Visit my Math for Economists class!

Here is a short video from tonight's Math for Economists class. Here the professor is working an example of an optimization problem with multi-variables and multiple constraints using Lagrange Multipliers. Most of the class is usually theoretical and derivations of theorems, with a few numerical examples. This is one of those cases.



Last week, I mentioned my professor's statement that many mathematicians believe in God or some higher power. Well, tonight as he scrolled up the chalkboard, we found writing from the prior class. This time several Old Testament books of the Bible were recorded: I Kings, Judges, etc. He then told us about a law in Tennessee where they have legislated that pi be equal to 3 (and not 3.14159..) because the Bible states in I Kings that it should be 3. Actually, I Kings 7:23 says the following: "Now he made the sea of cast metal ten cubits from brim to brim, circular in form, and its height was five cubits, and thirty cubits in circumference." So based on this verse it seems the circumference divided by the diameter is 30 / 10 = 3. The professor also referred to a law in Indiana where there was a law setting pi to be 22/7 based on their belief in the Bible. Out of curiosity, I did some searching on the web. This is what I found about the law:

It appears the Tennessee pi law is an urban legend which began as an April Fool's joke in 1998. As for the Indiana law he mentioned, a Pi Bill was proposed in 1897 but never passed. However, it does not appear to be religiously based at all. I couldn't find any evidence of it, anyway. It seems the law proposed either using 3.2 or 4 for pi, not 22/7.

One website I found defended the Bible in I Kings. It says that because pi is 3.14159 that since the circumference was really 30 cubits then the diameter mentioned in I Kings should have been 30/3.14159 = 9.54, not 10. That website claims that the circle's circumference was measured on the inside of the circle but its diameter was measured from the outside of the circle. It says that if the circle had a width of 0.23, the inner diameter would have been 9.54 but the outer diameter would have included the width on both sides, adding 0.46. This would result in an accurate measuremment in the outer diamenter of 10. "Evidence" for this is found in I Kings 7:26 - "It was a handbreadth thick." I'm not sure I buy this explanation though. My guess is that during that time measurements were not so exact plus they probably weren't trying for an exact figure but one that is rounded. Anyway, "pi laws", as far as I know, have never been passed in America. Stories stating so are just urban legends.

Visit my Applied Stats class!

While Democrats were anxiously watching returns and celebrating Northup's defeat and shocked at Shays' win tonight, I was in class at NYU. Interested in econometrics? Here is a short video of my class tonight. Here the professor is talking about a one-tailed test in hypothesis testing. If you want to learn more you can visit this UCLA website.

Game Theory Midterm Exam

Tonight I had a game theory midterm exam. Here are the first two questions (which were also the two easiest)...

1. "Competitive Bidding" Suppose two identical consulting firms (McKinsey & Boston Consulting Group) compete for the same client (Coca-Cola, Inc.) for which they propose to provide advisory services related to a possible merger. Each firm has an equal and constant marginal cost to provide the consulting services, c. Firms make competitive bids, simultaneously, to the client indicating the price at which they will provide the consulting work, b. The client will choose the lowest bid. If firms offer the same bid, assume they both expect to win the client with equal probability of 1/2 each. (a) Depict a strategic form game for this scenario. (b) Draw the best responses for both firms on one graph. (c) Identify all Nash equilibrium outcomes. (d) Now assume that firm one is more efficient than firm two so that if it wins the client, it will receive c1 < t="0,1,2,....">5, and
Q=q1+q2.
C1=1 and c2 = 3.

(a) Depict this industry in Extensive Form as a dynamic game. (b) Find a subgame perfect Nash equilibrium for this game. (c) In your equilibrium, which firm will exit the industry (produce no product) first? What is the logic behind this result?

Now suppose the firms face the same declining demand and have the same marginal cost c1 = c2 = 1, but each can only either produce a fixed quantity (firm 1's q=2, firm 2's q=1).

(d) Find a subgame perfect Nash equilibrium for this game. (e) In your equilibrium, which firm will exit the industry first? How does the result compare to that in (c) above?

Math & Religion

Tonight I had my Math for Economists course. It begins at 6:20pm each Wednesday evening. A sociology class meets in the classroom before we meet. Tonight, after the professor had filled up one board with mathematical formulas, the professor pulled down the sliding chalkboard to use the one underneath it. That board mentioned Jehovah, God, Elohim, priests, etc. Our professor said (paraphrased) "well maybe this does have something to do with economics.....actually, you know, a lot of mathematicians love math because it is so pure, so exact, and it is so beautiful....many mathematicians do believe in a higher power or God simply because math exists and it is so perfect." This quote was paraphrased but was very close to what he said. Despite being at a liberal northeastern university, I guess there are still teachers who break from the liberal mindset. I do not know for sure how my professor feels about religion, but I can tell that he is more conservative. From his discussions about economics, I do think he is more a follower of the Chicago school of thought rather than holding a purely Keynesian view. As far as what he said about God, I couldn't agree more. Mathematics is a truly amazing discipline, and I agree that it in itself proves the existence and reveals the glory of God.

Trick or Treat? Deluge!

Today is Halloween. I came home from class tonight to find neither a trick nor a treat. I found water pouring out of the ceiling in the hallway.



That's not good, because I live in the basement! Fortunately, my apartment was not that wet -- only the first foot inside the apartment by the door and the kitchen area. My napkins, paper plates, oatmeal, and towels were drenched in water. I called the landlord's maintenance guy and he came over right away. After searching for about 15 minutes and making several phone calls, he was able to get the water cut off. We also discovered the problem -- an upstairs toilet inside the Phobia Life Line had a leak:



My apartment does not really have any damage, but it is inconvenient to have the floor wet but no water in the pipes!

Halloween!

This afternoon, Washington Square Park on NYU's campus had games and candy for small children.



There was a big parade tonight on 6th Avenue and so the subway stop where I usually catch a B train home was completely packed with people:



Craziness! As I pushed towards the subway, it got more and more crowded! So frustrating - especially when I found that subway stop was shut down due to Halloween! So I slowly made my way over to Union Square to catch a Q train home.

Meanwhile, in Kentucky, my cousins children got all dressed up. Here's Luke (age 2.5) on his horse:



Here's Luke's younger brother John (about 5 months):



Here's Catherine (about 5 months):



Aren't they cute!

Return of the Hillbillies

Well, my grandparents and parents flew back home this afternoon. I took them out to JFK and waved goodbye as they went through security at about 2:30 pm. We've been busy up here! After church on Sunday, we ate lunch at the Peanut Butter Company where we had an Elvis.



Then we saw the campus of my university, New York University, where Will Smith is currently filming the movie "I am Legend."



Following that, we went out to look at Shea Stadium (where the Mets play) and Arthur Ashe Stadium (where the US Open is held). For dinner, we ate at a Pete's Italian restaurant underneath the Brooklyn Bridge with a nice view of the Manhattan skyline. On Monday (yesterday), we saw the Statue of Liberty and Ellis Island in the morning.



Then we took a bus from lower Manhattan past the World Trade Center site, Chinatown, Little Italy, Union Square and midtown. Along the way, Grandma made a friend on the bus. After taking lots of photos from the top of the Empire State Building...



...we swung by Macy's and then headed back to Brooklyn. We ate supper at a nice restaurant near my apartment which brought each of us a ton of food - unlimited bread and appetizer, soup, salad, main course (meats and vegetables), and desert.



None of us made it through the main course -- some not even through the salad. This morning we took the Staten Island Ferry from the tip of lower Manhattan past the Statue of Liberty over to St. George on Staten Island. We then took some buses to reach Coney Island,



a beautiful sandy beach in southern Brooklyn which is about 3 miles from my apartment. While there, we stopped by Nathan's, famous for its hot dog eating contest each July 4. We did see a lot in four days! Just hope we didn't tire my grandparents out too much!


It does look like they were enjoying themselves on this subway, but I do realize climbing all those stairs are hard on the old folks! Aren't they cute? OK, now I have to study for my Game Theory midterm....

At the Tabernacle

Yesterday, my grandparents, parents, and I attended church at the Brooklyn Tabernacle.



We were able to worship God with about 2,000 others. The church was a blend of many races -- A black family sat to our right, a Korean family sat in front of us, and an Hispanic man sat behind us. During the service, a missionary from Haiti spoke as well as a group from Western Michigan's Teen Challenge. One of the speakers was from western Kentucky. Here is one of the songs they sang.



Here is the chorus: Holy, Holy, Lord God Almighty! Worthy is the Lamb who was slain! Highest praises, honor and glory... be unto your name! Be unto your name!

Brooklyn Hillbillies!

On Friday morning, my grandparents and parents flew up to the Big Apple to visit me. This was the first time that my grandparents, who have visited all 50 US states, had ever been to NY City. I picked them up at JFK and brought them over to a hotel near my apartment. Actually, the hotel is really just a house in a residential area which has converted its rooms into hotel rooms. On Friday, we visited Castle Clinton National Monument, Battery Park, the American Stock Exchange, the site of the World Trade Center 9/11 attack...



...Trinity Church and its cemetery with the graves of Robert Fulton & Alexander Hamilton (of VP Aaron Burr duel fame), Wall Street, the New York Stock Exchange, and Federal Hall, the first US capitol where Washington was inaugurated on April 30, 1789. Federal Hall contains the stone Washington stood and the Bible he put his hand on during the ceremony. On Saturday, we saw St. Patrick's Cathedral, 5th Avenue shopping district, Rockefeller Plaza, the NBC tour with a view of the studios where Dateline NBC, Nightly News with Brian Williams, and Saturday Night Live are filmed. For a few minutes, we actually got to see the SNL crew rehearse the show that aired tonight.



After leaving NBC, we ate Thai food at Bangkok House on Restaurant Row (46th St), and then visited Yankee Stadium and Times Square. I don't have a car here, so we've ridden a bus and lots of subways - the 3, B, D, E, M, Q, R - and done lots of walking! I've been working them pretty hard. My grandparents, are after all 82 and 79 years old! But they are holding up pretty well, depsite all the stairs in the subways that they aren't used to climbing. They'll be here until Tuesday -- so we'll have more to see!

Muslims not responsible for 9/11 attacks?

Over the past month, I've been very busy with doing homework and studying for midterms. But I have found time to attend a few events on campus - the College Republicans, the Diwali dinner put on by the Hindu Student Council, etc. Tonight I dropped in on a meeting after my class finished. A female student was reading poetry and sharing her opinions about her faith as a Muslim in a large room full of students, most of whom were also Muslim. During her speech, she mentioned, "I do not believe that Muslims were responsible for the 9/11/2001 attacks on the World Trade Center." Wait, what? My first reaction was to look around the room to measure the response and outrage at her comments. There was none. I was a little outraged. I consider it a well proven fact that the hijackers on the planes were Muslims. I stayed for a few more minutes to listen as she read a poem about her emotions and feelings about September 11th.

I needed to catch one of the last B trains so I left after her poem. To be fair, I have no idea how her speech concluded. Anyway, as I was riding home, I reflected on what she had said. I think many non-Muslim Americans might have been offended by the student's claim. However, I tried to put myself into her shoes. What if Christians had been blamed for the terrorist attacks? Or what about abortion clinic bombers who have all claimed to be Christian. What about the Holocaust? Hitler claimed to be a Christian. But many Christians today would claim that Hitler was not really a Christian - that he just claimed to be for political purposes and the version he practiced was really a Nazi-manipulation. And I'm sure that is how this girl at NYU feels. She takes great pride in her faith because, according to her, of its love and peace, and perhaps she feels that the 9/11 hijackers were not true Muslims in their faith and actions -- only using the affiliation for al quaeda's own purposes. I had never considered this possibility before. Perhaps this is the truth, or perhaps this girl is completely wrong. Regardless, I now have a deeper understanding of how American Muslims might feel about 9/11. This is one good reason to try to walk a mile in someone else's shoes before criticizing them. It helps you better understand where they are coming from. (The other reason is that if they are angry after you criticize them, at least they will be 1 mile away and barefoot!)

I am Legend

All of my classes at NYU are at night. For the past week, Washington Square, the large public square about which NYU is located, has been lit up and full of the crew filming Will Smith's new movie, "I am Legend." It has been interesting to see the crew working, despite the inconvenience it causes with some sidewalks being blocked off. And, no, I haven't met the fresh prince of Bel-Air yet.

Midterm Exam - Math for Economists!

Tonight I had a Midterm Exam in my Math for Economists class! I did ok but I probably did make a few stupid mistakes. Here are three of the questions from the exam:

#2) Use Matrix Algebra to solve the following model:
Y= C + I + G
C=a + b(Y-T
I=c +dY +eR
where Y=income, C=Consumption, I=Investment, G=Government Spending, T=Taxes, and R=the Interest Rate. Also a>0, 1>b>0, and 1>d>0. Treat Y, C, and I as endogenous and T,G, and R as exogenous variables. a,b,c,d, and e are simply exogenous coefficients. Use the implicit function theorem to determine the impact of a change in R on each of the endogenous variables.

#6) The value of a tree is given by the following expression V(t) = 2 ^ sqrt(t) where ti s time and r is the discount rate. The present value is V(t) = 2 ^ sqrt(t) * e ^ -rt. What is the optimal time to cut down the tree (the point at which the present value is maximized?

#7) Write Total Costs function as TC=TC(Q) and Average Costs as AC(Q)=TC(Q)/Q, and use calculus to demonstrate that the Marginal Cost Curve intersects the Average Cost Curve at the minimum point of the Average Cost Curve.

Tax Madness in the Big Apple

Since I was living in China last April 15 when taxes are required to be filed, I got a six month extension on paying my taxes. Because October 15 was a Sunday, the tax deadline was Monday, October 16. And, of course, as a procrastinator, I waited until the last minute! There were some headaches in figuring it all out. I own some funds which invest in Sweden (EWD), Germany (EWG), and Japan (EWJ). These funds all paid taxes in foreign countries, and as a result I can get a discount off my taxes in America. But the process is more complicated than it should be and was more difficult this year because I had lived in China during 2005. I did report all of my income earned in China and also had to report the apartment I lived in at TFSU as indirect income. OK, so how much is that worth? It's really subjective, but I reported it at 1200 RMB (US$150) per month or $1,800 for the year. Fortunately, for tax purposes, in 2005 I only spent 16 days in the USA (August 4-August 19). This qualified me to get the Foreign Earned Income Exclusion.

Finally, I finished my taxes, but since it was after 5 PM, I only knew of one post office in New York City that would still be open in order to get the postmark of 10/16. I figured the later I went the less busy the post office would be. So I took my taxes to the 8th Avenue at 31st Street post office in Manahattan at 10:30 PM. I was shocked to find the place was packed full of people holding envelopes in their hands with the words "Internal Revenue Service" on them! I guess when you consider that few people e-file in New York and that this is the main 24 hour post office in the largest city in America, it shouldn't have been such a shock. Anyway, it seems you can't just mail your package and leave if you want the postmark after 7 PM. We all had to stand in a long line and get postmarked one at a time -- and at a fee of 95 cents per package. I had to wait about thirty minutes to get my postmark.

Nick & Laura's Wedding

I just got back from a wedding in Louisville, Kentucky, where my cousin Laura just got married. It was the first time I had ever met her husband Nick. I had a good time in Kentucky with my family. I flew down on Friday and back home today. Here are some photos:

My mom has 36 more photos of the wedding here online.

Deja Vu?

Quick quiz: It's the 11th of the month. On a warm autumn day, people panic as a plane crashes into a tall building in New York City. What day is it? 9/11/2001? That would work, but so would TODAY! Yes, today NY Yankees pitcher Cory Lidle gave the whole city a big scare when he flew his small plane into a luxury apartment building, killing himself and another passenger. Fortunately, no one else died.

The scary thing is it was so "easy" for him to jump in an airplane in New Jersey and fly over Manhattan. What would prevent terrorists from doing the same thing? In a response, figher aircraft were put into the air above several major US cities. The quick response is good, but what are we doing to stop the first plane from hitting?

Econometrics Midterm

Well, tonight I had my first midterm exam at New York University. It was in Econometrics and Applied Statistics. The exam wasn't too bad, but I know I missed a 1-point question about moment-generating functions. It was easier than I had expected. The test had 16 questions worth 1 point each and then 12 questions worth 7 points each. Here is the easiest of the 7 point questions:

You will draw balls without replacement out of a container containing 3 blue and 5 red balls. What is the probability of drawing a red ball on the third draw?

Zhong Qiu Jie Kuai Le!

Today is the Mid-Autumn Festival (Zhong Qiu Jie in Chinese). The date is based on the lunar calendar (8th month, 15th day), and it also known as the Moon festival or the Lantern festival in other Asian nations. In China, we ate lots of mooncakes. I've seen a few here in New York. We do, after all, have almost 400,000 people of Chinese ancestry living here!

I have a mideterm in my statistics class on Tuesday. I went to ask questions of the teaching assistant this afternoon. She told me she is a 5th year Ph.D. student from Shenyang. She almost fell over when I told her I was familiar with the capital of Liaoning province and the big Mao statue there. Anyway, she had to leave early for a Mid Autumn Festival party. Afterwards, I went over to look for free food on campus! I did discover an all-Korean party celebrating Ch'usǒk (the Korean name for Mid-Autumn festival), but I didn't go. Anyway, for the first time since 2003, I didn't eat any mooncakes on Mid Autumn day.

Chaos at Columbia

Last Tuesday, I received an email from the NYU College Repulicans that invited us to go to a speech at Columbia:

"3. Columbia has invited us to the event below. There will be a huge
protest so it would be nice to have a strong showing. E-mail me your name
by 9am tomorrow if you want to go.
Columbia students host The Minutemen and founder, Jim Gilchrist, for
their pre-election forum: “Defending America’s Borders”"

I didn't go, and it seems I missed a national event! If you haven't heard, protesters (supposedly from a socialist organization) crashed the speech and knocked over the guest speaker. You can read about the event at FoxNews.



I'm not sure what I think of the Minuteman Project. Honestly, I didn't read the email from the NYU CRs until after the event took place. So perhaps the chaos was good for them to get publicity. Still, shouldn't they be allowed to express their views? What happened to free speech? I never heard of the Minutemen until after this incident. Apparently, they self-patrol the Mexican border with guns. I'm not sure if I agree with that either though.

New York really is an interesting place to live!

Matzah!

As an evangelical Christian from the South, moving to Brooklyn has given me another opportunity to better understand another religious group. I live in a predominantly orthodox Jewish neighborhood in Brooklyn and encounter Jews everyday here. I have no problems with that, as they are friendly. I've encountered different religious groups everywhere I've previously lived - evangelical Protestants in Kentucky (my home state), Catholics in the Midwest, atheists in Silicon Valley, & Buddhists in China. But I don't think I've ever been so shocked before. Not that Jews here do anything shocking -- I'm shocked that I was so uneducated and unaware of their customs. We recently celebrated Yom Kippur here. That's not a big holiday in Kentucky or China, but, in my neighborhood, everything was shut down. When I walked outside to take the subway to class it was like living in a ghost town. The grocery store, the convenience store -- almost all businesses were closed. In Manhattan, the place I usually buy my dinner was open but had no food for sale. Anyway, this week, I searched the Internet and came across the following funny Matzah rap song.



No, I haven't seen anyone rapping in the neighborhood - but I can appreciate and understand some of the things in the song more now after living here. Just so you know, Matzah is unleavened bread eaten during Passover.

Brooklyn Bridge to Midwood

Today I rode the subway up the Brooklyn Bridge and then walked back to my apartment in Midwood, stopping to take photos along the way. Unfortunately my battery ran out of power before I made it home. Below are a few of the photos I took.


This is the famous Brooklyn Bridge, with part of the the Manhattan skyline in the distance.



This is "Kennedy Fried Chicken" which uses red and white in its logo. There are many around the New York City area. Kentucky Fried Chicken claims it is an intellectual property rights violation.



After seeing this ice cream cooler, I was homesick for China!



Here is a building with interesting archictecure near the Dekalb Avenue stop.



The Brooklyn Academy of Music.



This street food vendor also reminded me of China, until I saw his prices!



Pizza by the slice! There are so many stores in the NYC area that sell pizza by the slice for anywhere between $1.75 and $3 per slice.




I also got a few photos of a group of protestors yelling for the US and Israel to leave all Arab lands immediately. The group was yelling many different slogans as they passed.



The protestors had their own protestor! Following behind them, a man held this sign very quietly as he marched in the rear of their group.