Can you beat the law of gravity?
Well of course you cannot beat the law of gravity (but it does make a catchy title)! That’s what makes physics different from economics; as many laws of economics sometimes don’t hold. One of my favorite examples I recall from high school is a so called “Giffen Good”( http://en.wikipedia.org/wiki/Giffen_good). A “Giffen Good” sees an increase in demand when the price rises (violating the law of demand).
I’ve just been house-hunting in Singapore and I believe I have found another economic law that is being violated. The number of houses and apartments built and entering the market is enormous (sometimes this city feels like one big construction area with new high-rise condo’s popping up throughout the city). So supply is quickly increasing and according to the law of supply and demand, prices should go down. But that is not happening, on the contrary, prices are still going up. So why is that?
My theory is that home-owners have a very high confidence in the real estate market (which by the way is already very high, comparable to New York City). Instead of fearing the increase in supply, it is actually further boosting their confidence. The city is building so many new condos; apparently those constructors and investors know about and plan for an ever increasing influx of people moving to Singapore. Combining that with the fast growing economy and the limited amount of land leads to home-owners asking a premium price and not minding if some nay’s lead to the property staying empty a little longer.
Any economist that wants to react? Hope to be able to claim such a product as a “Kloprogge good”!
Thanks,
Peter
Why a sample works
If you’re in a casino watching the roulette table which of these sequences is most likely: RED-RED-RED-RED-RED-RED-RED-RED-RED-RED or BLACK-RED-RED-BLACK-RED-BLACK-BLACK-BLACK-RED-RED?
As a mathematician/statistician I am sometimes asked why a sample works? If you have a population of 100 million, how come that taking at-random just 200 people will give me a pretty accurate indication of the 100 million?
To understand this best to think of the RED’s and BLACK’s in a casino. The answer to above question is that both sequences have the same probability (they are both just as likely or unlikely to occur). However, most people would say that the sequence with the random red’s and black’s is more likely and the reason is that such a sequence has many, many more “look-alikes”. Another sequence (and a look-alike) with again the same probability would be R-B-R-R-B-B-B-R-R-B. Notice that there is only one unique sequence (with no look-alikes) with only reds.
Now let’s say that we have a big bowl of balls, about 100 million balls of which half are red and half are black (but obviously we don’t know that the reds and blacks are split 50/50). If we take out 200 balls each individual sequence of red’s and black’s is just as likely to occur and as such there is a chance that we only grab 200 red balls, but the probability of this happening is extremely small (so small that if all of humanity was able to take 200 balls every second with no sleep it would still be extremely unlikely to ever see an occurrence of 200 in all of our lifetimes, even if we all lived for a million years).
The reason this is so unlikely is that there is only one way to grab 200 red balls and that is to grab red, and then red, and then red, etc 200 times. It is much more likely that we grab close to 100 red and 100 black balls as there are simply so incredibly more ways of doing this. We could start with one red, then a black, etc or we could start with three blacks, then the first red, etc.
So with even a sample that looks small compared to the total population the number of ways you could sample that will lead to the right conclusion (in this case that half of the balls are red and half are black) simply outnumbers the number of ways you could come to a wrong solution. And by the way, this story as you now might understand is independent of the number of balls in the big bowl; this could be 100 million or just 100 thousand it does not influence the size of the sample we need.
So finally, what do you do if you are in a casino and you see the sequence RED-RED-RED-RED-RED-RED, what should your next bet be? Of course red, the bloody thing is probably broken!
Thanks,
Peter