Using the Japanese prefectural data for 1952, I found statistically the relations which can be generally shown by the equations (1)-(4) (P, R, W, and T: regional density of population, of retailers, of wholesalers, and of traders (retailers and wholesalelers), greek letters: parameters) (Fig. 1-4).
And I discussed tentatively the reason why the relations are found, by the hypothesis shown by the equations (9), (14)-(16), (22), (24), (25) and (12) (P
*, R
* W
*, and T
* regional population, the regional population of retailers, of wholesalers, and of traders, A: the area of a region, Y: per capita income, G, C, G
W, and C
W: the quantity of the commodity bought by one consumer from retailers, sold by one retailer to consumers, bought by one retailer from wholesalers, and sold by one wholesaler to retailers, the other characters), and the fact that α_??_η.
Based on the values of the parameters of the equations (5)-(8), we can conclude that, in Japan, in the region where P or R is large, the ratio R/P, W/P, and T/P, or W/R are high. This tendency would be due to the regional difference of per capita income in Japan (see the equation (vii) in the note [3].).
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