Mathematics for Economic Research
Optimising decision behaviour is at the core of most economic analysis. Whether we ask how a consumer should behave, how firms should compete in a market or how governments should decide on their monetary policy, the ability to solve optimisation problems is key to finding an answer. This module provides a thorough introduction to the techniques involved in optimisation required to take PhD level Economics courses. Topics include advanced calculus, dynamic programming, difference equations and linear algebra.
The whole content of this module is a neutral methodology that is applicable across disciplines and across geographic or national boundaries. It is taught by lectures with teaching and learning experience from many different countries.
All of the resources for this module are available on the ELE (Exeter Learning Environment).
The module will prepares for writing successfully a PhD at high academic standards.
Full module specification
|Module title:||Mathematics for Economic Research|
|Duration of module:||
Duration (weeks) - term 1: |
The module aims to introduce students to the essential mathematical tools used in economic analysis.
ILO: Module-specific skills
- 1. Demonstrate and be able to derive rigorous mathematical proofs.
- 2. Demonstrate the ability to work with abstract mathematical concepts.
- 3. Solve economic optimisation problems.
ILO: Discipline-specific skills
- 4. Demonstrate the ability to read and work with current economic research papers.
- 5. Critically analyze the logic of economic arguments.
- 6. Use and analyze economic models.
ILO: Personal and key skills
- 7. Demonstrate numeracy and the ability to handle logical and structured problem analysis.
- 8. Demonstrate inductive and deductive reasoning.
- 9. Apply essential research skills.
Learning activities and teaching methods (given in hours of study time)
|Scheduled Learning and Teaching Activities||Guided independent study||Placement / study abroad|
|32 hours||118 hours|
Details of learning activities and teaching methods
|Category||Hours of study time||Description|
|Contact hours||22||Lectures (2 hours per week)|
|Contact hours||10||Tutorials (1 hour per week)|
|Guided Independent Study||55 (5 per week)||Reading|
|Guided Independent Study||63 (approx. 6 hours per week)||Preparing problem set answers and preparing for examinations|
|Form of assessment||Size of the assessment (eg length / duration)||ILOs assessed||Feedback method|
|Weekly problem sets||One set per week with 3 questions each||1-9||Verbal in class and ELE|
Summative assessment (% of credit)
|Coursework||Written exams||Practical exams|
Details of summative assessment
|Form of assessment||% of credit||Size of the assessment (eg length / duration)||ILOs assessed||Feedback method|
|Average of weekly problem sets||30||Weekly problem sets with 3 questions each||1-9||Verbal in class and ELE|
|Examination||70||2 hours||1-9||Detailed grading|
Details of re-assessment (where required by referral or deferral)
|Original form of assessment||Form of re-assessment||ILOs re-assessed||Timescale for re-assessment|
|Problem sets and Examination||Examination (100%) 2 hours||1-9||August reassessment period|
1. Basics of linear algebra: determinant, linear dependence and rank of a matrix, inverse of a matrix, determinant of a matrix, eigenvalues and eigenvectors, trace of a matrix, quadratic forms
2. Calculus: differentiation, integration, Taylor expansion, concavity and convexity, quasi-concavity and quasi-convexity
3. Optimization: unconstrained optimization, constrained optimization with equality constraints (Lagrange), constrained optimization with inequality constraints (Kuhn-Tucker)
4. Comparative statics and fixed points: envelope theorem, implicit function theorem, correspondences, fixed point theorems
5. Dynamic programming
6. First-order differential equations
Indicative learning resources - Basic reading
Knut Sydsæter, Peter Hammond, Arne Størm, and Andrés Carvajal (2016): Essential Mathematics for Economic Analysis, 5th edition, Pearson
Knut Sydsaeter, Peter Hammond, Atle Seierstad, and Arne Strøm (2008): Further Mathematics for Economic Analysis, 2nd edition, Pearson
Daniel Leonard and Ngo van Long (1991): Optimal Control Theory and Static Optimization in Economics, Cambridge University Press
Jianjun Miao (2014): Economic Dynamics in Discrete Time, MIT Press
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Last revision date