End of term
I have removed most of the files related to this course. The tutorial on differential equations is still availlable, though.
Draft of solution to homework 3
About homework 3 ("Sympathy for the Devil")
Since there was no indication on how much marks was worth each question, I had to make one up. On a total of 100 marks, one could get respectively 10, 5, 10, 20 marks for question 1 a), b), c), d), 10, 5 marks for 2 a), b) and 10, 20 10 marks for 3 a), b) and c).
Question 1
- c) Some of you forgot to analyse the dynamics of the model. This also happened in d).
- d) There are many possible cases in this question (six actually). None of you found all of them. People had a lot of difficulties to characterise how the dot k = 0 loci would evolve with a change in g. Here are some details of the curve characterisation if you are interested.
Question 3
- b) All of you forgot to mention that
were valid constraints. Most of you forgot to include the transversality condition at some point in your problem.
- c) The market allocation in this context is NOT pareto efficient for two reasons. The first and obvious one is that
in question one. Hence, there are some ressources that are affected to things yielding zero utility. The second reason is that
and thus there is misallocation of dot k.
Solutions to homework 2
Right here (some minor corrections since the tutorial + correction in question 1 f) ).
About homework 1
I received your copies and I am done marking. Some general comments below.
Question 3
I must say that I'm impressed by the consistency of the answers across copies... Perhaps there was a solution in some book out there ?
Question 2
- a) A lot of simple algebra mistakes where done when trying to find eigenvectors/values. More importantly, when building the matrix V, one must put the eigenvector in the same column as the associated eigenvalue. E.g. : if
, then it must be that
. A good practice would be to check your solutions.
- b) A lot of people drew the linear approximations as if they stretched forever. Remember that these are approximations which are good only around the candidate equilibrium. As the distance increases, the real path diverges from this line, especially if you end-up crossing a stability loci/axis.
Question 1
- a) If you did not found the solution to one, revise the material.
- b) Most of you took the long way to solve this (linear, non-homogenous case) while the equation was separable.
- c) The professor's solution is somewhat complicated (but works !). Again, separability works, but roots of the equation (y = 0) and (y=1) works as well (roots => stability => dot y = 0). Nobody mentionned that.
- d) Notice that if
, simple differentiation allows us to find
. One should recognise from this the signature of an exponential function. A bad joke on the matter (the last one).
January 29th
Some slides for this friday. A correction in the definition of the Taylor expansion has been made.
A sketch of the solutions of the problems in the slides above.
January 22th
Here are the slides from the 22. I corrected a small error regarding the definition of eigenvectors and in slide 51.
My office hours
My office hours are thursdays, from 12pm to 14hpm, the weeks I do not give tutorials. I live (...) in DUN 337.