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

ity. In the hypothetical case of the government being perfectly informed
about everyone’s income earning abilities and health characteristics (£ in the
present analysis), lump-sum taxation could be used to obtain whatever dis-
tributional objectives the government had. In this case everyone would have
the same welfare weight (on the margin) after the lump-sum taxation had
been applied. In practice the government does not have perfect information
about individuals’ earning abilities and health characteristics. Distributional
considerations must therefore be achieved through distortionary taxation.
In this case it is not optimal to redistribute so much that marginal welfare
weights are equalized across the population.

To capture distributional considerations, we assume that the government
maximizes the sum over all persons of a concave transformation of expected
utilities, i.e. over Φ(n(y,^,p)) where is Φ is increasing and concave. The
social objective function is thus given by

This expression can be illustrated by a Figure similar to Figure 1. In
particular, since p^o is the same for everyone, we typically get a local minimum
at p^o or somewhere to the right. The value p¹ varies among persons, so the
aggregate curve will not have a kink at p¹ as in Figure 1. However, we may
very well have at least one non-concave section of the curve for aggregate
welfare in addition to the area near p^o. It is clear from Figure 1 that even if
we find a local optimum with a positive co-payment, this optimum must be
compared with the case of no co-payment and possibly also with other local
optima with positive co-payments.

From now on we only consider the case of an interior optimum, i.e. the
optimal p is in the interval (0,c). Differentiating (11) with respect to p and
using (7) and (8) gives the following first-order condition for the socially

<<   5   6   7   8   9   10   11   >>

More intriguing information