Graduate Microeconomic Theory

On-line review of mathematical concepts

This short on-line course is designed primarily to help students prepare for a graduate program in economics (masters or doctoral).  If you are beginning an MA in economics you should focus on Part A of the course.

At UCLA our doctoral students complete both Part A and Part B before arrival and then take a two week intensive "Math Camp" course. Click on "Mathematical Foundations" to see the list of topics in that course. This foundational mathematics is covered in more detail in the mathematical appendices of Essential Microeconomics 

Studying advanced economics, particularly at the doctoral level, requires a considerable degree of comfort with mathematics. Most students, even those with relatively strong mathematical backgrounds, find they benefit a lot by reviewing the concepts that they once studied. Often concepts were learned several years earlier and there has been some depreciation of human capital.  For such students it is primarily a matter of digging into their mathematical tool-kit and sharpening their tools. A considerable number of students find that there are gaps in their education and additional preparation is helpful.

There are nine modules. Hints are provided to help you and the answers are also provided.


Module 1: Calculus with one variable
Module 2: Maximization with two variables
Module 3: Probability and random variables
Module 4: Maximization with n variables
Module 5: Constrained optimization (applying the Lagrange Method)
Module 6: Constrained optimization (theory)
Module 7: Linear transformations
Module 8: General Equilibrium
Module 9: Constructing proofs

The modules in Part B contain somewhat more subtle mathematical material. If you run into difficulties try not be downhearted.  It will mean that you will have to open a text book to review the basic concepts. Or contact me by email. 

If you feel full of confidence, go directly to Module 9 and see if you can do all the exercises. If so you are well prepared and should be able to work through all nine modules quite quickly. However if you find the exercises hard then you really do need to devote a considerable amount of time to the Modules to be prepared for a first year gradaute course in microeconomics.

Some students also find "Optimization in Economic Theory"  by Avinash Dixit (Oxford Economic Press) helpful.  I also like Dixit's book a lot. It is very readable.

Some advanced theory courses present so much mathematics that it is hard to see the economic content.  Essential Microeconomics is a formal text that does not shy away from proofs.  However the primary goal is to build confidence in using mathematics to model economic issues and draw insights from formal models.

The only way to develop this skill is to practice and practice.  Thus exercises play a very important role in this course. Answered can be found in the back of the text book to all the exercises in the text.  Additional exercises and answers will be provided on this web-site.