Concerns for Equity and the Optimal Co-Payments for Publicly Provided Health Care



However, since δ(v)u'(y t) is lower the higher is y, it follows from (13) that
the positive values dominate, i.e. that the first integral in (17) is positive.
Since the terms [
t'(p~)] and [1 + t'(p)] are both positive, it follows that Δ 0
in this case.

The case in which δ(v) < 0 for all who initially choose to be treated is
obviously rather restrictive. However, even if some of those who choose to
be treated get increased marginal welfare weights, the negative
δ-terms in
the second integral may dominate the positive
δ-terms, so that the second
integral remains negative. And even if so many of those treated get increased
marginal welfare weights that the second integral becomes positive, Δ may
still be positive since the first term in (17) is always positive. This leads to
the following proposition:

Proposition 3 Assume that the value of £ is the same for everyone, but
that income y varies among persons. Assume also that the initial optimal
co-payment is such that some persons choose treatment while others choose
not to be treated. In this case increased concern for equity increases the op-
timal co-payment provided a sufficiently large number of persons who choose
treatment get reduced marginal welfare weights.

5 Interaction with a progressive tax system

So far, we have only considered tax changes that were identical for everyone.
This assumption may be justified as follows: Distributional considerations
are achieved through distortionary taxation. The optimal design of a distor-
tionary tax system implies that redistribution has been taken to the point
where the social gain from further redistribution is exactly offset by the in-
cremental distortion of higher rates of taxation. For an optimally designed
tax system of this type, social welfare cannot be increased by increasing or
reducing a tax component which is equal for all (and thus non-distortionary)
and adjusting the distortionary part of the tax system so that total revenue
is unchanged. On the margin, it therefore makes no difference whether an

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