Exam:
- One 3 hour exam undertaken in weeks 40, 41.