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to prove the existence of equilibria, and do not play any role in our welfare
analysis of tax reforms.
2.1.2. Government, income taxes, and fiscal budget rule We define a tax
policy by specifying a set of tax variables and a budgetary rule. Further,
as usual, we call instruments those policy variables that are independently
controlled by the central planner.
We consider a tax policy in which, at date 0, the planner announces a
system of ad valorem taxes (and/or subsidies, or allowances) on consumers’,
date 1, personal income. This system of taxes and allowances makes indi-
vidual taxation a non-linear function of income: different levels of state-
contingent personal income may be taxed/subsidized at different rates. As
we shall make clear as we go along, the type of taxation that produces in-
teresting welfare effects in our simplified setting is one that modifies the
state-contingent profile of the returns from portfolio holdings. For this rea-
son, hereafter, we shall focus on “capital income taxation”. State-contingent,
anonymous, lump-sum taxes/subsidies will only be introduced as a way of
achieving fiscal budget balance state-by-state: when capital income in state
s is taxed, its total revenue is redistributed lump-sum in the same state s .
The following alternative policy schemes, if introduced, would leave the
rest of the analysis and results substantially unchanged:
(a) a proportional, state-contingent, anonymous tax/subsidy system on in-
dividual total income (returns from portfolio holdings plus endowment
income);
(b) a proportional, state-contingent, asset (or sector) specific tax/subsidy
system on individual capital income.
In (b) we refer to the case in which bonds and equities can be taxed at
one or more different rates. Moreover, for bonds, (b) accounts for the case in
which interest payments are tax deductible, as well as for the case in which
they are not.
More formally, a portfolio θjh of a stock j ∈ J2 yields to h a before-tax
return θjh ysj in state s for all s inS. Similarly, a portfolio θjh of a bond j ∈ J1
yields to h, θjhRsj,ins for all s in S. Let Ts1 be an open bounded subset ofR
with typical element tS = -1, with T1 = ∏f=1 Ts1,2 and denote the set of
feasible state-contingent taxes (subsidies) by T = RS × T 1. We formalize
the following general fiscal budget rule.
2 An alternative way of defining of the tax domain is to assume that T 1 is the interior of
a unit (S - 1)-sphere. This would still be without loss of generality, since our analysis is
entirely local, around the zero vector of policy instruments.