California suffers from a housing paradox. Home prices keep rising, seemingly setting new records every month. But more and more people who want houses can't afford to buy one. The laws of economics suggest that this condition should not long endure.

With demand high, builders should be supplying new stock to serve it. And prices shouldn't be able to rise indefinitely, since by pricing out those at the bottom, the superheated market is eating away at the very demand that drives its dynamics.

But in many communities, builders cannot build more homes because the land has been used up.

Elsewhere, residents who don't want any more neighbors have erected legal barriers to new construction.

Yet the population keeps growing anyway. The resulting shortage had led to an affordability crisis.

The simplest fix would be to allow the construction of more housing. But with local politics often impeding that option, some have looked for other ways to help first-time homebuyers enter the market.

The most popular of these devices are known as "inclusionary zoning," local laws that require builders to set aside a portion of their developments for low-income buyers.

Cities and counties often adopt these rules because they believe they are a no-cost method of building housing for those who cannot otherwise afford to enter the market. But a new study of the concept suggests that it is neither free nor very effective.

The study, by San Jose State University professors Benjamin Powell and Edward Stringham, concludes that inclusionary zoning drives up the cost of housing, deprives government of tax revenue and might actually be making worse the problem it is intended to solve.

The research was funded in part by a grant from the housing industry, and was published by the Reason Foundation, a libertarian think tank that opposes government regulation. Despite the biases of its sponsors, though, the study's conclusions ring true.

The authors examined the results of inclusionary zoning in the San Francisco Bay Area, where 50 communities have such policies, the oldest dating back to 1973. They found that the policies are credited with producing a combined total of fewer than 7,000 housing units during that entire time. Yet the Association of Bay Area Governments estimates that the region needs more than 24,000 new affordable units every year.

Why hasn't more affordable housing been produced? One reason is that inclusionary zoning distorts the market when it forces landowners, homebuilders and homebuyers to subsidize low-income buyers.

Consider Mill Valley, in Marin County north of San Francisco. The difference between the average market price and the controlled price of a home there is about $750,000. Ten percent of new homes must be sold at the controlled price. So if a project had 10 units, and one was sold at the cut rate, the other nine would share the burden of that subsidy, effectively a tax of more than $80,000 per home.

If the buyers of market-rate houses are saddled with that cost, then prices will increase still further, pricing more people out of the market. If market forces preclude shifting the cost to new homebuyers, then developers or, more likely, landowners will eat the cost of the subsidy. That, in turn, makes housing a less attractive option for landowners, who will tend to put their land to other uses. This also forces prices up on the remaining stock of housing.

The study estimates that inclusionary zoning causes the price of new homes in the median Bay Area city to increase by $22,000 to $44,000. In the most expensive areas, including Cupertino, Los Altos, Palo Alto, Portola Valley and Tiburon, the increase is more than $100,000 per home, according to the report.

Any housing value not shifted in this way comes out of the hide of local government. By artificially reducing the value of some new homes, inclusionary zoning reduces the amount of property tax collected on those homes without reducing the cost of serving the residents.

Advocates of inclusionary zoning say the answer to many of these problems is the density bonus - allowing developers who build low-income housing to build more units than the existing zoning allows, to make up in volume what they have lost by giving the subsidy.

But many Bay Area housing policies don't offer such bonuses, and even where they do, they are not always effective. Some developers might conclude that higher densities will make their projects less marketable, and in some cases building more units requires using different building materials that can drive up costs. And in many neighborhoods, of course, higher densities draw opposition from existing residents who don't want the character of their community to change.

Even if you believe that inclusionary zoning comes at no cost to either the housing market or the treasury, it still appears that the policies are producing very little new housing.

Viewed under the best possible light, using inclusionary zoning to provide low-income housing is like fighting a forest fire with a garden hose. Under the harsh light this study shines on the policy, that hose might be spraying fuel, rather than water, on the fire.