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MIT student blogger Caroline M. '18

The Mathematics of People by Caroline M. '18

Guest post on Economics

== Guest Post by Spencer Pantoja ’20 ==

When I was 14, I “knew” I wanted to be an interior designer. When I was 15, I decided I actually wanted to become an economist. That one actually stuck.

My parents come from two very different ways-of-thinking. My dad is a nerdy engineer with a masters degree, who loves psychology, studies/practices Buddhist spirtuality, and lives in his head. My mom is a former bartender and studied at “the Holiday Inn University”. She also has 25 fiction books checked out from the library and is probably trying to make a shelter for the local squirrels right now.

Over the years, I realized that my brain very much functions like my dad, but often is more drawn to things like my mom. I now love talking to people, understanding their emotions, thoughts, and desires. In middle school, I was quiet, and I would just observe how people were interacting with each other from afar, and I started to learn very purposefully how to on my own. I was always very reflective and sought out people who were different from me. I was always very constant in my emotions, so much so that it really had bothered me for a long time that my emotions didn’t seem to work like the people I cared about the most. I’m now a practicing Buddhist, and after meditations I try to use my clear head to focus on and bring out my emotions and try to understand them. And so I have to do something that spends my thoughts focused on people.

And so with this mathematician’s brain, I discovered Economics, or “the mathematics of people”. It just took a random idea when I was in 9th grade that happened to play out. I was sitting in my Algebra class, I was really bored, and somehow came up with the idea of learning calculus. I had never heard of anyone doing this before, didn’t really know that self-teaching was a thing, and entirely ignored the fact that there was a math class in between Algebra and Calculus. I can’t tell you how I came up with this idea or why I thought it would work, but it did and I got hooked on OCW. I had heard about economics from my older brother and started taking a ton of economics classes. I took classes like principles of microeconomics, macroeconomics, microeconomic policy, intermediate microeconomics, game theory, and advanced competitive strategy all online. And if it weren’t for OCW, there would’ve been nothing else on my application that could’ve gotten me into MIT.

Because of the OCW preparation, I got to jump right into the graduate program’s curriculum this year. I’m taking the Microeconomic Theory core, Industrial Organization I-II, and Game Theory (14.126). While one of my favorite things about economics is how varied it is, I do find myself drawn to the micro theory side. In particular, I love learning about systems of people, from how individuals make decisions, to how organizations make decisions, and all the way to how it translates into a market with game theoretic strategy structures. So when you go to Verdes at 2 am, I can talk about why Verdes is placed where it is with the times it’s open, how it chooses its prices, why you seem to face no costs in using your credit card to buy that Arizona tea, why that tea is pre-labeled with “99¢”, what type of person chooses to work at Verdes, and why you are up at 2am doing a PSET when you could’ve not procrastinated it during the day.

I’m currently writing a research paper I’m really excited about. This IAP, I traveled to Italy to do research at the University of Sannio about the productivity gap between the North and the South. The North of Italy is much more productive than the South of Italy, and a lot of the gap is still left unexplained in the econometric sense. When I talked to non-economists- travelers of Europe, local Italian students, strangers on public transportation- they almost all reference this cultural attitude difference. They always said something along the lines of “The people in the North are very rigid, strict, and precise while the people in the South are flexible, looser, and more relaxed”. They take longer lunches, have more days off, and of course are nicer about people being late. Living in the South, I noticed this very loose attitude towards time immediately. But I probably read 20 papers on the productivity gap in Italy alone, and not a single one even mentioned this idea.

Then I took a train to Naples. The train was delayed, and the local showing us around said “oh, this train is always delayed”. When I got on the train, I had my idea: “what if I used train delay data to capture this cultural attitude?”. How this works is that there is really only one train company in Italy, Trenitalia, so all the stations in Italy would have the same access to technology, business practices, with the same organizational structures. Then if I could use census data to account for other demand factors (like income, age, education, and family-status), and adjusting for some route factors (distance, weather, station crowdedness), what I’m left with is theoretically how much the consumer base values punctuality. If a consumer base really values punctuality, then the station will be more likely to take costly measures to make sure the trains are more punctual.

I also came up with a really cool game theory model for punctuality, which was an exercise in translating how people choose their punctuality behavior to mathematical/computational models so I could see what was happening on a larger scale. I model it as a coordination/supermodular game, where people want to be about as punctual as their peers. It’s dynamic, so I have to put in a time component. I also added a memory-loss and a long-term/short-term memory component. Also, in the cultural sense, I assume that people observe (roughly) strangers showing up to places on-time or late, and everyone shows up to places according to random distribution. People do statistical testing in these review/memory periods to catch changes in the populations behavior. And I wanted to see how easy a “punctuality contagion equilibrium shift” could occur in this setting, so I simulated this model within a population using Python. And what seemed to be slowing down this contagion process the most was the fact that for late people, they only get to see that early people arrived before them, but they see the arrival times of the people who arrive after them. So they naturally have more information about late people still being late than do about early people, which makes it so much harder for them to recognize a cultural change especially when the “status-quo” was tardiness.

So in this paper, I get to:

  • Learn about the history of Italy
  • Read about cultural dynamics, like the connection of the culture of Japan to there insanely efficient/punctual train system
  • Use behavior psychology to construct a theoretical math model
  • Model this process in Python
  • Construct a regression structure/econometric approach to analyze data in a statistical software package

I will never get bored doing economics research because I get to do a little bit of everything, and for the rest of my life I will be doing the mathematics of people.


*aside on the Arizona tea*: Basically it’s an attempt by them to reduce the double marginalization problem of vertical structures, which basically means that given that Arizona is selling their drinks “wholesale” for $x per drink, they want the retailers to sell it for as low price as possible, so that there is a higher quantity sold and such the retailer has to buy more from Arizona. And so that’s also why it’s the cheapest thing at Verdes. I’m guessing the reason other drinks don’t do it is for whatever reason Arizona has more bargaining power, such that there isn’t a competitive enough ice tea such that verdes would just start carrying a different brand of ice tea instead so they could mark it up more*


Spencer is a good friend and on the Undergraduate Economics Association. He described his experience with Economics so well and hit on so many reasons why I love it too (despite hating and dropping AP Econ in high school). So I hope you enjoyed his journey and feel free to reach out to him and the UEA at [email protected] or me at [email protected] if you have more questions about MIT Economics, the new 6-14 major, or any of the other 14 majors!