Note: There will be a meeting to clarify questions ahead of the exam on Tuesday, June 17, at 13.15-15.00 in Bisp 214. See also this brief sheet of information on the exam.

- Brief Course Description
- Time and Place
- Required Reading
- Lecture Plan
- Exercise Plan
- Downloadable Course Material

This course is a natural continuation of our second year Micro course. We cover a mathematically precise version of general equilibrium theory, with an arbitrary number of goods, consumers and firms. We first take a closer look at the consumers' problems - among the new things we get a result on the existence of the utility function and an analysis of aggregate demand. Next, we give a brief treatment of the firms, including an analysis of aggregate supply.

General equilibrium theory provides the theoretical basis for Computable General Equilibrium models which are used to calculate in quantitative terms how changes in government policies and other exogenous factors change the equilibrium. Three guest lectures by Knud Jørgen Munk give a first introduction to these models. Material related to the three lectures and two exercise classes on Computable General Equilibrium can be accessed through a course site on Blackboard. In the Course Catalog, choose Økonomi, Samfundsvidenskabeligt Fakultet and then access the course: Microeconomics 3rd year - CGE models (Samf-CGEmodels).

Finally we reach the canonical model of generel equilibrium, with elaborate proofs of the two welfare theorems and of the existence of a Walrasian equilibrium. We also study the uniqueness and stability of the Walrasian equilibrium.

Our stringent approach clarifies the extent to which Varian's stated results are general. The approach offers a guide towards the assessment of intuitive reasonings in Economics.

Recommended qualifications:
This course assumes familiarity with intermediate microeconomics, e.g. from a course based on Hal Varian's *Intermediate Microeconomics: A Modern Approach,* Harvester Wheatsheaf.
We make use of basic mathematical skills, as contained in a typical course on Mathematics for Economists, but our textbook contains a mathematical appendix with all the necessary material.

Lectures are given every Wednesday at 8-10 and on Fridays in even-numbered weeks at 10-12.
All lectures take place in Bisp 214.
Most lectures follow quite closely the material of our main textbook.
All but three lectures are given by Peter Norman Sørensen, see contact details at the end of the file.
Peter is expecting a baby in early April, but the guest lectures by Knud Jørgen Munk are scheduled to minimize the chance of any disruption of the course schedule.
Nevertheless, you may wish to join a mailing list which will be used to announce any cancellations of lectures.
To do this, send an email to Peter Norman Sørensen at ` peter.sorensen@econ.ku.dk`

, and indicate that you wish to join the mailing list.

For the exercises, you can choose either the class on Tuesdays 8-10 (in English), on Tuesdays 15-17, or on Thursdays 8-10 (in Danish). Tuesdays 8-10 meet in Hjørneværelset, Studiestræde 6, the other two classes in Bisp 213. The classes are taught by Rasmus Westerlin Nielsen - the classes linked to the lectures on Computable General equilibrium models will be assisted by Katrine Gråbæk.. Some time is spent on the mathematics background from the textbook's appendix, but the classes mainly focus on helping you to solve the weekly problem set. You are expected to prepare in advance, by giving your best try at the problems. Such an active usage of the exercises will help you to master all of the course material. If you are only a passive listener at the exercise classes, you will not really develop your skills. I strongly recommend you to form groups of 2-4 members, to collaborate on the problem solving.

The course ends with a final exam on June 20. This is a four hour closed-book written exam. One half of the exam tests your understanding of the textbook through asking you to reproduce proofs from the book, or create new simple proofs. The other half tests your ability to apply the material to solve given problems.

The textbook is
*Microeconomic Theory,* by Andreu Mas-Colell, Michael Whinston and Jerry Green, Oxford University Press 1995.
We cover the chapters 1-5 and 16-17.
In addition, some notes on Computable General Equilibrium by Knud Jørgen Munk - these will become available as we need them.

We will give 23 lectures, all in Bisp 214. Every Wednesday at 8-10 and on Fridays in even-numbered weeks at 10-12. All lectures take place in Bisp 214. The following plan may be subject to changes (this version dates from April 30).

5/2 | Ch. 2.A-E | Introduction. Demand |

7/2 | Ch. 1.C,D and 2.F | Weak Axiom |

12/2 | Ch. 2.F and 3.A-C | Slutsky Matrix. Utility Function |

19/2 | Ch. 3.B and 3.D | Utility Maximization |

21/2 | Ch. 3.E | Expenditure Minimization |

26/3 | Ch. 3.F-G | Duality |

5/3 | Ch. 3.H-J | Consumer's Surplus. Integrability |

7/3 | Ch. 5.A-C and 5.G | Production, Profits and Costs |

12/3 | Ch. 5.E-F | Supply |

14/3 | Ch. 16.A-C | First Welfare Theorem |

19/3 | Ch. 16.D | Second Welfare Theorem |

21/3 | Ch. 16.E-F | Optimality and Welfare |

26/3 | Notes | CGE: Theoretical Structure |

2/4 | Notes | CGE: First and Second Best |

4/4 | Notes | CGE: Road Pricing |

9/4 | Cancelled | |

16/4 | Easter Vacation | |

18/4 | Easter Friday | |

23/4 | Ch. 17.A-C | Equilibrium in an Exchange Economy |

30/4 | Ch. 17.C | Existence of Walrasian Equilibrium |

2/5 | Ch. 4.A-B | Aggregate Demand |

7/5 | Ch. 4.C-D | Aggregate Demand |

14/5 | Ch. 17.D | Local Uniqueness of Equilibrium |

16/5 | All Saints (Store Bededag) | |

21/5 | Ch. 17.F | Global Uniqueness |

21/5 | Ch. 17.E,G,H | Overview: Aggregate Excess Demand, Comparative Statics, Tâtonnement. |

17/6 | Questions | |

20/6 | Exam |

There will be 15 exercise classes, each class given thrice. You can choose either the class on Tuesdays 8-10 (in English), on Tuesdays 15-17, or on Thursdays 8-10 (in Danish). Tuesdays 8-10 meet in Hjørneværelset, Studiestræde 6, the other two classes in Bisp 213.

week 6 | Chs. 1.B and M.A | Proof Techniques. Preference Relations. |

week 7 | Chs. 1, 2 and M.A | Problem Solving: Problem Set 1. |

week 8 | Chs. 2.E-F and M.D | Problem Solving: Problem Set 2. Solutions to Two Problems. |

week 9 | Chs. 3.B-D | Problem Solving: Problem Set 3. |

week 10 | Chs. 3.D-E | Problem Solving: Problem Set 4. |

week 11 | Chs. 3.E-G | Problem Solving: Problem Set 5. |

week 12 | Ch. 5 | Problem Solving: Problem Set 6. |

week 13 | Ch. 16.B-D | Problem Solving: Problem Set 7. |

week 14 | CGE | Problems in Computable General Equilibrium. |

week 15 | CGE | Problems in Computable General Equilibrium. |

week 17 | Ch. 16 | Problem Solving: Problem Set 8. |

week 18 | Ch. 17.B,C | Problem Solving: Problem Set 9. |

week 19 | Ch. 17.B,C | Problem Solving: Problem Set 10. |

week 20 | Ch. 4 | Problem Solving: Problem Set 11. |

week 21 | Ch. 17.D-F | Problem Solving: Problem Set 12. |

The following documents can be downloaded. The documents are in the pdf format, to be viewed in the free Adobe Acrobat Reader.

- Course Syllabus
- Adam Smith Quotation
- On the Exam
- Problem Set 1
- Problem Set 2
- Solutions to Two Problems From Set 2
- Problem Set 3
- Problem Set 4
- Problem Set 5
- Problem Set 6
- Problem Set 7
- Problem Set 8
- Problem Set 9
- Problem Set 10
- Problem Set 11
- Problem Set 12

Material related to the three lectures and two exercise classes on Computable General Equilibrium can be accessed through a course site on Blackboard. In the Course Catalog, choose Økonomi, Samfundsvidenskabeligt Fakultet and then access the course: Microeconomics 3rd year - CGE models (Samf-CGEmodels).

Peter Norman Sørensen

Økonomisk Institut, Københavns Universitet

Studiestræde 6

1455 København K

Ph. 3532 3056

Email ` peter.sorensen@econ.ku.dk`

Last edit: May 21, 2003.