Archive for February, 2007

Definition of a Nash Equilibrium

Monday, February 26th, 2007

If we start shooting around there [the other gang's territory], nobody, and I mean you dig it, nobody gonna step on their turf. But we gotta be careful, ’cause they can shoot around here too and then we all fucked.

— Chicago Gang member

The NeoAth delusion

Monday, February 26th, 2007

Once again I find someone more articulate on this issue… albeit, it wasn’t hard.

I suppose it’s possible that a few ambivalent souls may pick up Dawkins’ book The God Delusion and see “the empirical light.” But just a few–and these folks were already predisposed for conversion. How do I know this? Because no self-respecting, god-fearing person would ever pick up a book that so openly condemned and ridiculed their belief system. Dawkins is so blatant in his scorn for religion, so unequivocal in denunciation of belief in all its forms, that he makes room for only two types of readers: the like-minded, and the masochistic.

Governors…

Sunday, February 25th, 2007

… we tend to elect governors.

Discounting asteroids, again

Sunday, February 25th, 2007

A while back, I wrote:

It seems to me that history has a direction. For some good things to happen other good things needed to happen first. The transistor had to be invented before the computer could be (well pretty much). I want good things to happen sooner so the other good things that depend on those first good things might happens sooner so that those things can lay the ground work for subsequent good things and, well, you get the picture…

(by the way, its exceedingly cool to quote myself)

and I still believe that. John Quiggin argues that we only have time preferences because we’re afraid to die. An excruciatingly perceptive commentator wrote:

I think John’s substantive point regarding time preferences is that marginal benefits are discounted over time at the individual level because individuals fear they may die before they can consume in the future, but this reasoning doesn’t follow for the everlasting society, thus society shouldn’t have time preferences.

But we should think carefully about what we mean buy ‘consume’. What is the thing that’s providing us the marginal benefits, today and tomorrow? What is the thing that we’d be giving up today in exchange for it in the future?

That I value the marginal benefit of eating today higher than my marginal benefit from eating tomorrow (i.e. I’ve discounted my marginal benefit) seems to follow from my fear of death in the next 24 hours. I might not get the chance to eat tomorrow.

That I value the marginal benefits of ‘consuming’ new knowledge today, on the other hand, doesn’t follow from my fear of death. Knowing something today means I can know more things tomorrow. I have a time preference for learning today versus tomorrow because my consumption of learning today determines my consumption of learning tomorrow.

(The assumption of time separability has precluded my example, but it shouldn’t preclude it from the discussion… We, society, do and should have time preferences independent of our individual fears of death.)

That bit about time separability needs explanation. In the models Quiggin uses, and most economist use, to get a grip on these ideas he assumes benefits in each period are conferred by consumption in that period and only in that period. So your happiness today only depends on your consumption today.

This is a great assumption for two reasons. First, it seems true for most of the things we think about when we think about consumption. It seems right that me eating an apply today has little bearing on the happiness I’ll get tomorrow from eating a banana.

Secondly and perhaps more importantly for us that hate algebra, this assumption greatly simplifies the models we have to deal with.

But there’s lots of “consumption” that we do that does depend on how much was consumed in the past. That I learned stuff today means I can learn even more stuff tomorrow. That the PC was invented in the 70’s meant the internet could flourish in the 90’s. That DNA was mapped in the 90’s means great genetic drugs will be invented in the next couple decades.

It might be weird to think of these things as consumption, but in our models that’s what they’d be.

Who doesn’t have a preference for these things to happen sooner? Does that preference have anything to do with our impending demise? I don’t think so.

In any case, to relate this to the discussion of discount rates… I think the discount rate might be a sort of fudge factor in the models were we assume time separability. If we were better at algebra, we’d directly model the positive effect consumption today has on consumption in the future. Our simple models, however, don’t do this and they undervalue consumption today.

Because we’re not so good at the algebra, we discount future consumption to make up for this modeling error.

Best discussion of the bordered Hessian ever!

Sunday, February 25th, 2007

Ever wanted to know why the positive semi-definiteness condition on the bordered Hessian characterizes the maximum in a constrained optimization problem?

Yeah, me too.

I guess I never made the connection that when I put the constraints, multiplied by the Lagrangians, in the objective function, I was treating the constrained problem as an unconstrained problem. Unconstrained problems have their second order conditions characterized by a positive semi-definite Hessian. The bordered Hessian is just the Hessian of the new problem. Va bene!

Not sure why I never made that connection before…

Why are Price Controls bad?

Saturday, February 24th, 2007

The price of a good reflects its relative scarcity and the relative preferences for that good. Why is water relatively cheaper than diamonds? Because its less scarce. Why are Hondas more expensive than Hyundais? Because people prefer the former.

Price controls control prices but that can’t hope to control those underlying factors. If you fix the price of diamonds low, it doesn’t make them less scarce. Making Hyundais more expensive (by reducing the price of Hondas, say) won’t make people like them.

What does the history of thousands of years of price controls tell us?

The first thing undermined or destroyed is self-rationing. When you pay the full price of going to a doctor, you go there when you have a broken leg but not when you have the sniffles or a minor skin rash. When the government makes health care “affordable,” you go there for sniffles and a minor skin rash.

The underlying reality has not changed, however. The doctor’s time is still limited, and the time that you take up with your sniffles or skin rash is time that somebody else with a broken leg — or perhaps cancer — has to wait to get an appointment.

Government-run health care systems in countries around the world have longer waits — sometimes months — to get medical attention. In other words, the rationing goes on, but more haphazardly, because prices do not force people to ration themselves according to the seriousness of their problem.

It is the same story when housing prices are controlled by government. Rent control has allowed some people to take up more housing space than they would if they had to pay the full price that reflects other people’s demand for housing.

The net result, whether in New York or San Francisco or elsewhere, is a lot of apartments with just one person living in each, and lots of families who cannot find a vacant place to move into. Housing shortages have resulted from rent control in cities around the world.

Housing shortages mean that some people are forced to live far from their jobs and commute, and some become homeless on the street. Homelessness tends to be greater in cities with rent control — New York and San Francisco again being classic examples.

Economists have long been saying that there is no free lunch but politicians get elected by promising free lunches. Controlling prices creates the illusion of free lunches.

Thomas Sowell

I hate Algebra too

Saturday, February 24th, 2007

I don’t care who you are…

Friday, February 23rd, 2007

…abortion is gross. And if you want this point driven home, listen to these Supreme Court oral arguments.

About minute 35 Chief Justice Roberts asks, “So we just say your hypothetical about extraction of the [fetus'] leg it seems to be would not be covered by the statute.” Once, Roberts slips and calls the fetus a “baby” and all of the participants describe the killing of the fetus as its “demise.”

Hearing such a cool discussion of these gruesome facets of partial abortions evokes two emotions: First, I felt outrage that there should be any question as to what is legal or not, what is right or wrong with the acts that are being described (e.g. “the doctor only uses disarticulation when it’s necessary to clear an obstruction because the continued extraction”). Second, I felt pride that we have a system were such facts can be discussed coolly and thoughtfully, where all parties should leave the proceedings feeling their side was heard and that a fair judgment will be handed down.

That said, the state’s rights discussion starting at about minute 18.5 was interesting in that the Court seems somewhat awkward discussing the topic. I got the distinct impression that the Justices all know that the original principles of state’s rights have been violated, but that they’re stuck with this strange interpretation of the Commerce Clause. They don’t allow cameras in the Supreme Court, but I imagine if they did we’d have seen a few bitten lips on the one side and a shared knowing glance or two on the other.

How you’re going to die…

Friday, February 23rd, 2007

If we were to elect a Senator as President, it would be…

Tuesday, February 20th, 2007

John McCain.

We’re not going to elect a Senator as President, though.

Before 1960, it was impossible for Americans to elect a Catholic. Before 2008, it was impossible for us to elect a Mormon.

Or maybe we should be practicing our New York accents?