MSc Economic Evaluation in Health Care
WELFARE ECONOMICS
Topic 7
Market failure & the theory of second best
(i) Market failure
The first fundamental theorem of welfare economics
The first fundamental theorem of welfare economics (the direct theorem) introduced in
Topic 4 states that under certain assumptions a state (i.e. an allocation of goods and
factors) resulting from a competitive equilibrium is Pareto optimal. This requires the
following conditions:
1. Efficient exchange of goods and services (economic efficiency in an exchange
p *
economy): MRS a  MRS b  1
p2 *
2. Efficient allocation of the factors of production (economic efficiency in a production
r*
economy): MRTS a  MRTS b 
w*
3. Efficient output choice (overall efficiency): MRS = MRT
This result relegates the role of the public sector (the government) to that of providing the
institutional and legal framework under which the market operates and, possibly to
redistribute income.
We shall now consider the circumstances under which this ‘decentralised efficiency’ fails
to hold and whether there are non-market mechanisms that permit the exploitation of
existing Pareto improvements.
Causes of market failure
The central question ‘is why do markets fail? Or, alternatively, why should mutual utility
gains not be exploited by decentralised decision-makers (households and firms)? In other
words, we are concerned with reasons why actual markets may fail to achieve the Pareto
optimal properties ascribed by the first fundamental theorem of welfare economics.
There are many descriptive market imperfections. These can be reduced to the following
fundamental market failures:
1.
2.
Non-competitive behaviour;
Externalities resulting from a lack of property rights;
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3.
4.
Externalities resulting from jointness in consumption and production, including
public goods; and,
Informational externalities.
1. Non-competitive behaviour
An important feature underlying the first fundamental theorem of welfare economics is
that all of the participants are price-takers. This means that households and firms do not
influence market prices. This is reasonable only if the market is populated with many
buyers and sellers. In many cases there may be sufficiently few buyers and sellers that
they are aware that their actions can alter market prices. The extreme cases are that of a
single seller (a monopoly) and a single buyer (a monopsony) faced by price-taking agents
on the other side of the market.
The implications of price-setting power:
 P ≠ MC
 Supernormal profits may be earned by firms (monopoly, oligopoly)
 Firms may not operate at the minimum average cost (monopolistic
competition)
2. Externalities resulting from a lack of property rights
Whenever an activity by one agent influences the output or utility of another agent and
this effect is not priced by the market an externality is said to exist.
In order for the decentralised market to work, firms and households must be able to
exchange claims on the right to use a factor of production or consume a good. This
requires a well-defined system of property rights that excludes agents from using a good
or factor for which they have not paid. For many goods and factors of production it is
prohibitively costly or not feasible to enforce property rights. With common property,
some agents may be unable to appropriate all of the returns to a productive activity in
which they engage or, alternatively, other agents can free ride and enjoy the fruits of
another’s labour and expense.
A common property resource exists because property rights are not assigned. One
obvious solution is to assign property rights, either in the form of consumption or
production limits or to charge a price equal to the scarcity value.
Externalities arising from a lack of property rights in health care.
Assume a small, positive, constant marginal cost for the consumption of health care
(shown by the marginal cost [MC] curve). The marginal benefit (MB) curve for the
consumption of health care is downward sloping and the actual quantity of health care
consumed occurs where the MB curve crosses the MC curve (at x P). However, this is in
fact a private MB curve (MBP) and the social MB (MBS) curve is in fact lower at all
quantities of health care consumed (or at least at all higher quantities of health care
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consumed). Therefore the social optimum would be to consume less health care, where
the MBS curve crosses the MC curve (at xS). This can be achieved by imposing a
consumption limit equal to xS or setting a higher price so that xS is achieved using the
private MB curve.
3. Externalities resulting from jointness in consumption and production, including public
goods
Externalities may also arise from jointness in consumption and production. Jointness in
consumption means that a consumption activity taken by one household affects the utility
of one or more other household. Jointness of production occurs when one firm’s activity
affects the production possibilities of one or more other firms. The externality may be
positive or negative. It may also be unilateral or reciprocal. The externality may also
occur among households, among producers, or between households and producers.
The first fundamental theorem of welfare economics will generally fail in the presence of
externalities arising from jointness in consumption and production. This is because
decentralised households and firms in a competitive economy will not take account of the
external costs and benefits of their actions when making their (selfish) decisions.
With externalities arising from jointness in consumption the exchange efficiency
conditions are not satisfied. For example, suppose an economy where n goods (x 1, x2,
…xn) are consumed. Also suppose that the consumption of x1 by household A also affects
the utility of household B. This means that the utility functions of household A (UA) and
household B (UB) may be summarised as follows:
UA = f(x1A, x2A, …xnA)
UB = g(x1B, x2B, …xnB, x1A)
[1]
However, household A neglects the influence of its consumption of x1 on household B.
That influence may be positive or negative depending on whether the effect is an external
economy or an external diseconomy.
An analogous problem arises with externalities arising from jointness in production.
Externalities resulting from jointness in consumption and production in health care.
Assume a small, positive, constant marginal cost for the consumption of health care
(shown by the marginal cost [MC] curve). The marginal benefit (MB) curve for the
consumption of health care is downward sloping and the actual quantity of health care
consumed occurs where the MB curve crosses the MC curve. For household A this
occurs at xA, where the MB curve for household A, MBA, crosses the MC curve.
However, this level of consumption ignores the benefit to household B from household
A’s consumption of health care. This is shown by household B’s MB curve (MBB).
Therefore the socially optimal consumption of health care by household A would in fact
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be xS (which is greater than xA) shown by the intersection of the MBA+MBB curve with
the MC curve.
A similar analysis may be applied when the externality has a negative effect, in which
case MBB would be negative and the socially optimal output xS would be below
household A’s optimum xA.
Where there exists positive externalities arising from jointness in the consumption of
goods such as health care due to altruism, then the result is a caring externality. Such
caring externalities may also be reciprocal across households.
An extreme case of jointness in consumption and production occurs with public goods.
Public goods have two related features:
1. Non-excludability, which means that my consumption of the good does not exclude
your consumption of it; and,
2. Non-rivalry, which means that my consumption of the good does not decrease the
amount of it left for you.
Goods that possess both these qualities are known as pure public goods. Goods which
possess exactly the opposite qualities (excludability and rivalry) are known as pure
private goods. Goods which are neither purely public or purely private are called mixed
public goods. Mixed public goods are subject to congestion costs as the number of
users/consumers increases, where it is useful to think of congestion costs as altering
either the quality of the good or the amount of the good per user. Health care provision
may be thought of as a mixed public good because to a certain extent it is characterised
by non-excludability and non-rivalry with congestion costs.
Households who receive benefits without paying for them are called free riders, and they
are an important reason why the market fails to provide public goods in a Pareto optimal
manner. If the provision were left to the market place then public goods would be
underprovided. The reason is that individuals have incentives to understate their own
preferences in order to avoid paying and free-ride on the demands for others.
4. Informational externalities
The efficiency of the competitive market equilibrium depends on all of the decentralised
decision-makers (households and firms) having full information. The market itself plays
an important role in conveying information in the form of relative prices to decisionmakers about the relative costs and benefits of different actions. However, informational
externalities may arise due to asymmetric information in the market. Two important
sources of informational externality are:
1. Adverse selection. This is one example of an informational externality, when one side
of the market is more informed about the nature of the exchange being made.
Examples of adverse selection include the market for ‘lemons’, labour markets, and
the market for health insurance. One solution to the adverse selection problem is
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through signalling, where the more informed party attempts to inform the less
informed party by sending a signal.
2. Moral hazard is another example of an informational externality, where a problem of
excess use arises because the informed party brings about a level of provision
(demand or supply) of the good that is greater than the level of provision that would
have been achieved had both parties been equally well informed.
Market failure and the role of the public sector
We have discussed the important reasons why a Pareto optimal allocation of scarce
resources may not be achieved through the decentralised market system. In all cases of
market failure the marginal social benefit of devoting an extra unit of resources to a
particular activity will differ from the marginal social cost. Market participants,
motivated by private rather than social marginal costs and benefits will not be induced to
devote the optimal amount of resources to the activity. In some case there will be too few
resources used (in the case of public goods and positive externalities), in other cases there
will be too many resources used (in the case of non-competitive behaviour via barriers to
entry and negative externalities).
In the face of market failure there may exist a role for the public sector over and above
that of providing the institutional and legal framework under which the market operates
and redistributing income. The government may have to involve itself in the actual
allocation of resources.
A key question is why should the government be able to take mutually beneficial
allocative actions which private agents (households and firms) cannot? The answer lies in
the government’s monopoly in the legal use of coercive power: the government can
extract involuntary payments and prohibit activities with the threat of force. However,
while market failures indicate a possible role for the government this is not to say that the
government should necessarily intervene in the market. To warrant intervention, the
government must have at its disposal means that are capable of producing a Pareto
improvement. Also, even if such means are available there is still the question of whether
or not governments will work in the way that we hope they will in order to produce a
Pareto improvement: just as there are potential failures in the way that decentralised
markets work, so there are political processes and bureaucratic structures that may cause
government failures.
(ii) The Theory of Second Best
The first-best allocation of resources
The first fundamental theorem of welfare economics (the direct theorem) states that under
certain assumptions a state (i.e. an allocation of goods and factors) resulting from a
competitive equilibrium is Pareto optimal. This requires the following conditions:
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1. Efficient exchange of goods and services (economic efficiency in an exchange
p *
economy): MRS a  MRS b  1
p2 *
2. Efficient allocation of the factors of production (economic efficiency in a production
r*
economy): MRTS a  MRTS b 
w*
3. Efficient output choice (overall efficiency): MRS = MRT
If these three conditions are met, we will achieve what is called the first-best allocation of
resources (i.e. those implied by the three conditions for Pareto optimality – the ‘first-best’
rules).
Market failure
Unfortunately, in reality many sectors of a large economy will deviate from the first-best
rules due to market failure and so the first-best allocation of resources will not be
achieved.
Such market failures imply a potential role for government intervention to allocate
resources (in addition to providing the institutional and legal framework under which the
market operates and, possibly, to redistribute income). By intervening appropriately in
sectors of the economy where the first-best allocation of resources is not achieved
through the use of taxes, subsidies, regulations and/or public production decisions the
government may be able to allocate resources in such a way so as to improve social
welfare.
The second-best allocation of resources
Given that the first-best allocation will not be achieved, this leads us to the next logical
question: given that such imperfections are inherent in the economy, do we achieve the
second-best allocation of resources (i.e. the best feasible one given the existence of
market failures) by following the first-best rules whenever possible? This would mean
allowing the unconstrained sectors of the economy (those without market failures) to be
organised in the perfectly competitive manner discussed previously in an effort to achieve
the first-best rules in those sectors. Unfortunately the answer to this question is no. This
is the theory of second best: accept as a constraint that one or more of the necessary
conditions for Pareto optimality are violated in an economy. Then meeting the other
necessary conditions in the rest of the economy is generally not desirable on Pareto
optimality grounds.
Interpretation of the theory of second best
The theory of second best implies that perfect competition with no policy intervention in
the unconstrained sectors does not lead to the best feasible allocation of resources. This
clearly has implications for the appropriateness of piecemeal (single-sector) policies, and
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illustrates a general second-best result: in theory we can do better by policy intervention
in the market price setting process than the market would do on its own.
This has very negative implications for welfare economics. It means that the intuitively
simple ideas captured in the first-best rules cannot be relied upon without reservations.
Also, the rules for optimality under second-best conditions are far more complicated and
difficult than the first-best rules.
Clearly this introduces a further role for government intervention over-and-above
regulating market failures directly, providing the institutional and legal framework under
which the market operates and, possibly, redistributing income: there is an argument for
government intervention in price setting even in unconstrained sectors of the economy.
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