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

1 Introduction

From the insurance literature it is well known that positive co-payments
have two effects¹: On the one hand they reduce social efficiency by reducing
the risk sharing properties of insurance. On the other hand positive co-
payments increase social efficiency by reducing moral hazard. One important
type of moral hazard for health care is that if the price the patient pays for
some treatment is zero or low, the patient will purchase treatment even if
the willingness to pay for the treatment is considerably lower than the cost
of providing treatment. The optimal size of co-payments balances the two
considerations above, see e.g. Zeckhauser (1970), Ma and Riordan (2002).

In countries where health care is publicly provided and where equity con-
siderations play an important role in policy decisions, it is often argued that
an increase in co-payments is unacceptable as it will be particularly harmful
to the less well off in the society. The present paper gives a critical discus-
sion of this issue. Within a simple model of health care where people differ
in income and in severity of illness, it is shown in section 2 who gains and
who loses from an increase in the co-payment for a particular treatment.
The socially optimal co-payment is then derived by maximizing the sum of a
concave transformation of expected utility for each person (section 3). The
concave transformation reflects equity considerations, giving a person lower
weight in the social welfare function the better off this person is in terms of
expected utility. In section 4 it is shown how more concern for equity ("more
concavity") affects the optimal co-payment. Section 5 concludes.

2 Co-payment, taxation, and individual wel-
fare

The welfare of a person is given by u{y — t) if healthy, where t is a tax per
person (same for everyone, see below) and y is income net of any taxation
other than t. The function u is the same for everyone, while y varies among

¹See e.g. Arrow (1963, 1968), Pauly (1968), Shavell (1979).

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