Topkis question December 7, 2008

I have a question about Topkis. In order to apply Topkis, do we have to have maximizaton problem or minimization is fine, too? Our statement of Topkis has been for maximization of a supermodular function. You can write other (more general) forms that involve minimization and/or submodularity/decreasing differences. However, I always find it easiest to [...]

Revealed preference and strictly convex preferences December 4, 2008

In the revealed preferences arguments that we used in solving Question 1 in Consumer Theory Problem Set, even after we assume local nonsatiation, the question is still tricky because we are never sure if we can observe the entire choice set. We had to argue through many results relying on the fact that the optimal [...]

Choice under uncertainty questions November 19, 2008

I have some questions concerning the problem set and the notes of Choice under Uncertainty. First, for problem #3, I was confused by the question “state necessary and sufficient conditions on u(.), ensuring the consumer will underinsure/fully insure/overinsure”. In fact, I have solved the FOC, and find that the property of u’(.) rather than u(.) [...]

Working with Cobb-Douglas November 11, 2008

I wonder if you will be marking our final exam papers. If yes, I wonder if I can use the trick for Cobb Douglas type preferences/production technology, that we always get interior solutions, and that at the optimal solution the fraction of income spent on each good is determined by the exponent parameters. So that we [...]

Sufficiency of Kuhn-Tucker November 11, 2008

On page 212 of your latest updated slides, on the “sufficiency” of Kuhn-Tucker conditions, can the conclusion be true if we do not assume local non-satiation? If we do not assume monotonicity? strict monotonicity? It’s interesting if it is, because the would mean even if one of the two goods is a bad, or whatever [...]

Producer theory questions November 5, 2008

As I reviewed producer theory, I found a couple of things that I should have asked you a month ago: 1 On page 60 of the latest slides, I found the first bullet used to be “Closure ensures that \pi(p) is actually achieved.” Is it because the unboundedness or the asymptotic case might still prevent [...]

CV and EV questions November 5, 2008

Sorry to bother but I wonder if I could ask you a couple of stupid questions regarding CV and EV: If the new price p’ < p (for at least one) with fixed w>0, does the consumer have to be better off? Do CV and EV have to be positive? Yes. If p’ < p, [...]

Mistake in solutions to 2007 midterm exam November 5, 2008

I think there is a typo in the last midterm answers of question 2, letter b, iii… You’re absolutely right. The EV given in the solution is negative of what it should be. Sorry! Since prices have fallen, the consumer has become better off. Thus EV should be positive.

Parameter assumptions on utility functions November 2, 2008

I wonder if the \alpha in Question 3(a) of Problem Set 4 is required to be between 0 and 1. If not, would it still be Cobb Douglas? Also, could there be a condition on the \beta in 3(c) that \beta > 0 ? Otherwise it might not be a monotone increasing transformation of (a). Both seem like [...]

Utility function with max and min November 2, 2008

I just want to make sure i got the intuition behind the crazy utility function: u = max(ax, ay) + min(x,y). Because utility = max(ax, ay) + min(x,y), this means the consumer is able to substitute between two goods, and he is able to maximize one of them, consuming the less quantity possible of the [...]