The tax revenue of 1, 727 municipalities, excluding 23 wards of Tokyo, amounted to \17. 7 trillion in FY2009. It was 92. 82% of the determined collection amount. The collection expenditure, \559 billion, was equivalent to 3. 16% of the revenue. Raising the tax revenue requires increasing the collection costs at the same time.
Abbreviate the indexes representing municipalities. Denote the determined collection amount as ft, the tax collection costs as tc, the revenue as tr, the arrear np is given as np=ft-tr. The function of tc to tc is expressed as ytc=tc, that of tr to tc as ytr=atc, where a means the slope tr/tc ── the relationship between tc and tr is contemporary supposed to be linear, but it will be adjusted by a sort of elasticity ──, and that of np to tc as ynp=ytc-atc. We can derive the formula tc*=ft(1+a) where ynp=ytc. Through the additional tax collection expenditure, the net revenue tr-tc would marginally increase where ynp>ytc and it would marginally decrease where ynp<ytc. If tc* is calculated at the point ynp=ytc, tr*=atc* and np*=ft-tr* are given. Thus we can get tc*, tr* and np* at the point ynp=ytc.
Suppose that the municipalities where ynp>ytc could add the tax collection expenditure to the point tc*, while the rest where ynp<ytc could reduce the costs to the point tc* keeping the present tr. As the calculated result, the net revenue tr*-tc* in the 786 cities would increase by \815 billion [\109 billion in the 941 towns] and the ratio of tax collection would rise to 97. 71% [98. 67% in the towns] with injecting of the additional collection expenditure by \20. 6 billion [\1. 9 billion in the towns].
The municipalities where ynp<ytc have fewer rooms for increasing the tax revenue. They have to consider making an alliance with other municipalities and the prefecture for the tax collection as well as endeavoring to reduce the costs.