The subject of sprawl as it relates to jurisdictional fragmentation begs for analysis in the tradition of industrial organization. There are obvious advantages to the comparison between general purpose local governments in a metropolitan area and firms in an industry. At least some dangers are equally apparent.
Sprawl means excessive suburbanization. Excessive means more than can be utility enhancing. Of course, how much suburbanization is utility enhancing depends on context. Suburbanization, nearly universal during the last fifty or sixty years, has been evident in the United States for more than a century. Among the best-studied causes of suburbanization are rising incomes and falling commuting costs. Beyond doubt, both of these factors have been important, but neither relates directly to local government actions. Suburbanization has been both inevitable and mostly utility enhancing, but it can also be excessive.
My measure of sprawl is conceptually simple. Zoning, as it applies to housing, lowers the density-distance function, increasing the radius of the urban area for a fixed population. Thus on average, workers must commute farther to and from work than if there were no controls. Residents may be willing to commute farther as the price of controlled lower density, but no worker is willing to commute farther with controls than he or she would need to commute by moving far enough out to obtain the same density without controls. If the average commuting distance increases more than would be needed to achieve the same density without controls, controls impair welfare.
My measure of sprawl, which is in the context of fixed and centralized locations of jobs, is dramatically contrary to fact. There are many studies of employment suburbanization, but none that I am aware of places employment and population suburbanization in a model that carefully analyzes their interaction. I would welcome a study of this topic. Employment and population suburbanization not only influence each other, but are also likely to be influenced by other similar variables. Transportation improvements seem to be obvious candidates, but jurisdictional fragmentation may be another.