Week 2 in Review

1. Economic Analysis

I am increasingly inclined to think that macroeconomics isn’t as fun as microeconomics. What’s the big deal about Laffer curve, anyway? (I am a fan of Martin Gardner.) I do enjoy the algebra, though. Solving the first order conditions and deriving the steady-state consumption level is like doing a Sudoku puzzle; mind-numbingly fun.

Anyways, the point of this post was to review what I learned, like “lump-sun taxes are non-distortionary and consumption crowding-out” or “proportional-tax model predicts that the revenue maximizing tax rate is equal to the labor share in production which is empirically around 2/3”. Yawn.

2. Game Theory

The challenge problem of this week was to derive a condition analogous to WARP on a choice function such that a choice function generated by a quasi preference is satisfies the condition and a choice function satisfying the condition is quasi preference generated. A quasi rational preference is transitive and irreflexive, such as “xPy if x-1>y” where x,y are integers. Of course, I have not solved the problem (yet).

We also covered Gibbard-Satterthwaite theorem and started to build the formal concept of game theory.

3. Statistics

We departed with probability and entered the world of random variable and discussed several important discrete random variables, like the Bernoulli, binomial, geometric and Poisson. I should review these.

4. Real Analysis

The “fun” problem of the first assignment had nothing to do with real analysis, but was still interesting: A set of points in a plane and a subset of all the line segments connecting the points are given. Each point represents a switch. If a switch is flipped, then all other switches connected to that switch (via the line segments) are flipped. Initially all the switches are turned off. Prove you can turn on all the switches.

Apparently the problem can be brought into the realm of linear algebra and solved, but it seems there is a different approach as well. I was thinking about using Euler characteristic on planar graphs. I am yet to see if this goes anywhere.

We covered the definition of Riemann integral and the intuition of Lebesgue integral.