To maintain the current social security system in Japan, whose spending is rapidly increasing year after year due to population aging (to secure stable financial resources), the consumption tax rate was raised from 5 to 8 percent in April 2014. Then increased revenue on the consumption tax is supposed to be (in national portions) used for the four social security expenses (such as pension, medical care, long-term care, and measures to deal with the falling birthrate).
Nevertheless, since it was not discussed in the process of its decision-making whether or not most markets’ efficiency may be impaired by the tax hike, an introduction of reduced-premium tax rate, which has been adopted in other countries with even higher consumption tax rates than in Japan for them to provide people with free education and health care, was postponed in Japan. Besides, since the well known ‘reciprocal elasticity rule’ for such taxation, that is, the “infinitesimal ・・・ tax ad valorem on each commodity should be proportional to the sum of the reciprocals of its supply and demand elasticities” as stated in Ramsey (1927, p.56) has been believed, it did not seem to be thoroughly discussed on how to build an optimal tax system in Japan.
So in this paper we shed light on some shortcomings hidden in the model of tax ad valorem stemmed from Ramsey (1927), especially on a tax base. Moreover, we theoretically reconstructed an optimal taxation model by using a new ad valorem tax rate based on the price of pre-tax as well as all amount of its tax paid by the consumers only so as to derive a few of new rules on tax ad valorem such as a consumption tax different from the Ramsey’s tax rule of ‘reciprocal elasticity rule.’ In addition to those new rules for marginal sacrifice corresponding to our total surplus, we specifically calculate a closed-form solution, which no one has yet provided in the literature. And furthermore, it may be worth repeatedly noticing not only that if an optimal ad valorem tax rate for each market is uniform, then its market’s efficiency will be impaired but also that an optimal amount of tax revenue for every market, which is collected by our optimal ad valorem tax rate, say α, can be calculated as the closed-form solution given a total amount of the tax revenue R.
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