Messages

If you have questions on the maths, feel free to knock on my door at any time. (I am rarely at the office at 0800, but I am rarely gone at 1600.) I am, however, away on Thursday, daytime -- and also afternoon unless someone needs to schedule an appointment.

About the exam:

• Remember that you are allowed to bring all books, notes, and other written or printed matter with you, and pocket calculators too.
• The exam is not the right time to save paper -- you would want to write so clearly and legibly that we can read what you are doing (which is necessary to get credit).

My consultation hours the forthcoming Tuesday (20th) are cancelled, as I am away. You may of course knock on my door at any time.

Seminar 1: last time Monday May 19th: room 101 Harriet Holters building at 10.15-12.

• The solution to problem set #2 is now updated with (I) an embarrassing correction in Problem (4), and (II) more comments on the most common errors of yours.

• You can pick up your term papers on Friday after lunch.

• They are graded according to the usual scale, disregarding that it was a bit more work than an exam problem set (hey, you had two weeks on it). The grade distribution from A through E turned out as (21, 20, 9, 2, 1) -- no F, all accepted.

• I will have to change my consultation hours at least one week, stay tuned. (On the other hand, you are free to knock on my door any time.)

Seminar 1 today (grupperom 4, GS building), May 5th, is cancelled due to illness.

• No lecture on Friday. For the final lecture on Tuesday, I will conclude on elasticities and cover the term paper problem set.

• I hope to have a first version solution to the term paper problem set posted on Monday afternoon. I will update the solution with more comments when done with your papers.

• The problem set for the final seminar is out; I re-cycled an old set without any dates corrected.

An explanatory note on a detail on the example given in Tuesday's lecture:

The issue was whether the set defined by the constraints in the example is closed. It is not -- and the issue is that at certain points, the functional equation defining g has no solution (in the real numbers); consider x=0 and y so that the right hand side is 0 -- that is, y=-2/3. Then g must solve exp g = 0, which is impossible.

This is the similar phenomenon as the following example: max f(x,y) subject to ln x less than or equal to 0. Then x would not only have to be less than or equal to 1, but also >0 in order for the ln to be defined.

Hence, if f were -|x| - |y| (maximum at (0,0)), then the constrained problem would not have any solution; the best we could hope for, would be to choose y=0 and let x approach 0 from above.

For the purposes of this course: If an exam problem states that a function g exists, then you can safely assume it does.

As agreed with the seminar groups, the seminars have been postponed in order to leave more time to deal with the term paper.

• There are no seminars Wednesday 23rd and Thursday 24th this week, nor Monday 28th next week
• The Wednesday Seminar #9 will be the 30th. Obviously there is no seminar Thursday May 1st.
• Seminar # 10 will be week 19.

• As mentioned in the lecture, my presentation of the motivation for the envelope theorem last Friday was seriously flawed. Please delete from your notes everything before I started to use vector notation. I will give a correct version -- in terms of Lagrange multipliers -- on Friday. Then we'll start doing nonlinear programming.

• Some of you requested the last seminar to be postponed, to give you more time for the term paper. I have left the decision to the seminar leader who will ask each class separately.

The problem set for term paper #2 is now available.

The problem set for the upcoming seminar is now available, sorry for the delay -- I need to get used to the new seminar schedule.

The solution to the problem given in the lecture is available (under the new "Misc." heading).

• On Friday, at least one of the lectures will be dedicated to the term paper problem set. A note with solution is posted.
• I have moved to room 1243, next to the department reception.

Reminder: there is no lecture Friday 14th nor Tuesday 25th, and no seminar on Wednesday 26th.

From then on, seminars will run on the same days as before, so that seminar #6 (problem set available now) will be Thursday 27th, Monday 31st and Wednesday 2nd, and then Thu--Mon--Wed throughout April.

The term paper deadline is closing in. Time for a few clarifications from questions you've asked.

First, a correction: in problem 2c, delete the sentence "The integral is improper." It is not, my bad.

Then a few minor points and hints:

• In Problem 1, K is an arbitrary constant. The number of zeroes will -- possibly -- depend on K.

• In 1b, note that f is defined only for x nonnegative. That is: if you find zeroes x<0, they shall be disregarded.

• In 1c, still note that f is defined only for x nonnegative.

• In 2b, "expand" means to write out the product as a thrid-degree polynomial

• 2d: no, you are not supposed to calculate the indefinite integral.

The problem set for term paper 1 is now available, with an extended deadline (see updated schedule).

• Part of the problem set might be quite a bit hard; I want to see where the troubles are and besides it does not count in your grade.
• Since you won't prepare for any seminars in week 10 (there are none!), I extended the term paper deadline to Thursday that week.
• Although the problem set is available only in English, you may write your term papers in English or Norwegian.

Edit: Oh, and I see a small misprint, it is dated February 15th "2007" which should be "2008". Will update if anyone insists :-)

Two messages: (1) As announced in today's lecture, the schedule will be as suggested. I will update it with term paper deadlines shortly.

(2) Problems: do the remaining parts of the two below posted problem sets, and also the following: Show that f(z) = (1+r/z)^z (the "^" should be a superscript (power!), but that does not work in the messages ...) is increasing (in z) -- that is, that effective interest rate is higher the more often interest is accumulated. Proceed as follows:

• You may want to consider g(z) = ln f(z) = z ln(1+r/z) instead of f; point out that f is increasing if and only if g is (at least whenever the logarithm is defined).
• Find g'(z) and point out that g'(z) tends to 0 when z tends to infinity.
• Find g''(z) and point out that it is negative.
• What does the latter two points tell you about the sign of g'(z)?

This week's problem set is recycled from previous years; do this problem set except problem 4 (ii), and also do problem 2 from this set.

It seems inconvenient to have a lecture-free week as early as week 8 (matching ECON2130 Statistics 1), among other things because I will not have time to complete linear algebra before Easter.

My suggestion is to split the lecture-free week by calling off Friday the 14th and Tuesday 25th; I suspect that Friday before Easter 14--16 and Tuesday after Easter 0815 aren't the most productive times. Alternatively we could take the week after Easter. I'll poll you next lecture, which is next Tuesday (as Friday is cancelled).

Therefore, consider the lecture schedule preliminary. Term paper deadlines are not decided upon, but term paper 1 will cover approximately up to and including differential equations, while term paper 2 will -- I hope -- cover nonlinear programming.

Problems for the forthcoming week tba soon.

Welcome to the course. The first lecture is Tuesday 15 at 0815. The teaching-free week will be determined later, when I know what other courses you attend this semester.

• There is no lecture Friday 18 January.
• The seminars do not start until week 6 (Feb. 4). There will however be problems posted on this web site.
• Due to these delays, the course will last a week longer than initially announced. As of now, I have not yet made the appropriate corrections. A detailed lecture schedule will be posted when the teaching-free week is determined.

For Tuesday 15., I will give an overview of the course and cover a few practicalities. We will then start lightly by reviewing the exponential and logarithm functions.