However, they gain from the tax reduction that is implied by the increase in
the co-payment.
For those who choose to be treated, it follows from (3) that
— (1 — π)[-t,(p)]u'(y — t) + At>(p) — 1¼,(y — t — p) (8)
op
In this expression, the first term is positive. We cannot unambiguously sign
the second term without knowing more about t(p) than t'(p) < 0. However,
the concavity of и implies that u'(y — t) < u'(y — t — p) when p is positive.
It therefore follows from (8) that
ev(y'f-p) < [-f(p) — π]u'(y — t — p)
op
(9)
From (6) it follows that the LHS of (9) is negative for p sufficiently close to
0, and for p sufficiently close to c. From (7) and (9) we therefore have the
following proposition:
Proposition 1 If the initial co-payment is sufficiently low, everyone chooses
to be treated, and a small increase in the co-payment will make everyone
worse off. If the initial co-payment is sufficiently close to the treatment cost
and some people choose to be untreated at this co-payment, those who have
chosen not to be treated gain from an increase in the co-payment, while those
who have chosen to be treated lose from an increase in the co-payment.
Figure 1 illustrates how v will depend on the size of the co-payment for
a typical person. If p is so low that everyone chooses treatment (below p0 in
Figure 1), it follows from (6) that (8) can be rewritten as
°υ⅛,t,p) — (ι — ^[^(y — t) — u(y — t — p)] < 0
op
(10)
if ω(p) — 1
where the inequality sign follows from the concavity of u. A positive co-
payment can thus only be optimal if it is set so high that it makes some
persons choose not to be treated.
More intriguing information
1. The name is absent2. Behaviour-based Knowledge Systems: An Epigenetic Path from Behaviour to Knowledge
3. References
4. IMPROVING THE UNIVERSITY'S PERFORMANCE IN PUBLIC POLICY EDUCATION
5. Globalization, Divergence and Stagnation
6. Prevalence of exclusive breastfeeding and its determinants in first 6 months of life: A prospective study
7. NEW DEVELOPMENTS IN FARM PRICE AND INCOME POLICY PROGRAMS: PART I. SITUATION AND PROBLEM
8. The Interest Rate-Exchange Rate Link in the Mexican Float
9. Emissions Trading, Electricity Industry Restructuring and Investment in Pollution Abatement
10. The name is absent