And finally we're all done

The final exam and its solution is here.

According to what I saw in the second try, there are a few things you need to pay attention to:

1. From your answer to question 3(b), you still don't fully understand how to operate expected utility. Since this is a very fundamental concept and very important for your subsequent study, please check the solution and make sure you know where the problem is. (Or come to me to clarify if you still have trouble.)

The followings are "big principles" and may require quite some time to learn.

2. In your answers, very often you skip important steps of reasoning and mathematical manipulations. For instance, in question 5(b), you directly wrote down the conditions and their economic meanings, without providing a clue how the conditions are derived. The same situation happens not just once.

When you're writing a paper, it is very important to know what to write and elaborate (those crucial for the results) and what to omit (those trivial parts). And the steps you should (almost) never skip are where you begin with and when you need to cite other results to proceed (e.g. in question 2(f)).

3. Related to the last point, you should also avoid irrelevant things in your answers. It's nice that you've learned many stuffs, but putting irrelevant ideas can only distract readers. And worse, sometimes people may doubt whether you truly understand the question. For instance, in question 3(a), you also considered the case when x is larger than gamma, which leads to negative marginal utility from x. This is correct, but irrelevant, because in the question I've clearly assumed away this case.

4. You need to learn how to use math tools properly: use them if and only if necessary. For instance, in question 1(a), once you show how the utility depends on alpha, no calculus is needed. On the other hand, in question 1(c), it would be better to derive the exact condition when the budget constraint is not binding.