New York City could be the best place in the world to educate children. The city’s vast size could support competition and specialization in schools, just as it does in hedge funds. The dense agglomeration of smart New Yorkers should speed innovation in education just as it speeds innovation in the media. The city has a particular edge in serving children — public transportation enables children to access city-wide schools without a parental chauffeur. Schools share so many characteristics with other service industries, that there is no reason why people shouldn’t come to Manhattan for the schools, just like they come for the food.

Yet throughout most of the post-war period, parents have fled the city because of its schools. The great advantage of a big urban market is that niche producers can cater to individual tastes and try out new ideas.With its one-sizefits-all product, the vast public school system eliminated that advantage. If the garment trade in New York had been taken over by one big public monopoly, Vogue would contain page after page of gray sack suits. Even worse, public schools ended up being controlled by a union that fought incentives and change and often put the needs of their workers ahead of the needs of children. Mayors, like Edward Koch, who took on the teachers union paid for their actions at the ballot box.

A weak public school system endangers not only its students but also the economic health of the city. Across Northern cities, no variable predicts success better than average years of education. Since dense places, like New York, have succeeded as a center of knowledge-based industries, knowledgeable workers are vital. Bad schools hurt the city in two ways — by training students poorly and by repelling educated parents who care more about their children’s schooling. The middle class exodus from the city owes much to the fact that New York City parents either had to accept mediocre education or had to pay twice, once in city taxes and again in private school tuition.

Today, Mayor Bloomberg and Joel Klein recognize the importance of schools for the city’s future. Mr. Klein’s experience leading the Justice Departments anti-trust division gave him the right mindset for challenging the public school monopoly.They have created a city-wide market giving parents more choice among public schools.They have supported an explosion of smaller schools within the public school system that allow both specialization and a kind of competition. They have even supported the rise of charter schools that offer competition outside the existing system.

But this week has produced stories which remind us the fight for better New York City schools is far from over. On July 14, the education department produced a report widely hailed as showing that public schools out-perform their private competitors. In fact, the raw data in the report showed higher test scores in the private schools. As my colleague Paul Peterson argued in a response to the education department report issued two weeks ago, the report was able to deliver its politically correct punch-line only through the use of highly debatable statistical techniques. Since Adam Smith, economists have thought that competition delivers better value to consumers than monopoly. The enthusiasm that big city parents show for more schooling options makes it clear that education is not exempt from this rule. It is a tribute to the political strength of the education establishment that they have been so effective in muddying the waters.

On August 7, the Sun reported that the push for new charter schools was being stymied by a state-level cap limiting entry into this market. The mayor and the governor both want more schools, but the legislature has yet to come on board. It is hard not to think that the electoral power of the unions creates some of this legislative recalcitrance. Limiting school options doesn’t matter that much in the suburbs, where parental homogeneity and low density means that one school may come close to fitting all. But attempts to limit school competition particularly hurt our great cities. Mayor Bloomberg and Chancellor Klein must be supported in their efforts, but also pushed further. The case for vouchers is strong.Tax credits for middle-income parents that use private schools would also reduce the incentive for them to leave the city. With enough political will, New York City schools can be transformed from a public sector monopoly to a world showcase for how entrepreneurship can educate the young.

Mr. Glaeser is the glimp professor of economics at Harvard, director of the Taubman Center for State and Local Government, and a senior fellow at the Manhattan Institute.