Seventh Semester at College

How did I become a senior? It doesn't feel like orientation and freshman year happened that long ago.
Tomorrow is the first day of class for the 2013 fall semester. I'll be taking 8.07 — Electromagnetism II, 8.09 — Classical Mechanics III, 8.333 — Statistical Mechanics I (a graduate class), and 14.12 — Economic Applications of Game Theory. I'm looking forward to all of these classes along with continuing my UROP (which may transition sooner or later into a new project as I wrap up my current one). The bigger things I have to deal with though are graduate school applications and the Physics GRE. The latter will be over in a few weeks. The former will be going on until around the beginning of December, but I hope to be done a while before that. Hopefully this semester goes well. Good luck to everyone else for the start of their school year/job/whatever else!

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Cap and Trade and Soda

A few days ago, my family and I went on vacation. On the way back, my family and I were discussing various things including some matters of politics. One thing that came up was some of New York City mayor Michael Bloomberg's recent actions. I expressed the view that the ban on soft drinks larger than 16 ounces seemed rather heavy-handed. (After reading a little more about the exceptions for fruit drinks along with sales at grocery stores, I'm a little more happy to see that, but I still feel the ban was heavy-handed.) I then heard the argument that even if it is heavy-handed, it does help combat the obesity crisis by reducing access to drinking 16 ounces of soda at a time, because even if it is still technically possible for someone to fill up an 8-ounce cup twice, human psychology is such that said person would only fill up once, because for many people the convenience of filling up once trumps the desire to have as much as possible. I then wondered what other alternatives could be considered. The simplest alternative would seem to be a tax akin to taxes on cigarettes; if the large sodas are taxed heavily at such venues, people would naturally be discouraged from drinking as much. I have taken the class 14.03 — Microeconomic Theory and Public Policy, though, so I have seen that in many cases a Pigovian tax scheme like that may not achieve the most efficient outcome because it is difficult to adjust tax rates to control quantities precisely. Then I also remembered learning about cap and trade schemes to control quantities. Would that work? Let's take a look after the jump.

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Done with 6th Semester!

I'm done with junior year! The spring semester was a bit more manageable than the fall semester, but was still challenging nevertheless. I intentionally chose to take only 3 classes: 8.06 — Quantum Physics III, 8.14 — Experimental Physics II, and 14.03 — Microeconomic Theory and Public Policy. I did this so that I could spend more time on each of those classes (especially 8.14 — Experimental Physics II) as well as on my UROP. Speaking of my UROP, things were progressing rather slowly in the beginning of the semester and only slowed further from there, until just after spring break, at which point progress went extremely quickly. I'm really looking forward to being able to make more such progress in the summer; plus, I may even be able to start on a new project about the Casimir effect, about which I wrote a paper for 8.06 — Quantum Physics III. Before that, I'm spending two weeks at home. For these next few days, I'm just going to relax and spend time and travel with family. After that, I'll probably be able to start work again on my UROP; a few weeks into the summer, I intend to start looking seriously into graduate programs in physics. Anyway, at last, it is summer!

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Frictions, Subsidies, and Taxes

One of the things I learned in my high school AP Microeconomics class was that a tax causes the supply curve to shift to the left, making the equilibrium quantity decrease and price increase. Consumer and producer surplus both decrease, but while government revenue can account for some of the loss in total welfare, some part of total welfare gets fully lost, and this is what is known as deadweight loss. I didn't have a very good intuition for how this worked at the time (though I was able to get through it on homework, quizzes, tests, and the AP exam). At the same time, though, I thought that a tax should be fully reversible by having the government subsidize producers, and that as this would be the opposite of a tax, supply would shift to the right, the equilibrium quantity would rise and price would fall, and there would be a welfare gain.

Then, when I took 14.01 — Introduction to Microeconomics, we again discussed the situation with a tax. Then we talked about subsidies, but I was confused because the mechanism seemed to be in providing a subsidy to consumers rather than to producers. My intuition at that point was that taxes were creating deadweight loss because producers who wanted to produce and consumers who wanted to consume near the original equilibrium could not do so after the tax, so some transactions were essentially being prohibited. However, I still didn't quite understand why a subsidy would create deadweight loss, because it seemed to me like consumers who wanted to consume more and producers who wanted to produce more than the original equilibrium quantity could now do so, meaning it seemed to me like more transactions were being made possible. That said, I did understand why the government would never subsidize producers: unless the market is perfectly competitive, producers would rather collude and pocket their subsidies while keeping prices high when they can. On the other hand, consumers prefer consuming, so subsidizing consumers is a more surefire way of increasing the equilibrium quantity, even though the price would go up rather than down.

(In 14.04 — Intermediate Microeconomic Theory, we barely touched on deadweight loss in the way that it is covered in more traditional microeconomics classes.) Now, in 14.03 — Microeconomic Theory and Public Policy, I think I better understand the intuition behind deadweight losses stemming from taxes and subsidies, and why a subsidy is not the opposite of a tax. In a tax, the government might try to target some new equilibrium quantity below the original one, so the tax revenue collected, which increases total welfare, is the difference between the willingness of consumers to pay and the willingness of producers to accept at that quantity multiplied by that quantity. Consumer and producer surplus both decrease, and the tax revenue contribution to the increase in total welfare is not enough to offset these two, so there is an overall deadweight loss. A completely isomorphic way of picturing this is by considering the tax falling on consumers so that the demand shifts to the left; in both cases, the equilibrium quantity drops, the government collects its revenue, surpluses drop, so deadweight losses appear.
Meanwhile, for a subsidy, the government might target a higher quantity than the original equilibrium. The spending on that subsidy is the difference between the willingness of producers to accept and the willingness of consumers to pay at that quantity multiplied by that quantity. Consumer and producer surpluses both increase, but together they do not increase enough to offset government spending which is an overall drain on total welfare, so there exists a deadweight loss.

It's interesting that taxes and subsidies are not opposites. The intuition is that for a tax, the revenue is not enough to compensate for the welfare losses of consumers and producers because the new equilibrium quantity is lower. By contrast, for a subsidy, the spending is too high compared to the welfare gains of consumers and producers because the new equilibrium quantity is higher. It looks like it is not possible to spend money given by tax revenue to undo the effects of a tax; instead, the government can only overshoot and overspend. It reminds me very much of how friction works: moving in one direction on a surface with friction causes energy loss, while turning around to move in the other direction on that same surface most certainly does not cause energy gain. Essentially, in this model, the market is frictionless, and the government introduces friction.

Of course, this essentially contradicts Keynesian models of government taxation and spending and their respective effects. That's why care must be taken when putting microeconomic models in a macroeconomic perspective. This also doesn't consider externalities, less than perfectly competitive market structures, et cetera. Anyway, I hope my musings on this may help give other people some intuition on simple issues of deadweight loss in microeconomic theory.

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More on 2012 Fall

Last semester, I was taking 8.05, 8.13, 8.231, and 14.04, along with continuing my UROP. I was busy and stressed basically all the time. Now I think I know why: it turns out that the classes I was taking were much closer to graduate classes in material, yet they came with all the trappings of an undergraduate class, like exams (that were not intentionally easy). Let me explain a little more.

8.05 — Quantum Physics II is where the linear algebra formalism and bra-ket notation of quantum mechanics are introduced and thoroughly investigated. Topics of the class include analysis of wavefunctions in 1-dimensional potentials, vectors in Hilbert spaces, matrix representations of operators, 2-state systems, applications to spin, NMR, continuous Hilbert spaces (e.g. position), the harmonic oscillator, coherent & squeezed states as well as the representation of photon states and the electromagnetic field operators forming a harmonic oscillator, angular momentum, addition of angular momenta, and Clebsch-Gordan coefficients. OK, so considering that most of these things are expected knowledge for the GRE in physics, this is probably more like a standard undergraduate quantum mechanics curriculum rather than a graduate-level curriculum. That said, apparently this perfectly substitutes for the graduate-level quantum theory class, because I know of a lot of people who go right from 8.05 to the graduate relativistic quantum field theory class.

8.13 — Experimental Physics I is generally a standard undergraduate physics laboratory class (although it is considered standard in the sense that its innovations have spread far and wide). The care and detail in performing experiments, analyzing data, making presentations, and writing papers seem like fairly obvious previews of graduate life as an experimental physicist.

8.231 — Physics of Solids I might be the first class on this list that actually could be considered a graduate-level class for undergraduates, also because the TAs for that class have said that it is basically a perfect substitute for the graduate class 8.511 — Theory of Solids I, allowing people who did well in 8.231 to take the graduate class 8.512 & mdash; Theory of Solids II immediately after that. 8.231 emphasized that it is not a survey course but intends to go deep into the physics of solids. I would say that it in fact did both: it was both fairly broad and incredibly deep. Even though the only prerequisite is 8.044 — Statistical Physics I with the corequisite being 8.05, 8.231 really requires intimate familiarity with the material of 8.06 — Quantum Physics III, which is what I am taking this semester. 8.06 introduces in fairly simple terms things like the free electron gas (which is also a review from 8.044), the tight-binding model, electrons in an electromagnetic field, the de Haas-van Alphen effect, and the integer quantum Hall effect, and it will probably talk about perturbation theory and the nearly-free electron gas. 8.231 requires a good level of comfort with these topics, as it goes into much more depth with all of these, as well as the basic descriptions of crystals and lattices, reciprocal space and diffraction, intermolecular forces, phonons, band theory, semiconductor theory and doping, a little bit of the fractional quantum Hall effect (which is much more complicated than its integer counterpart), a little bit of topological insulator theory, and a little demonstration on superfluidity and superconductivity.

14.04 &; Intermediate Microeconomic Theory is the other class I can confidently say is much closer to a graduate class than an undergraduate class, because I talked to the professor yesterday and he said exactly this. He said that typical undergraduate intermediate microeconomic theory classes are more like 14.03 &; Microeconomic Theory and Public Policy (which I am taking now), where the constrained optimization problems are fairly mechanical, and there may be discussion on the side of applications to real-world problems. By contrast, 14.04 last semester focused on the fundamentals of abstract choice theory with a lot more elegant mathematical formalism, the application of those first principles to derive all of consumer and producer choice theories, partial and general equilibrium, risky choice theory, subjective risky choice theory and its connections to Arrow-Debreu securities and general equilibrium, oligopoly and game theory, asymmetric information, and other welfare problems. The professor was saying that by contrast to a typical such class elsewhere, 14.04 here is much closer to a graduate microeconomic theory/decision theory class, and the professor wanted to achieve that level of abstract conceptualization while not going too far for an undergraduate audience.

At this point, I'm hoping that the experiences from last semester pay off this semester. It looks like that has been working so far!

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More on My Photonic Crystal UROP

In my post at the end of the summer, I talked a bit about what I actually did in that UROP. Upon rereading it, I have come to realize that it is a little jumbled and technical. I'd like to basically rephrase it in less technical terms, along with providing more context on what I did in the 2011 fall semester. Follow the jump to see more.

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Sixth Semester at College

Today is the first day of my sixth semester at college. I'll be taking 8.06 — Quantum Physics III, 8.14 — Experimental Physics II (also known colloquially as "J-Lab"), and 14.03 — Microeconomic Theory & Public Policy. I feel like taking three classes apart from J-Lab was too much last semester, so taking two this semester should make my schedule feel a lot more sane and manageable. Plus, now I have a handle on what J-Lab expects, so striving to meet that should be easier now. Finally, I did this because my UROP sort of fell to the wayside last semester, and I don't want that to happen this semester, so now I should be able to spend more time on both classes and that. Hopefully this semester will be a good one; good luck to all my fellow classmates out there!

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Featured Comments: Week of 2012 December 16

There was one post that got a comment this past week, so I am reposting that one.

Done with 5th Semester!

Reader Mechatotoro said, "Good work, my friend! It's great to hear you also made it through this intense year. Enjoy your free time--you earned it!"

Thanks to him for that comment during the past week. This coming week, I will be spending time with family out of town, so I don't anticipate posting much until after new year's day. Anyway, if you like what I write, please continue subscribing and commenting! Also, happy past-doomsday, happy holidays, and happy new year!

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Done with 5th Semester!

Wow. This semester was longer and far more difficult than any previous one here. Most of that is courtesy 8.13, though 8.231 and 14.04 were certainly contributing factors. Final exams were also fairly challenging as well this time. My only regret is that my UROP somewhat fell by the wayside as a consequence. I really enjoyed learning what I did in my classes, and the experiences I gained were immensely rewarding in the end, but I am so glad that I am done with it now. Right now, I'm just focusing on going home in a few hours and spending quality winter break time with family and friends. I will be back over IAP to continue my UROP. After that, in the spring semester, I intend to take fewer classes, because I realize that I may have bitten off a little more than I could chew this semester. Anyway, happy holidays everyone!

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Fifth Semester at College

Well, it has indeed happened. I am now a junior! Wait, what? When did this happen all of a sudden?
Classes start tomorrow, and this semester I'm taking 8.05 (Quantum Physics II), 8.13 (Experimental Physics I, also known as "J-Lab"), 8.231 (Physics of Solids), and 14.04 (Intermediate Microeconomic Theory); in addition, I am continuing my UROP from the summer. I'm most scared about J-Lab, because I've seen other friends take it in the past and I've seen how they have had essentially no time to do anything else (often even to the detriment of other classwork). Well, I'll see how it goes; while 4 classes and a UROP will be quite a time-crunch, I think I'll make it through OK. That said, this blog will probably see many fewer posts over the course of the semester. I guess I'll wait and see how that goes too.

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Done with 4th Semester!

Oh my goodness. I am done with half of my undergraduate career at MIT. This is crazy!
This past semester was even more crazy than the one before that. The great thing was that my classes this semester were way more interesting on the whole and will be far more useful especially towards the UROP that I will be doing over the summer.
For now, though, I'm not thinking much about my UROP. I'm thinking about what I'll do to relax and unwind at home. And by the way, one of the things I had originally intended to do was write a few more reviews, but because I stupidly forgot my USB flash drives in my dormitory room, that will not be happening until I get back to campus. Oh well. I'll find other stuff to do too!

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Fourth Semester at College

Yesterday my fourth semester here started. This semester, I am taking 8.04 (Quantum Physics I), 8.044 (Statistical Physics I), 14.02 (Principles of Macroeconomics), and 18.06 (Linear Algebra). In addition, I am continuing my UROP (though my work will likely change soon) and doing some other work too.
It's going to be a busy semester, but given that I am now used to this kind of workload from last year, I think I will be able to manage it better. Plus, now that my classes start each day no earlier than 11am, I can get more sleep! Yay! That aside, it's going to be an exciting semester, though I can already feel the heat with problem sets and such.

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Done with 3rd Semester!

I'm finally done with my 3rd semester! Yay! Although this semester I was just taking the classes for my major/that I wanted to take, thanks to the combination of 4 classes (all of which have problem sets and exams), a UROP, and grading, this semester was way more grueling than any previous semester. Thankfully, I think I've done fine, so I feel like I would be better prepared to do the same (4 classes, a UROP, and grading) next semester.
But before I need to worry about next semester or even IAP, I get to go home for winter break! Woohoo!

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Third Semester at College

Today was the first day of my third semester at MIT! I was excited to start with the classes that I want to take (and am not just taking to meet some requirements). This semester I'm taking classes in wave mechanics, special relativity, thermodynamics, and microeconomics.
There are a couple new things I noticed. First, there seems to be a lot of restoration work. I wonder why, given that the sesquicentennial celebrations have come and gone. Second, I've noticed that a lot more on-campus Athena computers that previously used Microsoft Windows now use Ubuntu, which is cool. Related to that, the Ubuntu version used has been upgraded to version 11.04 "Natty Narwhal"; Classic GNOME as opposed to Unity is the default, though Unity is an option when logging in, as are TWM/Ratpoison, WindowMaker, and a few others.
I'm really excited for this semester not just because of the classes I'm taking, but also because I'm going to start a new research opportunity regarding solar cells. It's pretty cool stuff, and I'll probably write more about it a few weeks after I actually start.

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Done with 2nd Semester!

Today is my last day of my second semester at MIT, and that also marks the completion of my freshman year in college. Woohoo! I can finally relax for a few days. Finally.
Of course, that's only going to be for a few days, because next Monday I start my internship at NIST, and that'll be for 10-12 weeks. I'm excited about that too.
This semester was definitely harder than last semester, which is why I'm so much happier that I'm done with it now. Part of that is because the classes I took this semester were harder than the ones I took last semester. Part of that is because I enjoyed the classes last semester more than I did the classes this semester. And part of that is because of the pressure of grades; last semester was Pass/No Record, while this semester has been A/B/C/No Record.
If you're in school or college, how did you feel about this semester/academic term and/or academic year? Do you have any plans for the summer? Let me know in the comments below!

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Nearing the End of Second Semester

My second semester at MIT is nearing its close. I have turned in my last final problem sets of the semester (mostly — one remains to be seen), and I've finished all my exams, including the last exam (there is no exam for that class during the week of final exams) for my probability & statistics class. I've mentioned that class before, and since then, it's only gotten harder, so I'm glad to be done with it now.
I'm excited that I have less than two weeks until summer starts! This summer I'm interning at NIST again, so that'll be exciting.

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First Day of Second Semester

Well, today my second semester of college starts. Luckily, as I haven't had lecture for that class yet, one of my recitations has been canceled, and my PE class doesn't start until next week. What this means is that I don't need to go to campus until 1pm! Yay!
That said, it's snowing like crazy here; I can barely see outside my window. It's going to be tough getting to class in the afternoon; hopefully I can make it!

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Second Semester Starting Soon

Well, I had a nice, long winter break by virtue of the fact that this time I chose to stay home during MIT's winter session. That's come to an end, and I'll be heading back tomorrow.
I'm glad that I've been able to write as much stuff here as I did over the last month and a half. Unfortunately, that's probably going to end for a while, as classes start next Tuesday (and this semester will be a little more stressful than the last due to the introduction of grades (as opposed to pass/no record for first-semester freshmen)). I'll try to have something here at least once a week (it'll probably be a little more), but in any case, don't expect much more than that.
Thanks to all the readers who have read and commented on these posts and subscribed. Please do continue!

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Done with 1st Semester!

Yay! I'm done with my first semester here at MIT! Overall, final exams worked out pretty well.
I'm going back home either tomorrow or the day after that. When I do, I'll be able to spend more time with loved ones and more time relaxing (and writing here).
For those people in school/college, how did your term go?

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