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



optimal co-payment, where we use the shorthand notation v for v(y,P,p):

(1 - π)[-t'(p)] [[       Φ'(v)√(y - t)dF(y,P)

√⅜∕)[o,i]

+ ^[-t>(P)] [[      φ7v>⅜ - t)dF(y, ŋ

J JMWf)

π[f + t'(p)] [[       Φ'(v)(y - t - p)dF(y,P) = 0 (12)

J J(y,QΩ(p)

The two first terms in this expression are are positive, implying that the
last term is negative, i.e. we must have 1 +
t'(p)0 at the optimal value
of
p. We shall use the expression above to answer the question what is the
effect on the optimal co-payment of an increase in the concern for equity?

4 Co-payments and equity concerns

Consider a change in the function Φ(v) in the direction of stronger prefer-
ences for equity, i.e. a "more concave" function. More precisely, let Φ(
v)
be replaced by Φ
*(v) f (Φ(v)) where f' > 0 and f'' < 0. Calling Φ'(v)
and Φ
*'(v) the "marginal welfare weights" before and after the change, the
change in marginal welfare weights is given by
h(v) = Φ*'(v) - Φ'(v). Since
the level of the function
f ' is of no importance, it is convenient to chose this

level so that

/ /

C,b[o,i]


h(v(y,P,p))√(y - t)dF(y,P) = 0


(13)


It is easy to verify that the definition of the function h(v) implies that
h,(v) 0 at the value of v giving h(v) = 0. Denoting this value of v by v* it
therefore follows from (13) that
h(v) 0 for v < v* and h(v) 0 for v > v*.
In words, marginal welfare weights increase for persons with "low" expected
utility (
v < v*) and decline for persons with "high" expected utility (v > v*).

The normalization given by (13) implies that the first of the three terms
in (12) does not change as the function Φ(
v) changes. The total change in



More intriguing information

1. The Macroeconomic Determinants of Volatility in Precious Metals Markets
2. The Impact of EU Accession in Romania: An Analysis of Regional Development Policy Effects by a Multiregional I-O Model
3. The name is absent
4. The Clustering of Financial Services in London*
5. Voluntary Teaming and Effort
6. The name is absent
7. Revisiting The Bell Curve Debate Regarding the Effects of Cognitive Ability on Wages
8. CONSIDERATIONS CONCERNING THE ROLE OF ACCOUNTING AS INFORMATIONAL SYSTEM AND ASSISTANCE OF DECISION
9. How to do things without words: Infants, utterance-activity and distributed cognition.
10. Linking Indigenous Social Capital to a Global Economy