Figure 1: Expected utility as a function of the size of the co-paymant
As p increases beyond p0, more and more persons choose not to be
treated. The person illustrated by Figure 1 chooses treatment provided the
co-payment does not exceed p1. For p > p1 expected utility is increasing in
p, cf. (7). In Figure 1, v is strictly concave for p ∈ (p0,p1). Generally, this
need not be the case. And even if V is strictly concave for p ∈ (p0,p1) with
a local maximum at p*, it is not obvious which of the three values V (y,£, 0),
V (y,£,p*) and V (y,£,c) is highest.
3 Co-payment and social welfare
The objective of the government is to maximize the sum of welfare for all
persons. However, for a government concerned about equity it is not reason-
able to assume that this sum is unweighted. If the government cares about
equity, it is reasonable to assume that persons with low expected utility have
a higher weight in the sum of welfare than persons with high expected util-