Are There Returns to Scale in City Size?

A question central to the issue of optimal city size is whether scale economies exist in urban production. Over a third of all Americans who currently live in metropolitan areas live in one of the dozen largest. If it can be shown that these areas have a significant production advantage over the remaining ones, then welfare analysis could be applied to learn whether the extra output produced in these metropolitan areas outweighs the drawbacks of 'their greater disamenities. Economists have long recognized that wages and output per worker in large cities exceed those in smaller ones (Alonso, 1970; Fuchs, 1967; Hoch, 1972; and Izraeli, 1973). Workers have apparently known about this too, and as a result the size distribution of cities has been shifting in favor of the largest cities for much of the past century. But before one can pass welfare judgments about this trend it is necessary to have in hand an empirically-based theory of production and income in urban areas and of the role, if any, played by city size. Our main concern is to develop such a theory -to explain variation in worker incomes across a set of metropolitan areas. We do this for 58 areas using data for 1967. As a part of the study capital stock data were estimated for each of the areas. A marginal productivity theory of factor incomes is assumed and justified empirically. Two-thirds of the variation in gross metropolitan income per worker is explained. We found that the largest SMSAs-those with a population of two million or more had a return to factors 8% higher than the remaining SMSAs. The reason for this was not increasing returns to scale in production -we observed constant returns both across the entire sample and within several smaller city/larger city partitionings of the sample. Rather, there is an effect that seems to obtain for areas of more than two million -a change in the constant term causing a shift in the production function. The reason for this effect, apparently, is that economies exist in transport and communication in the very largest cities with the result that the benefits from agglomeration more than offset congestion costs. A marginal productivity theory of distribution in cities is developed briefly in the next section. This is followed by an empirical section which describes the data and relates the findings.