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M. Tirelli
with most of the GEI literature, our results are not driven by changes in rela-
tive spot prices (as, for example, in Geanakoplos and Polemarchakis (1986),
Geanakoplos et al. (1990), Cass and Citanna (1998), Citanna et al. (1998)).
Yet, relative price changes would certainly increase the level of complex-
ity of any policy analysis, by introducing an additional policy transmission
channel. Another potential source of complexity is the policy scheme. Here,
we have used a very simplified definition of constrained suboptimality, with
very strong restrictions on the type of policy interventions allowed to the
planner: interventions are anonymous; publicly announced when all mar-
kets are still open (i.e., they are also ex-post constrained efficient); fiscal
budget is required to balance in every date and state of the world (see Defi-
nition 1). All these assumptions, if changed, would increase the complexity
of equilibrium computations, and policy evaluations.
Remark 1 (Extending Theorem 1 to E - tI with tI = 0). Our main result
holds when the initial state is a regular equilibrium with a non-trivial tax
system, tI . Although we do not provide a complete argument in support of
our claim, the reader can check that this is true by adapting the proof of
Theorem 1 below.
3.2. Concluding comments
Our results contribute to highlighting the welfare properties of personal
income taxation in incomplete market economies. As pointed out in the
introduction, we focus on a particular aspect of state-contingent taxation,
namely, its ability to affect private risk-sharing opportunities through direct
asset span effects. A local marginal change of the tax system acts directly on
the asset span, changing (but not augmenting) consumers’ ability to redis-
tribute income across contingencies. Thus, even if the tax reforms consid-
ered do not reduce the degree of market incompleteness, they may modify
individual risk-sharing opportunities, allowing consumers to reallocate re-
sources in a direction that was initially financially unfeasible. When this
happens, we may say that the tax reform has social insurance effects.
Before going further, recall that the use of tax reforms entails a different
constrained optimality criterion with respect to the one traditionally used in
the GEI literature which we refer to as Diamond constrained efficiency (or
simply CPO; see Diamond (1967), Geanakoplos and Polemarchakis (1986),
and Geanakoplos et al. (1990)). Thus, to ease the interpretation of our re-
sults, a comparison of the welfare properties of equilibria under the two
constrained optimality criteria may help the reader. Moreover, since the defi-
nitions of the set of CPO allocations, and the welfare properties of equilibria,
are different in a pure exchange economy in comparison with a production
economy, we shall keep the two cases distinct. Again, this is possible since,