ECO4AQA

Not currently offered

Credit points: 15

## Subject outline

In this subject, students will learn about optimisation theory and its application in economics. The main focus of the unit is on techniques for static optimisation. The types of problems to be addressed will include unconstrained optimisation, equality constrained optimisation, and inequality constrained optimisation. Optimisation problems in which there are both equality and inequality constraints might also be considered. Students will also learn about the comparative static properties of solutions to parametric optimisation problems. If time permits, an introduction to dynamic optimisation might also be provided. The emphasis throughout the course is on the application of these techniques to a variety of economic and business problems.

Credit points15

Subject Co-ordinatorDamien Eldridge

Subject year levelYear Level 4 - UG/Hons/1st Yr PG

Exchange StudentsNo

## Subject particulars

### Subject rules

Prerequisites ECO2CFC and ECO2IQA (or equivalent maths subject)

Co-requisitesN/A

Incompatible subjects ECO3AQA

Equivalent subjectsN/A

Special conditionsN/A

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsMathematics for economistsRecommendedSimon, CP and L Blume (1994)WW NORTON AND COMPANY, USA (ISBN: 0-393-95733-0)

## Graduate capabilities & intended learning outcomes

01. Upon successful completion of this subject, you should be able to define the concept of a Nash equilibrium for a finite non-cooperative game. Know and derive the Nash equilibrium existence theorem for finite non-cooperative games in which best-response functions are single-valued. Know and derive the Nash equilibrium existence theorem for finite non-cooperative games in which best-response functions might not be single-valued (that is, the case of best-response correspondences). Explain the possible implications of various failures of the conditions underlying this existence theorem. Find all of the Nash equilibria, or show that no such equilibria exist, for particular examples of non-cooperative games. In the latter case, explain which of the assumptions of the existence theorems are no

Activities:
TBC

02. Upon successful completion of this subject, you should be able to define the concept of a Walrasian equilibrium for an exchange economy. Know and derive the Arrow-Debreu-McKenzie equilibrium existence theorem for an exchange economy in which demand functions are single-valued. Know and derive the Arrow-Debreu-McKenzie equilibrium existence theorem for an exchange economy in which demand functions might not be single valued (that is, the case of demand correspondences). Explain the possible implications of various failures of the conditions underlying these existence theorems. Find all of the Walrasian equilibria, or show that no such equilibria exist, for particular examples of exchange economies. In the latter case, explain which of the assumptions of the existence theorems are not sati

Activities:
TBC

03. Upon successful completion of this subject, you should be able to define the concepts of an optimal value function and the associated control functions for static optimisation problems. Find these functions for various static optimisation problems in microeconomics and derive their properties.

Activities:
TBC

04. Upon successful completion of this subject, you should be able to define the various properties that might be endowed upon a preference ordering and derive the implications of those properties.

Activities:
TBC

05. Upon successful completion of this subject, you should be able to know and derive the first and second fundamental theorems of welfare economics in the context of an exchange economy. Explain the possible implications of various failures of the conditions underlying these theorems.

Activities:
TBC

## Subject options

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