When a sport or other game is played all over the world (chess for example, or soccer), it is natural that there should be international competition. The oddity of the Olympics is that they are presented as athletic competitions between nations, rather than between teams each of which presumably would have a permanent residence in one nation yet might recruit team members from other nations as well. Nations in the grip of nationalist emotion or wanting to advertise their power to the world (nations such as Hitler's Germany, which made the 1936 summer Olympics, held in Berlin, a major propaganda event; East Germany and other communist countries; and now China) invest heavily in training their Olympic athletes. China is estimated to have spent as much as half a billion dollars to train their athletes for the Olympic games now underway in Beijing. The heavy investments that nations that regard Olympic competition as a propaganda opportunity in turn spur other nations to invest heavily in training their own Olympic athletes.
The nationalistic fervor and great-power aspirations that Olympic competition stimulates seem to me a negative externality. In addition, some unknown but doubtless large fraction of the expenditures on training athletes have no social product, but are in the nature of "arms race" expenditures. If one nation spends very heavily on training its Olympic athletes, other nations, if they want to win a respectable number of medals, have to spend heavily as well. The expenditures are offsetting to the extent that the objective of competition is to win rather than to produce an intrinsically better performance. Economic competition produces better products at lower quality-adjusted prices, and this effect dominates the costs of competition in duplication of facilities and offsetting advertising. The balance in athletic competition is different, because the main product (as in war) is winning, and it makes little difference to the consumer whether the winner ran a mile in 3.05 minutes or in 3.01 minutes. Moreover, Olympic competition is inherently lopsided since, as Becker explains, success is largely determined by a nation's population, per capita income, and (in the winter Olympics) climate. Why should Americans feel good if an American team beats a team from Costa Rica?
Since the United States is acknowledged to be the world's most powerful nation, it has nothing to prove by doing well in the Olympics, and so we are sensible not to allot any tax revenues to financing the training of our Olympic athletes. Doubtless we would were it not for the private donations that generously support the United States Olympic Committee. Since other countries do not have the same tradition of charitable giving as the United States, and so rely on tax revenues to finance activities that in the United States are financed by private charity, our charitable support of Olympic competition actually places pressure on other nations to support their Olympic teams out of tax revenues.
Becker raises an interesting point by asking whether Olympic competition creates a positive externality that might warrant public subsidy, though he recommends against subsidization. The Olympic games are immensely popular, but, given advertising-supported television, it is apparently impossible to finance them (and in particular the training of the Olympic athletes) out of television-advertising revenues. There are, however, as he notes, other (private) sources of revenue of Olympic participants, such as endorsements by champion athletes. Moreover, were there no public subsidies of Olympic competition, this would not doom the Olympic games; it would just reduce the amount of training that Olympic athletes received (the arms-race effect). This would reduce the number of new world records set, and marginally reduce the quality of play and hence the pleasure that the audience for the Olympic games derives, but would actually tend to sharpen Olympic competition by reducing the effect of a nation's per capita income on its Olympic prospects.