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

Figure 2: Expected utility as a function of the severity of the illness

Δ = H⅜)>'(y — ^t) У δ(u)dF(y, €)

— [¹+ ^t'(p)]^u'(У — ^t — P) 2" δ(υ)dF(y,€) (15)

Moreover, (13) can in this case be written as

ʃ δ(υ)dF(y,€) = ʃ δ(υ)dF(y,€) < 0

since δ(v) > 0 for € > L. The first integral in (15) is in other words negative.
The second integral in (15) is positive, since δ(v~) > 0 for € > L. Since the
terms [—t'(p)] and [1 + t'(p)] are both positive, it follows that Δ < 0 in the
present case. From our previous discussion we thus have the the following
proposition:

10

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