[Note for bibliographic reference: Melberg, Hans O. (1997), Justifying the welfare
state : Biased but useful (Review of Barr), www.oocities.org/hmelberg/papers/971127.htm]
[Note: I am not fully satisfied with the quality of this review; it still needs
quite a lot of polishing, and I probably overstate my case a bit. There are also
additional arguments, such as the nature of liberty, that I would have liked to discuss.
Nevertheless, since I have promised to make something available every week, since I am
short on time, and since I believe there are at least some sound and valuable arguments in
this review, I have decided include it among my papers.]
Justifying the welfare state
Biased but useful (Review of Barr)
by Hans O. Melberg
The Economics of the welfare state
Nicholas Barr
Weidenfeld and Nicolson, London, 1993
ISBN: 0 297 82158 - X (Paperback), 495 pages
Introduction
The central argument of Nicholas Barr's book The Economics of the Welfare State is
simple and clearly stated:
"The welfare state [i.e. income support, health care, education and housing] is
much more than a safety net; it is justified not simply by any redistributive aims one may
(or may not) have, but because it does things which private markets for technical reasons
either would not do at all, or would do inefficiently. We need a welfare state of some
sort for efficiency reasons, and would continue to do so even if all the distributional
problems had been solved." (433)
The term "technical reasons" is shorthand for information problems and
externalities. For instance, since people themselves can affect the probability of
becoming unemployed, it is very difficult to create a well-functioning private market for
unemployment insurance (the problem is technically known as moral hazard). Another problem
with unemployment insurance, is that the failure to take buy such insurance (if it were
possible), has external effects. It is not only you who suffer the consequences if you
become unemployed, but your dependants may starve, I may be hurt by rising crime committed
by the unemployed, and there might be a cost in terms of reduced "social
solidarity". Altogether, the problems of moral hazard and externalities - in Barr's
opinion - make a strong theoretical case for compulsory and publicly provided unemployment
insurance. Publicly provided because no private firm will offer insurance when there are
great moral hazard problems; Compulsory because of the externalities involved.
In a manner similar to that above (appealing to externalities and information problems)
Barr argues in favour of different parts of the welfare state (health programs, education,
income support, social insurance). The question is then: Is this really a good
justification for the welfare state?
My first response is that the argument is certainly not ideologically neutral, as he
claims. Second, I think the argument is incomplete and somewhat biased. Incomplete because
there are many links between the welfare state and efficiency which are not discussed, and
biased because some of the negative links that are discussed are either discussed very
briefly, or often dismissed as inconclusive.
Neutrality and John Wayne
Consider the claim that welfare economics is "an area in which economic theory is
capable of strong results which can justify the general idea of the welfare state to a
surprising extent without resort to ideology" (3).
The problem with this argument, is that aggregate externalities do not automatically
justify compulsion at the level of the individual (see p. 194). For the sake of argument,
imagine a single stubborn individual - call him John Wayne - who decides that he does not
want unemployment or poverty insurance. Being single, we cannot use the externality
argument of starving children (see p. 194 for his list of externalities justifying
compulsion). Imagine too, that he will not become a criminal if he becomes unemployed (not
all unemployed people become criminals!). Still trying to justify compulsion, we might
then argue that him being poor causes me displeasure, but I would question whether we
should count these kinds of preferences. This is an issue Barr does not discuss, but I
think that accepting a person's preference for other people's welfare in this way implies
that we also have to count changes in utility caused by envy (which we do not want).
Lastly, there is the argument that there are costs associated with disposing of the body
of John Wayne (if he becomes unemployed and starves to death). Apparently Barr thinks this
is an argument worth mentioning, but these costs are - in my opinion - far from
significant enough to outweigh the utility John Wayne receives from "being
independent", and hardly significant enough to justify infringing his rights. In sum,
for this individual the externality argument does not apply (or, more weakly, it is not
strong enough), and compulsion is not justified. To argue that we nevertheless, for the
sake of the well being of most people who are not like John Wayne, should have a
compulsory system, is not a neutral political position. (I am not one of them in this
case, but libertarian like this exist).
The example of John Wayne who does not want unemployment or sick-insurance, may sound
far fetched, but consider the following example with the same structure (from the
newspaper Vaart Land, 25. November, 1997). Three researchers have estimated that
the total cost of alcohol in Norway was about $10 billion (included lost work hours,
alcohol related health-problems, crime and more). However, the state only receives 1.4$
billion from the sale of alcohol [I do not trust these figures, but that is not the point
here]. In other words, there is an externality: The people buying alcohol do not pay all
the costs. Does this imply that we should raise the price of alcohol?
The problem, of course, is that not all the people who buy alcohol commit crimes, stay
away from work and so on. If we raise the price for all we also force those who do not
abuse alcohol to pay the price for those who does. This is not efficient (economically
speaking), it does not appear fair, and it is certainly not a "neutral"
position.
Neutrality and means
Another claim that Barr repeatedly makes, is that his arguments are amount the best means
to realize a policy aim. The specification of the aim is ideological, but the
specification of means is a positive issue: It is simply a question of finding the means
that most effectively realize you aim. These questions, he thinks, can be settled without
value judgements.
My immediate reaction is that this is an example of "ends justifying the
means" - a position which in turn may imply using quite unethical means to achieve
your aims. However, Barr can counter this argument by saying that the fact that we object
to some means really imply that we have an aim which we did not specify initially. In this
sense the statement is still true, although close to meaningless.
A more problematic difficulty is the fact that means and ends are not as independent as
one may think. For instance, Barr writes that "... the treatment of private property
is not an end in itself but a means towards the achievement of stated aims" (428).
The problem with this is that an instrumental justification for something may not have the
desired effects. As an illustration consider the following quotation:
"But there is a deeper question: can the planners implement constitutional reform
without a normative commitment to individual rights? If they introduce a constitutional
system and abdicate from some of their powers simply in order to get the economy going,
the economic agents will always fear that the rights will be abolished as soon as the
economy gets into trouble ... " In short, "the instrumental benefits of freedom
are essentially by-products, and will be forthcoming only if freedom is valued for
non-instrumental reasons." [Elster, Jon (1988), Jon Elster Goes to China, London
Review of Books, vol. 10, no, 19 (27. October), pp. 7-9]
Hence, to choose property regime according to its instrumental efficiency in fulfilling
some aim, may be self-defeating: only non-instrumental justification will bring about the
full benefits of private property (and, you cannot instrumentally choose to be
non-instrumental and expect to be credible). As an illustration consider a potential
private farmer in Russia. He will not start to work buy land unless he can be sure than
the government will not change its mind and collectivise the farm again. A government that
justifies private land by efficiency reasons leaves open the possibility that land can be
collectivised, and hence the farmer may decide that the risk of buying and working on his
own plot is too high. As a result, the instrumental justification for private land is
self-defeating.
[Note: This argument is not simply that you should consider how the choice of means
affect your the fulfilment of your aim before you choose the best means. The problem is
that the means-end framework cannot be used to produce what Elster defines as
"essentially by-products" - states that by their very nature cannot be brought
about if you consciously try to do so, e.g. if you try to hard to fall asleep you will
most likely fail. I do not know to what extent the economic growth resulting from private
property really is an essential by-product; this is an empirical question which I know
little about.]
Sub-conclusion on neutrality
The case for and against the welfare state can never be decided in a neutral fashion
simply by appealing to positive economics (see also Atkinson in Barr and Whynes, 1993, p.
43). Moreover, the argument that positive economics is simply about finding the best
possible means to achieve whatever aim the policy-makers specify (a neutral and technical
exercise), sometimes run into the problem that instrumental reasoning in itself defeats
the aim.
Economic arguments: Biased and incomplete
The headline of this sub-chapter may appear a bit negative, so I shall immediately admit
that Barr has produced a very useful, clear and systematic overview of the argument for
and against the welfare state. The same cannot be said for some right wing authors, such
as Robert Skidelsky's book After Communism who proceed in a less rigorous and
organized manner (see my review of Skidelsky).
What is the right frame for deciding questions of state intervention? Barr's starting
point is the Invisible Hand Theorem which says that under certain assumptions free markets
produce an outcome in which nobody can be made better off unless some are made worse off
(i.e. the outcome is Pareto efficient; the first theorem of welfare economics). Moreover,
it can be shown that all possible distributions can be achieved simply by making changes
to the initial assignment of property rights (the second theorem of welfare economic). The
intuition behind this was given by Adam Smith more than 200 years ago, but it was first
formalised by Arrow and Debreu in the 1950s (this kind of work is known as general
equilibrium analysis). In sum, the free market seems to be the best mechanism to maximize
welfare given our preferences, resources and technology.
To show that state intervention can improve on the free market, we have to show that
the market somehow fails. One way of doing this is to examine whether the assumptions
behind the Invisible Hand theorem hold in the real world. If they do not, intervention may
(but it need not) produce a better result than the free market left to itself. The three
major assumptions, as presented by Barr, are: Perfect competition, perfect information, no
market failures.
Perfect competition implies that nobody in the economy are strong enough to influence
the price (i.e. have monopoly power). In the real world, we sometimes find that this is
not the case; Microsoft can certainly influence the price of computer operating systems
and unions can influence the wage rate.
The condition of no market failure, as discussed by Barr, includes the conditions that
it must not be possible to enjoy the full benefits of a good which another has bought
(e.g. if I pay for the defence of our country it is impossible to prevent you from
free-riding on my contribution); there must be no external effects (effects which are not
taken fully into consideration by the decision-maker e.g. pollution); and no increasing
returns to scale (when a doubling of the inputs more than double the outputs).
Lastly, perfect information implies that you must know the real price of the product,
the quality of the product, and probabilities of future events (e.g.. when you are going
to die, how likely it is that you will suffer an industrial injury etc.).
These are, as Barr points out, very strong conditions. But, as he is less keen to
point out, the failure of these conditions do not automatically imply that intervention is
desirable. The first problem is that when one of the conditions do not hold, the breakdown
of the other conditions need not be a problem (the general theory behind this is known as
the theory of the second best and was developed by Lipsey and Lancaster, 1956). For
instance, there might be a small externality in the production of good X, but X may also
be complementary to another product (Y) which has very positive external effects. Thus,
intervention to raise the price of X will reduce the negative externality associated with
X, but it will also reduce the consumption of Y and thus the good externalities associated
with Y. In sum, the net effect of intervention is unknown: it can be positive as well as
negative.
The problem is simply that often we do not know enough to be sure that intervention
will produce a positive result. The consumption and production of goods are linked in so
many ways, the conditions for a second order optimum so complex, and our knowledge of the
causal mechanisms in society so limited, that intervention is not automatically justified
as soon as we discover an externality (see, Ng Welfare Economics for a good
discussion of the complexity and the information required to fulfil the conditions to
achieve the second best solution).
From the discussion above it should be clear that one need not be an extreme
libertarian to be weary of arguments for intervention based on externalities. On the
contrary, traditional conservatives always argued that we simply do not know enough about
society to justify large scale intervention (Burke, Oakeshott). This is a pragmatic
argument, not one based on rights. In Barr's overview of the three major political
theories (Libertarian, Liberal and Collectivist), the "conservative" position is
called "empirical libertarianism", in contrast to moral libertarians (Nozick).
The other two main directions are also divided; Liberals can either be utilitarians or
"Rawlsian" and Collectivists are either Socialists or Marxists.
It is also a bit unfair of Barr to accuse Hayek of taking "little account of
information problems" (103). First, it is unfair to accuse somebody who wrote before
the problems of moral hazard, adverse selection and the rest of modern information
economics were known of "failure to acknowledge" these problems (433). Second,
Hayek's main focus was on those information failures which led intervention to fail, for
instance that the government do not know the preferences of people as well as people
themselves; that the government cannot gather the information that the price system so
efficiently communicates; and that the government do not have the necessary knowledge of
how society works to be certain of achieving the desired result. This investigation may be
biased, but understandably so knowing the time in which he was writing; and Barr's
relative lack of focus on these issues is no less biased.
Although Barr does not give us a systematic defence of the government's ability to
intervene to produce a better general equilibrium, he does give some evidence that
intervention at least have predictable and positive partial effects. For instance, to show
that poverty is reduced by income transfers and the pension system "removed from
poverty over 80 per cent of the pre-transfer poor" (p. 146). Thus, intervention does
work in increasing the income of the poor today. However, it the question is phrased
slightly differently - not whether the system implies that the poor gets more money at a
given point in time, but whether poverty is reduced over time - the answer is less
satisfactory (see David Whynes in Atkinson and Whynes, 1993, p. 64). The introduction of
social insurance and other measures were thought to gradually eliminate the need for
public assistance, yet the opposite happened: "As a percentage of total expenditure,
national assistance increased, rather than fell" (Atkinson in Bar and Whynes, 1993,
p. 27). Hence, while the intervention was and is successful in relieving poverty at one
point in time (which itself is generally accepted as a good thing), it has failed in
reducing the problem of poverty over time.
Leaving aside the question of whether the government has the ability to
intervene to produce a better total outcome, we might question whether it has the desire
to do so. The government consists of people who, like most of us, have personal and
selfish interests. Hence, instead of intervening to produce a more efficient and/or fair
result, they may end up doing what is in their own personal interests. For instance,
giving in to lobbyists in order to get money to be re-elected.
Altogether, intervention is not easily justified. We must show that there is a market
failure (not only locally since one failure may cancel another), that intervention has the
potential to improve the situation (again, not only locally and statically, but a new
better general equilibrium and preferable reduce the problem over time), and that
intervention actually will produce a better result. Finally, we must accept a political
theory which allows us to use compulsion as a means to achieve a better result.
Left out
Having discussed the general theory behind state intervention, I will no go on to discuss
three possibly relevant mechanisms which are not mentioned in Barr (the risk of too much
intervention, private but non-market provision and the non-linear cost of taxation). The
failure to mention these is one reason why I think the account is somewhat biased, and
this time the accusation is more fair that Barr's claim against Hayek since these issues
are well known.
A slippery slope: The risk of too much intervention
At one point Barr notes that government spending as percentage of GDP has grown from 21%
in 1920 to 41% in 1992. Moreover, welfare spending as a percentage of government spending
has increased from 28% in 1920 to 60% in 1992 (p. 174, all numbers refer to the UK). The
question is then whether this increase represent a problem?
Conservative like to argue that the increase indicates the growth of state power at the
expense of civil society. Left wing academics often reply that the conservative argument
fails to distinguish between government controlled spending and transfer payments.
Transfer payments, like pensions, increase the state share of GDP, but the state does not
actually decide how to spend the money the pensioners get. The left is right in that we
should distinguish between transfer payments and other types of government activities, but
this does not necessarily solve the problem. Even if they are transfer payments, they
still represent an increase in state power. It is the government which decides the size of
your pension and the degree of redistribution in society.
Regardless of the debate about the difference between transfer payments and government
consumption, there are several reasons why we might be worried about the growth of the
state controlled sector. One of these is that the scope for unproductive rent-seeking
activities increase. Different groups invest time and resources in persuading the
government to listen to their demands. Another problem is simple that a large government
increases the risk of abuse of government power.
As an illustration of the last point, consider the system of state transfer of money to
support voluntary organisations in Norway. Lately, and predictable one might add, there
were several major scandals associated with these transfers when it transpired that some
organisations had claimed higher membership than they in fact had had. The government
reacted by enacting new rules; from now on they had to report more details about each
member (name, address, date of birth and so on). In itself this may seem innocent and
reasonable, but consider the use a "bad" government could make of this
information. How much easier would it not be for the Nazis if the Norwegians already had
had a register of the names and addresses of the members of an organization working for
Jewish interests in Norway. How much easier would it not have been for the Communists to
purge the old elite when they occupied the Baltic countries if they could find all the
names of the leaders of most voluntary and political organisations on a computer file?
To some these arguments sound far fetched. There is little chance, they say, that the
information will be abused in this way. I am no so sure. History has made many strange
turns, and we cannot exclude the possibility of future "bad" governments. Note
also that even if most people are not evil and power hungry, the state must still be
organized to consider the possibility of its "worst" members coming to power.
The reason is that politics may under certain circumstances be dominated by the mechanism
of adverse selection, only the worst - the most ruthless and power hungry - survive.
Hence, as an analogy to Rawls' maxmin rule (the best society is that which maximizes the
life prospects of the worst off), we might offer the following maxmin rule: The
relationship between the state and civil society ought to be organised so that the worst
possible government can do the least possible harm. [Both rules, incidentally, seem too
risk-averse]. A large state does not fulfil this condition.
In what sense is this discussion relevant to Barr? First, Barr argues in favour of
interventions that would both increase the size of the state and its information about
citizens. Second, Barr's approach is to decide each issue on its own, based on
considerations of costs and benefits. Looking at each market separately, one might
conclude (as he does) that the benefits of government intervention is larger than the
costs. However, each measure may also have an externality: An increase in government
power. Isolated this externality may not be enough to affect the cost benefit
consideration in one market, but in aggregate the result may be a state that is more
powerful than we would like.
Private, non-market provision
In his discussion Barr focuses on two major alternatives for organising social insurance
and assistance: Private vs. Public. He then tries to demonstrate that some forms of
insurance is impossible to provide in the market, and that public intervention can remedy
the situation. For instance, moral hazard and common shocks makes it difficult to organise
private insurance against inflation. Similarly, the impossibility of insuring fully
against inflation makes public intervention in the pension system desirable. So, given the
failure of private markets to provide insurance, public intervention is necessary.
The option that is ignored in this argument, is private non-market provision of social
insurance and assistance. For instance, in traditional societies the young are often
obliged by norms and traditions to take care of their own parents. One could argue, as
some conservatives do today, that as the state takes more and more responsibility for
tasks that used to be provided on a non-market private basis, it creates a self-fulfilling
process whereby private non-market provision breaks down and the need for public
assistance only increases (until it becomes too large to handle ...).
Personally I do not know what to make of this argument. It is certainly coloured by a
rather romantic view of how things were done in the past; yet it is also true that the
state can never afford to pay for all kinds of care, or that "paid" care can
ever fulfil the same function as care within the family.
Although Barr does not discuss private non-market provision of social insurance, he
does consider private charity as an alternative to social assistance. In that connection
he makes a rather interesting argument about how the income distribution is really a
public good: I may be willing to give in order to decrease poverty, but the effect of my
contribution is so insignificant that it is not worth the costs. To solve this problem,
many people may agree to each give some money only as long as the others also give
("I give as long as you give"). Although I did not want to give money alone
(since it would not decrease poverty significantly), I may be willing to support this
scheme (since if many give the same amount it will reduce poverty significantly). The
argument is both true and interesting, but one may doubt whether this is really how people
who fail to give think. Is it not more likely that donations are motivated by
bad-conscience, pure altruism and individual concern for a concrete family that suffers -
than an abstract concern for the aggregate income distribution. If donations are motivated
by the first three mechanisms, the free-rider problem does not exist.
The non-linear cost of taxation
A third problem not mentioned as far as I could see by Barr, is that the marginal cost of
increasing the tax rate to raise money for social assistance is larger than the average
cost [This is also an argument for considering the system in aggregate, not only the
isolated costs/benefits]. True, it may be possible to raise money is less costly ways
(negative income tax), but in practise revenue is usually raised in ways that cause
dead-weight loses.
A simple model illustrating the non-linear cost of increasing the tax rate, is
presented by H.S. Rosen in chapter 14 (taxation and efficiency) of his book Public
Finance (see, p. 312 for the mathematics). In short, we are trying to estimate the
size of the so called "dead-weight triangle" resulting from taxation. The area
of a triangle is given by:: (1) A = 1/2 base * height
in our case:
(2) A = 1/2 (di) * (fd)
fd is simple the change in price, so (using D as a symbol for delta)
(3) fd = D p
(4) D p is the same as (1 + t) p - p = t p
Hence, fd = t p
Now, di is the change in quantity ( D q).
(5) D q = D q (Dp/Dp) = (Dq/Dp) Dp
Recall that the price elstaticity (n) is defined as:
(6) n = (Dq/Dp) * (p/q)
which implies that
(7) Dq/Dp = n (q/p)
Using this result we have:
(8) di = n (q/p) Dp
which can be transformed into
(9) di = n (q/p) t p
We now have expressions for di and fi so A =1/2 di * fd becomes:
(10) A = 1/2 n b t t p
(11) A = 1/2 n p b t2
The important point to note about equation 11, is that the deadweight cost of taxation
increases exponentially; increasing the tax from 20% to 21% is more costly than increasing
the tax rate from 10 to 11%. If we are willing to draw policy implications from this
(which is dangerous given the already mentioned problem of first best vs. second best), it
is that we should think twice before making the state sector so large that it requires
high rates of taxation.
Bias II
One source of bias was arguments simply not discussed. Another source, is arguments
discussed very briefly. For instance, the topic "government failure is discussed on
two pages, that is less that 0.5% of the whole book. A balanced book trying to discuss the
pros and cons of state intervention should give more space to this topic.
Another source of bias, is that the author quite consistently concludes that his own
arguments are strong, while the conservative counter-arguments are complex and uncertain.
To justify my argument, I offer the following sample of quotations:
* About his own arguments for the welfare state:
- "In all these cases there is an overwhelming case for compulsion ..." (199);
"These arguments are compelling." (201)
"... there is a cast-iron efficiency argument for at least some public involvement
with pensions." (218)
- "The efficiency case for substantial public, PAYG involvement is therefore
strong." (237)
- "Thus there are solid arguments of both efficiency and social justice for public
provision of subsistence benefits on a non-insurance basis." (244)
* When discussion possible arguments against his proposals:
- "These insights, however, should not be overstated" (94, about government
failure and the public choice arguments)
- the literature is "large, complex and controversial" (203); "The
simplicity of the original argument disappears the deeper one digs ..." (204, when
discussing whether unemployment benefits cause unemployment)
- "considerable controversy" whether funded is more than effective that PAYG
pension system in increasing output (223)
- "... the issue remains unsolved" (230, about the effects of savings, pension
system and economic growth)
- Welfare state and economic growth : "terra incognita" (436) and no
"obvious correlation" (436)
Of course, it might really be true that his arguments are strong, and all the others
weak and uncertain. However, the choice of words to express this, and the detailed
dissertation of counter-arguments in contrast to the less critical attitude to his
"strong" conclusions, makes me suspect that his own "moderately egalitarian
aims" (437) have made the presentation somewhat biased.
To mention one possible example of this, consider the effects on innovation of public
vs. private pensions which Barr argues is "theoretically indeterminate" (229)
and empirically "unresolved" (230). Two pages later he suggests that the
introduction of robots could be one answer to the demographic problem (i.e. the growing
number of pensioners compared to people in the work-force). At this point one might make
the connection that in a system with privately (employer) provided pensions, the firm has
a great incentive to introduce robots (save pension expenses). In a public system,
however, this motive for introducing robots is weaker since you do not receive the
benefits in terms of reduced pension-payments when you introduce robots. Barr does not
make this incentive argument. Moreover, his list of supply side measures (232) to avoid
the demographic problem leaves me wondering whether he has discovered a simple way to
increase economic growth which is not exploited today. Clearly his measures also have
costs, and the question is whether the costs are larger than the benefits; increasing
education always sound good but at one point the net return from education also turns
negative.
Conclusion: Good (and Bad)
I want to re-emphasise that this book is by far the most rigorous, systematic and clear
overview of the pros and cons of the welfare state that I have ever read. In a review
there is a tendency to focus on points of disagreement, and this gives a negative
impression of the book. This is not my intention, and not my opinion. Overall I thought
this was a very useful book. The style was clear, although the author goes a bit over the
top when he constantly organises his discussion using the "first, second, third"
framework.
Appendix: A model of the the insurance market, including adverse selection and a
critique
(From Barr (1993) p. 111 - 131)
Note: I think there is an error in the third equation on p. 123, above equation 5.17.
This is corrected in the following presentation.
* Demand for insurance
y1 = income in bad year
y2 =income in good year
p1 = probability of bad year
p2 = probability of good year
Expected income : y = p1 y1 + p2 y2
Expected utility : U = p1 U(y1) + p2 U(y2)
There are two ways of achieving expected utility: By receiving a certain income (y*) every
year, or by recieving y1 with probability and y2 with probability p2. The difference
between the average income and y* represents the amount you are willing to pay in order to
avoid the risk of income fluctuations (v = Value of certainty):
v = y - y*
The difference is larger the more risk-averse an individual is.
So, the individual will demand insurance as long as the value of certainty is larger than
the net cost of insurance (c):
Demand condition: c > v
The net cost of insurance is the gross price (g) minus the expected benefit: pL (where p
is the probability that the event will happen and L is the size of the benefits if it
happens). In short,
c = g - pL
* The supply side
The gross price (premium) is defined as G, the expected outlay to the claimants is pL, and
the costs of operation (administration etc) is defined as T. Hence,
G = pL + T
In short, the insurance company will not sully insurance unless they price they receive
from selling insurance is hogher than their outlays and their administrative costs.
* Altogether
We must have positive demand, technically feasible supply, and demand and supply must
intersect (it is possible to have damnd and supply curves which do not intersect):
Positive demand: v > y - y* (i.e. there must be risk aversion)
Supply conditions: p must be
1. independent across individuals
2. less than one
3. estimable
Intersection:
Recall, net premium c = G - pL
An intersection exist only if
v > G - pL
(Its value must be greater than the price) which implies:
y - y* > T
In other words, individual risk aversion must be strong enough to cover the administrative
costs.
Adverse selection
Assume that there are two types of individuals: Low risk and High risk. Since there is a
difference in risk, they will have to pay differnt price for insurance; the higher risk,
the more you pay:
Gl = pl L + T
Gh = ph L + T
If the company cannot distinguish between high and low risk, the might try to charge a
premium based on average risk:
G = (a ph + (1-a) pl) L + T
However, at this price the low risk individuals will find it profitable to buy less
insurance, and high risk individuals to buy more insurance. Thus, the pooling eqilibrium
is inefficient: Some buy too much and some do not buy enough. Moreover, the pooling
equilibrium is not be stable since a company that offered a contract with a lower price
and a lower premium will attract the low-risk individuals. Neither is the separating
equilibrium always possible (stable). In short, either the result is inefficienty, or the
market fails to exist at all.
A short critique
Recall that according to Barr necessary conditions for supply is that p must be: 1.
independent across individuals; 2. less than one; 3. estimable
. I do not think 1 and 2 are logically necessary conditions:
On Independence
Inflation is a "common" shock (if there is inflation, we all experience
inflation, not only some individuals), and as thus it cannot be insured against, Barr
argues.However, if people have differnet probability estimats of the likelihood of future
inflation, I still think it is possible to insure against inflation even if it is a common
shock. A rich person believing that inflation will be lower than 5% is willing (and able)
to bet against some poor pensioners who fear (and strongly believe) that inflation will be
10%. Also, as Barr notes, it is possible to achieve some insurane against inflation using
the futures market; which in turn is inconsistenw with the statement that common shocks
like inflation cannot be insured against. Barr might be more correct if, as he sometimes
does, argues that inflation cannot be insured against completely, but this argument
implicitly concedes that independent p's is not a logical and necessary precondition for
the existence of insurance.
Estimable probabilities
It is not necessary that p is estimable, only that people think it is
estimable. For instance, the probability of different rates of inflation 20 years ahead
may be inherently impossible to estimate. Still, people might have different beliefs, and
this in turn makes insurance possible. Whether this kind of insurance is efficient is
another matter.
[Note for bibliographic reference: Melberg, Hans O. (1997), Justifying the welfare
state : Biased but useful (Review of Barr), www.oocities.org/hmelberg/papers/971127.htm]