Week 1 in Review

I had an ambitious goal of keeping a daily journal of what I learned, but my ambition died the first day and I decided to keep a brief weekly journal instead.

1. Economic Analysis

First lecture was a review. The main point of interest was that the amounts of labor and consumption are equal in a single-sector economy (Robinson Crusoe economy) and in a two-sector economy (decentralized market economy) given the same preference and technology. The natural question is, of course, why that is true. I frankly couldn’t answer the question and embarrassingly I still have not found a satisfactory answer. A point I need to think a little more.

The second lecture was the beginning of a tax analysis, and since we did not finish the model’s analysis, I have an excuse to delay a log on it.

2. Game Theory

The lectures were very satisfying in that they provided mathematically vigorous definitions of preference relation and choice function. Ever since I took the real analysis class, I wanted some exposure to mathematical rigor in economics, and this class seems to provide just that at the right level. The core of the first week’s lectures was proof of Houthakker’s theorem, which is interesting enough that I may write a post about it later.

3. Statistics

So far, we only had somewhat boring lectures on probability. There was one interesting question given during the class, which was pretty elementary but still quite confusing: There are 49 balls in a jar, each numbered from 1 to 49. You choose 7 numbers and 6 balls are drawn. What is the probability that exactly 3 balls drawn show the numbers you chose? There are 49C6 ways in which 6 balls are drawn from the jar. Of those 6, we want 3 balls to have numbers you chose; there are 7C3 ways that 3 drawn balls match with the 7 chosen numbers. The remaining 3 balls should have numbers you have not chosen and there are 42C3 ways in which 3 balls do not match the numbers. So the probability is (7C3)(42C3)/(49C6), which is around 0.0287. The curious part of the problem is that one can think in terms of numbers you choose instead of balls you draw; this yields the probability of (6C3)(43C4)/(49C7) which is seemingly different from the previous one, but is in fact the same.

4. Real Analysis

I thought the second quarter would be better and I was wrong. This is the class that I feel very lost during the lecture so I should really review the materials on a daily basis, but I have not even done that. So far, we have proved that differentiable implies continuous, chain rule, mean value theorem, and l’Hopital’s rule. Sadly, I don’t think I fully understood any of them. The problem set is also discouraging and I have not touched it yet, so not much to discuss yet.