Thursday, February 14, 2008

Do flowers have a Nash equilibrium?

My wife recently bought me flowers for Valentine’s Day. When I thanked her for them, she cheekily asked me: “How do you know they’re from me?” Since I am not currently having an affair, the odds of them coming from anyone other than Marisa were low. However, suppose I was having an affair and I received flowers from an anonymous admirer. Should I thank my wife assuming it was her? Game theory may shed some light on the subject. The table of results is as follows:

Flowers from Thanks Result
Wife Yes Status Quo
Wife No You seem like an impolite bastard; no sex for a week
Mistress Yes Wife assumes you are cheating. Hell hath no fury like it.
Mistress No Status Quo

In more compact table form, this gives as values:
Yes No
Wife 0 -100
Mistress -9999 0

From this table, two things are clear: if you are having an affair, receiving flowers is a losing proposition, with little upside and significant downside. Secondly, if you are having an affair and receive flowers, shut up about them. You'll spend an evening on the couch instead of a year in divorce court.

Sunday, February 10, 2008

Too many dimensions

I started reading The Elegant Universe today, a book about string theory and its 10, 11 or 24 dimensions. I then read Marry Him!, an interesting article that discusses how to select a male life companion, which comments on a different set of dimensions. One particular line caught my attention: "Why should I settle for anyone less than my equal?"

If desirability is a universally objective measure (like normalized income or body mass index), applying this rule to both parties forces an exact desirability match to form a union. In reality desirability is highly subjective and quite different from one person to the other.

Say there are N different dimensions on which desirability is measured (in the range 0 to 1), and each individual assigns a different arbitrary weight to each, in such a way that all the sum of all the weights is 1. We have: Total desirability = Σ D[i] * W[i]. It is still easy to pair off individuals, as long as W[i] is chosen independently of the distribution if D[i] values.

Real life situations show that the weights are not independent from the distribution of desirability, as we generally assign a higher value to rare attributes. More importantly, we tend to highly value dimensions in which we excel, artificially boosting our own total score. This correlation creates huge matching problem, when applying the "equal score rule" stated above, since you actually need an exact match in each dimension for the match to be possible. Lets approximate this as my weights are proportional to my score in this dimension.

My desirability = Σ Dme[i] * (k*Dme[i])
Others' Desirability = Σ Dother[i] * (k*Dme[i])

From these equations it is obvious that a reciprocal match requires Dme[i] = Dother[i] for all dimensions. The fragmentation of the pair matching market can be measured as a function of the "number of events" in Dme[i].

Communism Promotes Protectionism

The taxation of capital and investment income creates all kinds of distortions in the markets. For example, shares are only taxed upon their sale, so investors will hold on to shares that have gained value just to delay their tax bill by another year. The reverse also occurs, selling off stocks that have lost value in order to get an immediate tax credit. Taxation is thus a contributing factor to the instability of the stock market.

For this reason and many others, I propose to eliminate corporate taxes and taxes on all investment income. This could be done implicitly, by removing contribution limits on RRSPs, while keeping the tax system otherwise intact. Or it could be done explicitly, making RRSP accounts only useful to even out spending over one's life time. In the following example, I will calculate the an individual's worth and tax contribution over a 10 year investment period separating labor from spending. I will assume that taxation is flat at 50%. Government bonds' real yield is 2% a year and average individual investments' real yield is 4% a year.

With investment taxation explicitly removed, labor is taxed as soon as it is earned. This gives:
Individual after 10 years = (Labor * (1 - 0.5)) * 1.04^10
Government after 10 years = (Labor * 0.5) * 1.02^10

With investment taxation eliminated by removing the cap on RRSP, labor is taxed only when it is spent. This gives:
Individual after 10 years = (Labor * 1.04^10) * (1 - 0.5)
Government after 10 years = (Labor * 1.04^10) * 0.5

Both approaches give the same amount of money to the individual, but the second approach gives a bit more money to the government, at no cost to the individual.

Investments by individuals are unlikely to be truly global. They have more knowledge of the value of local capital (shares of local companies), like shares of Bombardier Transport. When the local government needs to buy new subway railcars, they should rationally prefer the local supplier, since the government owns about half of the capital of that company through the RRSP of its citizens. Only the explicit elimination of investment income tax solves this problem.

Unfortunately, the taxation of labor combined with the loss of man hours resulting from the reallocation of human capital (that is recycling the workers at Bombardier Transport into some other field of work) also lead to the state effectively owning local capital. Education is a form of capital from which the state collects investment income tax as a subset of the tax on labor. One's time is quite easy to re-allocate anywhere in the economy, but one's education may not be easily used in another industry. To decouple the state from all forms of local capital, we would have to find a way to not tax the education part of worked time and to only tax the "universally re-allocatable talent" of workers. I don't really know where to start to achieve this distinction.

In practice, highly educated workers in rich countries (those that own the most human capital) are not very vulnerable to foreign competition. Lowly educated workers are very vulnerable, but the cost of reallocating their labor is small. Finally, workers in the middle (ex: technicians) have the most human capital to lose from foreign competition. Minimizing the regulatory overhead in reallocating mid range educated workers is the way to go.

Another solution would be to impose a head tax, effectively detaching the interests of the state from all forms of local capital, including human capital. Not so popular, though.

Sunday, February 3, 2008

From Quebec with Love


I injured myself in an unfortunate event involving my right leg and volleyball net post last Thursday. A bear attack would have produced a similar result: three equally spaced grooves spanning about 20 cm. On the bright side, it looked much more painful than it felt.

By the time I got home that night all stores were closed, so I had to make a bandage with whatever was at hand: duct tape played a central role! The next day I used Google to find out how badly injured I was, and what I had to buy at the pharmacy to make a decent bandage. After two days of treating myself, the deepest grove did not seem to be healing as quickly as the rest, so I decided to have it looked at on Sunday morning, going to the closest state sponsored clinic (CLSC).

Upon arrival, I was pleased to see an empty waiting room. Perhaps the treatment delays encountered in our public health system were not as bad as portrayed by the media. The front desk looked much like that of a bank in an unsafe neighborhood, with two tellers sitting behind a thick glass, which spanned from the top of the counter all the way up to the ceiling. In the waiting area sat one elderly women and one security guard behind a makeshift desk.

A sign was posted on the protective glass, which said: "Today, February 3rd, no doctors are available for unscheduled patients. A nurse is available, however." I walked up to the first teller, and she asked: "Does your family doctor work in this clinic?". Since I seldom need to see a doctor (my last doctor visit was 13 years ago), I answered no. She said: "Unless your family doctor works here, we will not be able treat you at any point in time. We can put you on the waiting list to get a family doctor assigned to you if you want." This was clearly not the solution to my immediate problem.

I explained that I had a badly bruised by right leg, and I wanted to know how to treat it. Perhaps I needed stitches, I said. I had not mentioned when this had happened, yet the secretary said: "If it has been more than 24 hours, stitches can no longer be applied." Later I learned this was inaccurate.

She then gave me a list of twelve other public clinics in the area which may have spare capacity. Unfortunately only one of them was open on Sundays. I then asked if there was a private clinic anywhere in the area. She answered, "Hey, I work in the public system. We don't give out this kind information."

Considering all options, I opted to see the nurse, given the other public clinic was a good hours' walk away, and given that it was the only other open facility, I figured it must not have had any spare capacity.

After waiting fifteen minutes, I met with the nurse, who was very courteous and helpful (though the front desk was not a hard act to follow). I explained to her how I had been taking care of the wound, she looked at it, said I was doing the right thing, that I did not need stitches but I did need a tetanus shot. She vaccinated me and sent me home. It took ten minutes.

Price controls create shortage, requiring glass windows and security guards. I'm starting to think that the security lobby is the force behind universal health care. I knew health care was not universal in Quebec, especially in delivering specialized surgery for the ailing, but I was flabbergasted to learn first hand that it is not universal even for minor interventions directed at healthy citizens. So whatever you do, never injure yourself on a Saturday evening!

Who are you protecting?

Anyone who has ever seen their brother, boyfriend or pals yelling at the television while the coach makes the worst decision possible can tell you that sports fans are mostly a male, testosterone-laden bunch. So it’s no surprise that any city that hosts a large sporting event such as the Olympic Games or World Cup sees a huge spike in the demand for sex. In anticipation of Vancouver’s hosting of the Olympic Games in 2010, a group of Vancouver prostitutes is proposing to open one or many legal brothels that would allow sex workers to operate in a safe environment free from the threat of violence. This has brought a chorus of condemnation from social workers, academics and social conservatives who object to “legitimizing” prostitution and see it as a form of slavery. So who’s right?

All economic activities (and paying for sex is a fundamental economic activity, which predates Adam Smith by some time) are influenced by the law of supply and demand. When an activity is made illegal, this affects the supply: providing the good or service becomes more costly, so the result is to lower the volume of trade while raising the price. This is one of the reasons why a 12-ounce beer is a dollar while cocaine is 100$ per gram. The other impact is to push the activity to the margins of society, which, combined with a high price, moves it into the realm of organized crime. When an activity is legal, organized crime usually leaves it alone. Nobody has smuggled vodka over the 49th parallel in a very long time.

Canada is in an awkward middle ground: prostitution, defined as selling sex services, is legal, but soliciting is not, which is why urban magazines are full of ads advertising escort agencies at 200$ per hour. More importantly, operating a “bawdy house”, known to speakers of English as a brothel, is also illegal. This largely prevents prostitutes from operating under safe conditions, since they are forced to meet their customers in locations not of their choosing. This also means that street prostitutes are committing a criminal offense any time they contact a potential customer, and this shady underworld they live in makes them easier targets for pimps.

Many people oppose prostitution because it leads to human trafficking: indeed, human trafficking is a deplorable crime that preys on the weak and should be prosecuted to the fullest. But this is throwing out the baby with the bathwater: in the same way that society condemns drunk driving while allowing general alcohol consumption, so too prostitution can be allowed without condoning those who would enslave women into the sex trade. If anything, making prostitution legal would reduce the profitability of human trafficking, though it’s hard to say if this would have a big impact on the number of victims.

The single biggest improvement that could be made to this situation would be to legalize brothels: it would improve the life and conditions of prostitutes immensely while probably reducing the incidence of street prostitution that bothers so many people. Prices would come down, which would benefit customers (yes, affordable and safe sex is service that many people would value immensely), safety would improve, the odds of contracting a sexually transmitted disease would decrease, and the government could even collect taxes from an industry that could finally exit the underground economy.

Ultimately, the strongest argument that can be made in favor of a legal brothel in Vancouver is that it is the prostitutes themselves who are proposing it. They are the best judges of what is in their interest, and the ivory tower complaints of those who claim that we are “dehumanizing” them by tolerating prostitution ring hollow. That it will probably please thousands of sports fans as well is just a bonus.