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.

Before the judgement day

As the final exam of Microeconomics I approaches, perhaps it would be helpful to you to have a review session. It probably will last from 2-3 hours. From the your busy schedule for next week and the fact that I won't be in Lucca after next week, the afternoon of Wednesday (9th) or Friday (11th) seems the only options (unless you want to organize it after 5pm).

During the review session, I will: (i) give a quick scan of what we've done two months ago, and what you should be able to do; (ii) do selected exercises proposed by you or me; and (iii) give some information about the exam.

Participation is entirely voluntary. I will also email or post on the blog the exam information so you don't have to worry about missing something important about the exam. If you plan to come, please send me an email or replying on the blog, together with your preferred time and suggested exercises (or questions). Due to time constraint, we won't be able to go through a lot of exercises or go to very details. But I'll try to accommodate most people's needs.

Please send your reply before next Monday so that I could book the classroom. Finally, to exploit scale economy, this review session will only be held in the case of more than 5 people. (If less than 4 of you have questions, you can simply use the office hours.)

Slides are here.

We believe, and we move

We will finish this course with dynamic games with incomplete information. The last lecture will be held on May 14th, 10am-1pm. It will cover perfect Bayesian equilibrium, signaling games and some belief-based refinement, and common knowledge if time allows. Please read MWG 9.C-D, 13.C, 13.A.A, FT 8.1-3, 11.2, and EX. 14.4.

On the same day Elira will present Dessein's paper on authority and communication within an organization. The paper can be downloaded on JSTOR; presentation slides are here.

Slides are here. Suggested exercises are here.

Everybody has some secrets

The last two lectures will be devoted to games of incomplete information. On May 13rd, 2-5pm, we will talk about static games of incomplete information. We will first introduce the notion of "type" and "belief," and the equilibrium concept in this environment, namely, Bayesian equilibrium (MWG 8.E, and FT 6.1-5). As an application we will talk about mechanism design (MWG 23.B, D, E, and FT 7.1-4).

On the same day we have two presentations about two applications of mechanism design. Ilaria will present public goods provision (MWG 23.D and/or FT 7.4.3), and Caterina will present Armstrong's 1996 paper on multiproduct nonlinear pricing. You can download the paper on JSTOR. There slides are here and here.

Slides are here. Suggested exercises are here.

The next dance, and next, and next

On May 8th, 10am-1pm, we will talk about the dynamic game under perfect information. We will introduce subgame perfect equilibrium in both finite- and infinite-horizon games. Please read MWG 9.B, 12.D, 12.App.A and B. It's also helpful to read F-T Chp 4 (and Chp 3 and 5 if you have more time).

Also on that day Peng and Virginia will present two applications of repeated game, namely, tacit collusion and efficient wage bargaining, respectively. Peng's presentation will be based on the paper by Ivaldi et. al. (2003); and Virginia's presentation will be based on Paz Espinosa and Rhee (1989), which can be downloaded at JSTOR. Their presentation slides are here and here.

Slides are here. Suggested exercises are here.

Turbulent office hour schedule

Due to the coming conferences, in May and June I will be in Lucca for the following Thursdays and Fridays:

May 8 (Thu) and 9 (Fri)

May 23 (Fri)

May 29 (Thu) and 30 (Fri)

June 5 (Thu) and 6 (Fri)

My July schedule is still uncertain, but very likely I'll only be in Lucca during the second week of July (roughly from 7-13th).

Those who want to come on this Thursday, May 8th, can sign up here.

``Too technical''

I've read your feedbacks on the first part of the course. Thanks for these comments.

I surely share the common feeling that there is severe time constraint, and agree that there are quite a few things to improve. Here are some remarks about the ``technicality'' issue.

A plain truth in this profession is that, while applying economic theory to interesting and relevant real life experiences may be, and should be the drive to pursue a career as an economist, the ability to be formal and rigorous is a threshold you need to pass in order to be qualified as an economist in the first place. Whether you plan to become a theorist or not, rigor, precision, and being formal are fundamental in scientific writing. This means you need to be able to read and write papers in that way.

For most people, I believe, it takes time, efforts, and even some pain to build this ability. This is the ``gap'' I mentioned before, and helping you during this process is what I meant to make this transition period as smooth as possible. The bottom line is, you will need this ability soon. If we don't tackle this together in the classroom, you'll have to deal with it by yourself.

That said, and my presentation skills aside, I do not consider the material I presented in class ``too technical.'' On the contrary, I think it is not technical enough. You must have noticed that what's in the slides are mostly simplified MWG, and on the whiteboard I used mainly figures or number examples. The first part of MWG is pretty much what one would expect from a PhD student everywhere. As most people, you may have difficulties in the beginning, but eventually you'll need this level of technicality.

It starts the first tango

From the next lecture we will move to game theory. The 7th lecture, to be held on May 7th, 2-5 pm, will introduce the notion and elements of a game (MWG 7), simultaneous games with perfect information (MWG 8.A-D), and, if we have time, correlated equilibrium (F-T 2.2).

This clip will help you appreciate the importance of information in game theory. It points to a key assumption in almost all games. (Try to identify which one!) If you know something about games under imperfect information, modeling that situation is a good exercise.

Slides are here. Suggested exercises are here.

Those who will present

Should have received my email about the preliminary ideas of presentations, including when and what. Please write to me IMMEDIATELY if either you have told me before the deadline that you wanted to present but haven't not yet received the email, or you didn't say you want to participate but got the message. Please note that I won't be here next week, so email is the only way to contact me.

In this capricious world

The second part of the course will be concerned with choice under uncertainty and game theory. In the 6th lecture, to be held on April 30, 2-5 pm, I will cover uncertainty theory, including expected utility theory, risk attitude, stochastic dominance, and, if time allows, state-dependent utility. Please read MWG 6.B-E.

Slides are here.

Suggested exercises are here.

Office hour April 17 canceled

Due to some emergency, I won't be able to stay in office, or Lucca today. Sorry about the last minute announcement...

The first time they meet

The 5th lecture, to be held on April 16 from 2-5pm, will be the first time we encounter the magic word in economics: equilibrium. We will bring together supply and demand under the partial equilibrium framework. We will cover two market structures, perfect competition and monopoly, each with specific topics.

Under perfect competition, we will pay attention to its welfare property, especially the First Fundamental Theorem of Welfare Economics. For monopoly, if we have more time to talk about more than (simple) monopoly pricing, we'll also discuss price discrimination and durable goods monopoly (Coase conjecture). Please read MWG 10.B-F for the perfect competition part, MWG 12.B for monopoly pricing, V 14 for price discrimination, and Chp 1 of Tirole's IO book for durable goods monopoly.

Slides are here.

Exercises are here.

A break, well, not really...

Because of this week's tight schedule, I will not post suggested exercises until Thursday or Friday. If you need something fun to do, MWG surly will not disappoint you.

Something old something new

The 4th lecture, to be held on April 15, 2-5pm, will be devoted to producer theory. The same optimization approach as in consumer theory will be applied to what we call "neoclassical firms."

I will mention very quickly common results (profit optimization and cost minimization), and spend more time on what we didn't do in consumer theory (comparative statics with calculus) and issues specific to firms (short-run and long- run). Please read MWG 5.B-D. Varian Ch 1-6 are also useful. If you have more time, you can take a look of Separation Hyperplane Theorem (MWG M.G.2).

Slides are here.

Suggested exercises are here.

Let's speed up

From first week's reaction during the class and quiet office hours, it seems that we can "raise the bar" and proceed more quickly. So I'll modify the plan and finish producer theory in one lecture. Game theory will take all the saved time as well as presentations, if any.

The new contents for each lecture are therefore:

Lecture 3 - applications of consumer theory

Lecture 4 - producer theory

Lecture 5 - perfect competition and monopoly

Lecture 6 - choice under uncertainty

Lecture 7 to 10 - game theory

Office hour April 17

You can sign up here with your questions.

and practical

A change of time: The third lecture will be held on April 14, 10am-1pm, instead of the originally scheduled April 15.

To finish our discussion of consumer theory, I will focus on two applications of the theory we've learned, including welfare analysis (MWG 3.I), and endowments as well as labor supply (V 9).

If we have more time, I'll speak shortly about integrability (MWG 3.H) and revealed preference (MWG 1.C and 2.F).

Slides are here.

Suggested exercises are here.

Now let's get something real

The second lecture will be held on April 10, 10am-1pm. I will talk about consumer's utility maximization, expenditure minimization, and duality. Please read MWG 3.D, E, and G. Slides are here.

Suggested exercises are here.

If you want to present

You can sign up here. The registration deadline is April 18.

Office hours April 10

Those who intend to come, please sign up with your questions (if any). I will update here the contents after receiving your responses.

Where it all begins

The first class will be held on April 8, 2-5pm. You are going to hear something about me, the course, and consumer preferences and constraints.

I will distribute syllabus, handout (introduction and the basic elements of consumer theory), and exercises. Please, if you have the book, read MWG 1.B, 2.B-D, 3.B, and 3.C before going to the class.