An Empirical Study of City Sizes

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We construct our own metropolitan data set to estimate the magnitudes of agglomeration economies for Japanese cities. In the estimation of aggregate production functions our major findings are as follows.(1) Agglomeration economies are small for small cities but fairly large for cities with population larger than 200,000. Cities with population between 200,000 and 400,000 have especially large agglomeration economies : doubling the size of a city increases productivity by about 25% in the Cobb-Douglas production function case. The productivity increase is about 7% for cities with more than 400,000 residents and about 1% for cities with less than 200,000 residents.(2) In our cross-section estimation of a metropolitan production function, the coefficient for social overhead capital is either statistically insignificant or negative. We therefore omit the variable production function. We have also estimated a modified Cobb-Douglas form in which the agglomeration effect interacts with social overhead capital in a highly nonlinear manner. Agglomeration effects are substantially smaller in this case than in the simple Cobb-Douglas case.Using the estimates for agglomeration economies, we have tested if the Henry George Theorem for optimal city size is satisfied. We found that the total land values are very high compared with the total Pigouvian subsidies in all cities, but the ratio for Tokyo is slightly below the average for 17 largest cities in Japan. Thus, there is no evidence supporting the hypothesis that Tokyo is too large. Note however that this comparison is made in terms of ratios. Because Tokyo is much larger than other cities, the absolute difference between the differential urban rent and the Pigouvian subsidy could be extremely large.