increase in health expenditures is financed by a non-distortionary tax in-
crease (i.e. a tax increase that is the same for everyone) or by an increase in
distortionary tax rates. The assumption that any change in the co-payment
is balanced by a change in the tax rate t that is the same for everyone is
therefore less restrictive than it may immediately seem.
From the reasoning above it follows that as we vary the size of the co-
payment p, the change in social welfare (as measured by (Il)) is independent
of whether the variation in p is matched by a change in t or some other tax
component in the tax system, as long as the tax system initially is optimally
designed. However, since a change in p normally will change all components
of an optimally designed tax system, the change in expected utility for any
particular person will be different from what we derived in Section 2. In
particular, equations (7) and (8) and Proposition l will no longer be valid.
The first-order condition (12) for the optimal p is valid also when all
components of the tax system are optimally set. However, as the income
term y is gross income minus all taxes other than the tax component t,
this income term will in this case depend on these other taxes as well as
on the distribution of gross income. When social preferences become more
equity oriented, it is reasonable to assume that the optimal tax system will
be changed, implying a change in y for any given level of gross income. The
effect of this change in the distribution of y is not taken into consideration
in our analysis in Section 4.
The case considered in Section 4.1 will not be affected by the assump-
tion that the tax system is optimally designed, since incomes in any case are
identical in this case. Proposition 2 thus remains valid. For the case consid-
ered in 4.1 on the other hand, the derivations and results will generally be
changed if the change in social preferences also changes the distribution of
y. The main result hover, that the optimal co-payment might increase as a
response to increased concern for equity, remains valid. To see this, consider
the case where the distortionary costs of a progressive element of the tax sys-
tem increase sharply once this progressive element reaches some threshold.
If we are at this threshold before preferences are changes, increased concern
for equity will only give a very small increase in this progressive element of
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