the tax system. The change in the distribution of y will therefore be very
small, implying that the derivations in Section 4.1 remain almost the same
as for the case where the progressive element of the tax system was assumed
to be constant.
Even if the progressive element of a tax system increases significantly a
response to increased concern for equity, the optimal co-payment may also
increase. To see this, consider the following simple example. There are three
groups in society: "Rich and very healthy", "poor and quite healthy" and
"poor and weak". The "rich" never get ill, while the income and probability
of illness is the same for two "poor" groups. For the "quite healthy", the
utility loss in case of illness is much smaller for than the treatment cost, while
the opposite is true for the "weak". In such an economy it will be socially
optimal to give the "weak" treatment in the event of illness, while treatment
for the "quite healthy" is inefficient. The co-payment should therefore be set
so high that the "quite healthy" choose to go untreated in the case of illness.
Given this constraint, the co-payment should be set as low as possible, in
order to achieve income smoothing across states for the "weak".
Now consider an increased concern for equity. The tax system would then
change so that the "rich" get lower income and both "poor" groups get higher
income. Since the "quite healthy poor" now will get an increased willingness
to pay for treatment, they will choose treatment if the co-payment is held
constant at its original level. In order to prevent this socially inefficient
outcome, the co-payment must be increased so much that the "quite healthy
poor" continue to choose to go untreated, in spite of their increased income.
In the Appendix we give an alternative fully specified numerical example
with a linear tax function where both the marginal tax rate and the co-
payment increase as a response to increased concern for equity.
6 Concluding remarks
In the Introduction, we argued that concern for equity is often used as an
argument against any proposal of increasing co-payments for health treat-
ment. By this logic, we would expect that increased concern for equity, as
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