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.

Chinese Monetary Policy

On Friday, the People's Bank of China (PBOC), the equivalent of the Fed in the US, raised the bank deposit reserve ratio from 9 to 9.5%, increasing reserves at banks. This is the 3rd time this year China's central bank has performed this kind of monetary policy, and it will, in effect, decrease the amount of excess liquidity. Interest rates have also been hiked twice since April.

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.

The Economy, stupid!

In Bill Clinton's 1992 presidential campaign against former President Bush, James Carville put a sign up with 3 points on it, the second of which read "the economy, stupid". Well, finally finally the Republicans are going to shift focus from Iraq to the economy. I don't know why they haven't talked this up so far. The stock market is at an all time high, inflation is in check, unemployment is below 5%, and the economy continues to expand at a good pace. Of course, maybe political strategists believe that it is easier to get someone to vote out of fear of terrorists than due to economic numbers.

Speaking of reminding voters of terrorists, watch this new Republican ad:


Some Democrats are saying the GOP is just exploiting Osama for political purposes. They have a counter ad:



The election must be close!

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.

Peace to Yunus

Bangladeshi microcredit pioneer Muhammad Yunus and his Grameen Bank were awarded the Nobel Peace Prize on Friday for their work in advancing economic and social opportunities for the poor, particularly women. The economist and the bank he founded will share the prize. They were cited for their efforts to help "create economic and social development from below" in their home country by using innovative economic programs such as microcredit lending.

Grameen Bank has been instrumental in helping millions of poor Bangladeshis, many of them women, improve their standard of living by letting them borrow small sums to start businesses. Loans go toward buying items such as cows to start a dairy, chickens for an egg business, or mobile phones to start businesses where villagers who have no access to phones pay a small fee to make calls.

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?

Columiba Prof wins Econ Nobel

Columbia University professor Edmund Phelps on Monday won the 2006 Nobel prize in economics for pioneering work on the relationship between employment and inflation, which has influenced central banks around the world. Phelps, 73, is the first solo winner of the $1.37 million prize since 1999.

During the 1960s, Phelps built on what is known as the Phillips Curve, which held that when unemployment fell, there was a one-time rise in the rate of inflation.

Phelps felt that view didn't take into account the fact that consumers and businesses operate with incomplete information. He theorized that inflation depends on unemployment and expectations for future inflation.

As a consequence, the long-run rate of unemployment is not affected by inflation but only by the functioning of the labor market. Cutting interest rates or taxes to stimulate employment works temporarily, but can lead to higher inflation.

Further, policies that promote low inflation today will produce lower inflation expectations, aiding policymaking in the future. Phelps also looked at economic trade-offs, showing that deferring consumption in the short run to fund research, education and other business investment can improve economic conditions in the longer run.

Chinese Caution

Many people ooh and aah over the potential market power of China. 1.3 billion consumers. A cheap labor force in the millions. GDP growing steadily at about 10%. What's not to like? You hear reports about how America's day has come and gone and how China will soon overtake the USA.

Hold your horses. China has a good chance to become a major world power, that is true. But it won't happen as fast as many think. Poverty is widespread, most of its workforce is uneducated and unskilled, the legal system is showing promise but corruption is still widespread, and capital markets are young and untested.

Well, just this week we found out Malcolm Bricklin's Visionary Vehicles will be forced to delay the arrival of its Chinese produced Chery cars in the USA. He had been claiming a 2007 arrival date, but that has now been postponed to late '08 or early '09. Starting an automotive company is difficult, as it is a highly capital intensive industry. I seriously doubt the long term viability of Bricklin's cars. I do feel Chinese produced cars will be shipped to the US in the near future due to the cheap labor there, but I think established car companies such as GM, Toyota, and Volkswagen will most likely be the ones to be successful at this. The global automotive industry is already in bad shape. The market is mature, oil prices are rising, the industry has an excess of capacity, profits are dwindling. China will soon be an economic force to deal with, but its days as a fully developed nation are still far off in the future.

Boot Camp at NYU

Classes don't start until next week. So why am I at NYU now? Well, I'm attending an optional, free, "math boot camp" to review calculus, differentiation, integration, linear algebra, etc. The boot camp is meets 5 hours per day for 3 days. The two teachers leading the boot camp will be the two teachers who teach the two different sections of "Math for Economists" this fall. I thought one of the professors did a better job at explaining and was more logical in thought. After attending class today, I came home and switched sections!

This is Warren Weaver Hall, where the math boot camp is being held. Once the semester begins, however, I will not have any classes in this building.

This is the giant arch in Washington Square Park on NYU's campus.

Chinese Financial Markets

I may be in India but I can still write about China....

Last July China revalued the currency (from 8.28 to 8.11 to the US dollar) and now floating the currency against a basket of currencies (versus directly pegged to the dollar). This move increased the risk of foreign currency for many businesses operating in China. The People's Bank of China (PBC) is urging firms to hedge against foreign exchange risk. Also, this past week (on Feb 10), the first ever RMB interest rate swap transaction was completed. Finally, a new financial derivatives futures market is being established in Shanghai.