Messages - Page 2

Those who have already had a look at last year's set #2: I have added 2011 problem 3 (and removed the problem already given).

It turned out that my attempt to explain how to show that the C-D function is concave without differentiating was not correct after all. Sorry about that!

The problem is more difficult than what I first thought, as you need to use a result related to quasiconcavity.

The argument is as follows: we have f(x)=exp(lnA + ln x1 + lnx2 + lnx3)). Now, the argument in the paranthesis is concave, and therefore also quasiconcave. Thus, Theorem 2.5.2 in the English textbook (Setning 4.7.2 in the Norwegian Version) asserts that f(x) is also quasiconcave. Then you can apply Theorem 2.5.3 (Setning 4.7.3) to conclude that f(x) must also be concave, since all the conditions of the theorem are satisfied (not very difficult to check).

Ingvild.Mageli [?tt] gmail [d?tt] com 

(lightly spamshielded address) will take care of ovations, insults and - hopefully - constructive suggestions. 

Rigth after each seminar, I am going to publish my hand written solutions to the problems. In order to still make it useful for you to attend the seminars, I will have an approach where I combine exercise solving with summarizing and explaining the concepts, with the goal of giving you an overview. Thus, my seminars will include information that is not included in the solution notes. Also, please tell me if I have some mistakes in my notes, that might typically occure sometimes.

(Sorry that I start my note by writing Norwegian. I change this to English afterwards. Still I think you will understand the first part since most of the writings are mathematical notation.)

The final exercise about Jensen's inequality will be included in next week's notes.

Espen

Seems that the course page puts the problems in the right-hand margin, while the link to the old exam problems is found in the left-hand margin. At least that's how it looks as of now.  - Nils

The schedule now has the first few weeks' topics. For the first lecture, there is one concept which is going to be new (and presented in a way many find difficult! Do not despair, it will get easier.)

However, before we jump into the most abstract part of the course, we will fix some terminology - vectors, matrices, the gradient, the Hessian (and the Jacobian, which you might not have encountered in Math 2).

Knut Syds?ter and Arne Str?m compiled this list of prerequisites - you might want to check for gaps in your knowledge.