Before proceeding to the SMCF calculation, we briefly justify the adoption of the welfare criterion (Equation 9) in the M-R model.
We turn to calculating the SMCF for increasing redistribution in the M-R economy.
Since the SMCF is defined in terms of raising an additional dollar of tax revenue from the economy, we divide d W/da in Equation (11) by n.
a]), as evaluated according to a utilitarian social welfare function, and the second RHS term is the associated SMCF from increasing the tax rate t ([SMCF.
In appearance, the normalized SMCF, formula in Equation (15) differs substantially from that in Equation (16).
The above analysis suggests two possible ways of estimating the SMCF for increasing redistribution in practice.
By contrast, we utilize the political equilibrium characterized by M-R to study a different normative question: the SMCF on the basis of the plausible assumption that the existing tax system itself represents a political equilibrium.
When the tax system is assumed to be arbitrary, a common feature of previous SMCF studies with heterogenous consumers is that the SMCF formulas they derive are closely akin to our Equation (16).
Analogously, we would believe that our political economy approach to the SMCF is a useful research device; at least, it can complement the usual apolitical approach.
The basic reason why we can transform the SMCF formula from Equation (16) into Equation (15) is due to our exploitation of the trade-off at the margin between the distortionary cost of taxation and the redistributive benefit from taxation in political equilibrium.
The distributional weights of the SMCF are derived from a social welfare function that reflects the society's distributional preferences.