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

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-

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