Income taxation when markets are incomplete
117
It should be clear, by now, that our focus on “capital income taxes” is
made without loss of generality. Our analysis and all our results extend
substantially unchanged to either of the following alternative tax policies:
(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 (a), if the two components of individual income can be taxed inde-
pendently, no further instrument is required to achieve state-by-state fiscal
budget balance. On the contrary, if income is subject to a state-contingent
uniform tax a second policy variable is needed in each state to achieve
within states-budget balance; a variable that does not introduce any further
distortion is a state-contingent, anonymous, lump-sum transfer as the one
considered in Definition 1. This last observation applies to (b), where up to
J policy variables can be used in each state. Yet, now such an increase in
the number of tax variables implies the loss of anonymity (taxes/subsidies
become firm-type specific).21 If bonds are taxed, (b) accounts for the case in
which interest payments are tax deductible, as well as for the case in which
they are not.
Remark 2 (Asset span versus relative spot price effects). A marginal tax
reform, dtI ∈ RS, induces a first-order welfare effect on (the indirect utility
of) h that, in a multi-commodity GEI, is equivalent to:
(i) the second-order effect (pecuniary externality) produced via a change
of relative spot prices by a planner acting under the CPO criterion as in
Geanakoplos and Polemarchakis (1986) and Geanakoplos et al. (1990);
(ii) the second-order effect (pecuniary externality) produced by the taxation
of trades in assets in Citanna et al. (2001).
Indeed, in an exchange GEI, a marginal change in tax instruments has the
following key effect on the utility of h (see Equation 8 in Section 4):
duh = λhZhDtIMdtI
^ dt1I ∖
= (λhhzhh,... ,λhszhs) ... I Mdt1.
dtSI
In an exchange GEI with multiple commodities, a similar effect is obtained
through changes in relative spot prices: when dq = 0, dus = λsZsDζpdζ,
21
A fiscal policy like (b) has been analyzed in Tirelli (1999).