Health Insurance for Rich and Poor

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Health Insurance for Rich and Poor
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Health Insurance for Rich and Poor
Outline
In this lecture we will look at some
considerations on health insurance
particularly the different impacts of different
sorts of health resource distribution on rich and
poor people in an economy
We shall look at a system based on private
insurance
and a system based on public provision
We shall consider who gains and losses in each
system
and what peoples perception of the public system
might be
and how a public system could be changed to
improve perceptions
We shall assume that rich and poor have identical
probabilities of illness
and identical utility functions with respect to
money
In order to sustain the last assumption, we shall
assume
the utility function exhibits constant relative
risk aversion
So to start we shall examine the idea of constant
relative risk aversion.
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Pratts constant relative risk aversion
Health Insurance for Rich and Poor
Suppose we have two individuals with the same
utility function
but one is poor
and the other rich.
The rich person has a prospect with the same
proportional value of assets between events one
and two as the poor person
X2
If the utility function had a constant relative
coefficient of risk aversion
Optimal prospect rich
the two optima would lie on the same ray through
the origin
Initial prospect rich
Optimal prospect poor
or
Initial prospect poor
X1
the ratio of
to
is the same everywhere
If each is offered the same insurance price, we
have two trading lines
and two optima.
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Pratts constant relative risk aversion
Health Insurance for Rich and Poor
X2
AND
If the utility function had a constant relative
coefficient of risk aversion
Certainty equivalent rich
Initial prospect rich
Certainty equivalent poor
Initial prospect poor
X1
the ratio
to
is the same everywhere
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Health Insurance for Rich and Poor
Two short technical notes
1).In a utility function that showed CONSTANT
ABSOLUTE RISK AVERSION the absolute distance from
the value in state of the world1 and its
certainty equivalent would be constant along the
ray, no matter what the value of initial outcome.
2)Pratts coefficient is measured as followed
If
U f(X)
Pratts coefficient of risk aversion is
where represents the derivative of the utility
function, U is utility and X money value of assets
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Health Insurance for Rich and Poor
Now lets consider the main issues of the lecture
the impact of differing systems health provision
financing
on different groups in the economy.
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Pure private health insurance system
Health Insurance for Rich and Poor
Insurance companies offer FULL insurance to their
poor clients at an unfair premium rate (price)
based on (but greater than) their probability of
illness
The insurance companies offer the same rate for
FULL insurance to their rich clients
PAY MORE than the poor
So the rIch -
RECEIVE MORE EXPENSIVE TREATMENT than the poor
X2
Insurance trading line rich
Full insurance for rich
Health insurance payment rich
Insurance trading line
Initial prospect rich
Full insurance for poor
Health insurance payment poor
Initial prospect poor
X1
Premium for rich
Premium for poor
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Pure private health insurance system
Health Insurance for Rich and Poor
The insurance companies offer the same rate for
FULL insurance to their rich clients
PAY MORE than the poor
So the rIch -
RECEIVE MORE EXPENSIVE TREATMENT than the poor
X2
But many people would regard this as unfair
Insurance trading line rich
Full insurance for rich
or socially divisive
Health insurance payment rich
Insurance trading line
Initial prospect rich
They would prefer a system showing social
SOLIDARITY
Full insurance for poor
Health insurance payment poor
Initial prospect poor
X1
Premium for rich
Premium for poor
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Introduction of a Government determined PUBLIC
health resource provision scheme
Health Insurance for Rich and Poor
Suppose the Government intervenes to insist that
everyone in the scheme, e.g. NHS or compulsory
insurance, gets the same level of expenditure on
treatment if they are ill
(say at the level previously enjoyed by the rich)
Pay the same
Rich and poor -
Receive the same health expenditure
Government trading line (at E(V))
X2
Insurance trading line
Prospect of rich in public scheme
Standard health insurance payment
Health insurance payment rich
Government trading line (at E(V))
Prospect of poor in public scheme
Initial prospect rich
Insurance trading line
Standard health insurance payment now for poor as
well as rich
Initial prospect poor
X1
Premium for poor
Premium for rich
Because treatment and admin costs are standard,
the government charges (through tax or compulsory
premium payment) the same rate, equal to the odds
of illness, for both poor and rich
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Comparing gains and losses gains and losses
between the private insurance system and public
resource allocation system
Health Insurance for Rich and Poor
So as we have just seen, the poor benefit most
obviously from the public health resource
allocation system compared to the private
insurance system goes to.
BUT notice in this model, as a consequence of
cheapening administration costs, there is scope
for mutual gain .
The costs are reduced because of the
simplification of the scheme arising from
rich and poor each PAYING the same
PREMIUM
and
rich and poor each RECEIVING the same
MONEY VALUE of TREATMENT
SO NOW CONSIDER ALL THE COSTS AND BENEFITS
What form the gains may take?
Are there any losses, if so to whom?
Will people be satisfied with the public health
service?
What might be done to ameliorate any losses and
improve satisfaction?
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What form the gains may take?
Health Insurance for Rich and Poor
POOR gain extra health expenditure
RICH pay lower premium
X2
Government trading line (at E(V))
Insurance trading line
Government trading line (at E(V))
Initial prospect rich
Initial prospect rich
Health expenditure on poor (PUBLIC HEALTH PAYMENT
SCHEME)
Insurance trading line
Health expenditure on poor (PRIVATE INSURANCE
SCHEME)
Initial prospect poor
Initial prospect poor
X1
X1
Rich PUBLIC HEALTH SCHEME premium/tax
Rich PRIVATE INSURANCE premium
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Possible Losses
Health Insurance for Rich and Poor
POOR might (and this example do) pay more for the
extra healthcare expenditure
X2
Government trading line (at E(V))
Insurance trading line
Government trading line (at E(V))
Initial prospect rich
Initial prospect rich
Insurance trading line
Initial prospect poor
Initial prospect poor
X1
X1
Poor PRIVATE INSURANCE premium
Poor PUBLIC HEALTH SCHEME premium/tax
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Will people be satisfied with the public health
service?
Health Insurance for Rich and Poor
Not the POOR since, as just shown, they might pay
more.
Additionally, they are not OPTIMISING on the
cheap public scheme price of health
X2
and receive a smaller health benefit than the
Governments compulsory expenditure level scheme
So the poor would CHOOSE
to pay less
Government trading line (at E(V))
Compulsory public scheme prospect
Reduction in expenditure for optimum poor
prospect from compulsory prospect
Maximising expected utility would put them
Insurance trading line
Optimal prospect for poor with public scheme
to private insurance
Note that the optimal public health scheme is
still preferable
Initial prospect poor
Initial prospect poor
X1
X1
OPTIMAL PUBLIC HEALTH SCHEME premium/tax from
POORs perspective
Compulsory expenditure level premium/tax
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Will people be satisfied with the public health
service?
Health Insurance for Rich and Poor
Not the RICH.
They are not OPTIMISING on the cheap public
scheme price of health
X2
Government trading line (at E(V))
Maximising expected utility would put them
Increase in expenditure for optimum rich prospect
from compulsory prospect
Optimal prospect for rich with public scheme
Insurance trading line
Compulsory public scheme prospect
to private insurance
Note that the optimal public health scheme is
still preferable
So the rich would CHOOSE
to pay a bit more
Initial prospect rich
Initial prospect rich
and receive a bigger health benefit than the
Governments compulsory expenditure level scheme
X1
X1
OPTIMAL PUBLIC HEALTH SCHEME premium/tax from
RICHs perspective
Compulsory expenditure level premium/tax
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Health Insurance for Rich and Poor
So we have the rather odd situation that although
both rich and poor might benefit from the
introduction of a publicly resourced health
scheme to replace a private insurance health
resource scheme
both might feel dissatisfied with the result!
The private insurance scheme can reach a Nash
Equilibrium
but is not social welfare optimal
The public scheme is not a Nash equilibrium
but is social welfare superior to the Nash
equilibrium
So could the public scheme be tweaked to
improve peoples subjective satisfaction?
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Tweaking the public scheme
Health Insurance for Rich and Poor
Redistributive taxation
But the RICH must pay a higher than premium tax
POOR pay less than the fair premium/tax
So the welfare of the rich is REDUCED by their
subsidy payment
X2
Government trading line (at E(V))
But possibly IMPROVED by moving closer to an
optimum prospect
Subsidising public scheme prospect of rich
So the welfare of the poor is improved
Government trading line (at E(V))
Subsidised public scheme prospect of poor
Initial prospect rich
Initial prospect rich
Health expenditure on poor (PUBLIC HEALTH PAYMENT
SCHEME)
Initial prospect poor
Initial prospect poor
X1
X1
fair premium
fair premium
subsidy
subsidy
Actual premium/tax paid by rich
actual premium/tax paid by poor
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Can the rich gain some benefits even after
redistribution
Health Insurance for Rich and Poor
Suppose the rich can take out full private
insurance after contributing to the public scheme.
The premium rate will be cheap because most of
the burden of paying for health now falls on the
public system
X2
Government trading line (at E(V))
Insurance trading line
Full insurance after buying top-up private
insurance
Increase in health expenditure for prospect from
top-up private insurance
Compulsory public scheme with redistribution
prospect
Initial prospect rich
Initial prospect rich
So the rich are now more satisfied with their
level of health expenditure
X1
X1
fair premium
Private insurance premium
subsidy
Total health premiums and tax
Public premium/tax paid by rich
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Health Insurance for Rich and Poor
Political pressure to change system to private
insurance
Allowing top-up insurance to grow in an
unconstrained manner may create a moral hazard.
The rich may substitute some public amenities for
private ones
Pure insurance trading line
X2
Pure insurance trading line
And argue for a reduction in the size or scope of
the public system
Topup Insurance trading line
Government trading line (at E(V))
Pure full insurance
Full insurance after buying top-up private
insurance
Compulsory public scheme with redistribution
prospect
Pure full insurance
Initial prospect rich
Initial prospect rich
X1
Which would be IRRATIONAL for the rich in this
case
Which would be RATIONAL for the rich in this case
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Health Insurance for Rich and Poor
A few theoretical notes
Because we have assumed constant relative risk
aversion
The arguments in this lecture could be applied to
the case of flexible insurance contracts with
which people would optimise on PARTIAL insurance
Most results follow from the standard analysis
assuming only convex to the origin indifference
curves
In cases where that is not so, the words MIGHT or
COULD have been used in the argument.
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Health Insurance for Rich and Poor
Conclusion
So from an allocative point of view
private insurance works
though it is certainly not Pareto optimal
From a distributive perspective, many judgements
lead to
the implementation of a public scheme
which may benefit everyone
But public schemes without a redistributive
element may
be too expensive or inflexible for the poor
give too low a level of healthcare expenditure
for the rich
Public schemes with some redistribution
may be objected to by the rich on the grounds
that they do not wish to subsidise the system
may still give too low a level of healthcare
expenditure for the rich
The last point may however be ameliorated by
allowing top-up private insurance for those who
can afford it.
However allowing unrestricted top-up insurance
may cause a political moral hazard there may be
pressure from the rich to abandon the public
scheme