MSc in Economic Evaluation in Health Care
WELFARE ECONOMICS
Topic 1 notes: Overview and introduction to welfare economics
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Scarcity
Positive economics versus normative economics
In welfare economics (and the economic evaluation of health care programmes)
we are interested in being able to rank different social states (or allocations of
resources).
Society’s welfare ultimately depends on the welfare of its constituent households.
Therefore to make value judgements of the desirability of different social states
to society we need to have a theory of household behaviour. Put another way, we
are interested in how households rank different social states.
A formal statement of the household’s utility maximisation problem is given by:
maximise U = u(x1, x2, …., xn ) subject to
n
p x
i 1
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7.
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i
i
y
The solution the household’s utility maximisation problem is given by: MRS
 dx 2
p
 1
=
dx 1
p2
In practice most economies are populated by millions of households, most of
whom have different tastes and different budget constraints. Somehow we need
to distil welfare statements about the desirability of a social state from its effects
on millions of different households. One option is to use the Pareto Principle.
According to the weak Pareto criterion, if the utility of every household is higher
in state x than state y then state x yields a higher level of societal welfare than
state y and is preferred.
According to the strong Pareto criterion, if the utilities of some households are
higher in state x that in state y and the utility of no household is lower in state x
than state y then state x yields a higher level of societal welfare than state y and is
preferred.
If state x allows a welfare improvement over state y according to the Pareto
criterion, then state x is said to be Pareto superior to state y, and state y is said to
be Pareto inferior to state x.
If all households enjoy the same level of utility in state x and state y then states x
and y are Pareto indifferent.
If state x is neither Pareto superior, nor Pareto inferior, not Pareto indifferent to
state y then states x and y are Pareto non-comparable. Pareto non-comparable
states are ones in which some households are made better off but others are made
worse off in moving from one state to another.
A feasible state is one that can be achieved given the economy’s resource
constraints.
Any feasible state for which no feasible Pareto superior state exists (i.e. there is
no scope for Pareto improvement) is said to be Pareto optimal. If a state is Pareto
optimal then there is no change that can be made in the economy, given current
resource constraints, that can make any household better off without making
another household worse off.
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15. There are a number of problems with the Pareto Principle: the Pareto ranking of
states is incomplete (there exists Pareto non-comparability); the Pareto Principle
is neutral to the distribution of utility; and, the Pareto Principle can conflict with
liberalism.
16. An attempt to partially overcome the problem of Pareto non-comparability and
increase the power of the Pareto Principle is given by the compensation principle.
Two different versions of the compensation principle have been proposed. The
compensation principle proposed by Kaldor says that state a is preferred to state b
if the gainers from the move to state a can hypothetically compensate the losers
so that everyone is better off. The compensation principle proposed by Hicks says
that state a is preferred to state b if the losers from the proposed move cannot
hypothetically bribe the gainers not to make the move.
17. There are a number of problems with the compensation principle: the
redistribution is hypothetical only; the hypothetical redistribution is assumed to
be costless; the Pareto Principle is still unable to rank different Pareto optimal
allocations relative to one another (there are still Pareto non-comparable states);
and, the compensation principle may lead to contradictions (as shown by the
Scitovsky Paradox).
18. The most important and useful aspect of the Pareto Principle is the relationship
between Pareto optimality and the equilibrium of an economy in which resources
are allocated by an ideal market mechanism. The first fundamental theorem of
welfare economics states that under certain assumptions a state (i.e. an allocation
of goods and factors) resulting from a competitive equilibrium is Pareto optimal.
19. The first fundamental theorem of welfare economics requires: efficient exchange
p *
of goods and services  MRS a  MRS b  1  an allocation is achieved on
p2 *
the Community Indifference Curve; efficient allocation of the factors of
r*
production  MRTS a  MRTS b 
 an allocation is achieved on the
w*
Production Possibilities Curve; and, efficient output choice (overall efficiency)
 MRS = MRT  an allocation is achieved where the Community Indifference
Curve is tangential to the Production Possibilities Curve.
20. Geometrically, the efficient exchange of goods and services and the efficient
allocation of the factors of production may be reached by attaining a point on the
contract curve in the relevant Edgeworth box.
21. A complete and consistent ranking of social states is called a social welfare
ordering (SWO). Just as with household preferences, if a continuity assumption is
also made the SWO can be represented by a social welfare function (SWF) that
assigns a number to each social state so that they might be ranked.
22. We cannot achieve an SWO without someone making value judgements about
the desirability of different social states. Value judgements are statements of
ethics that cannot be found to be true or false on the basis of factual evidence.
The value judgements found in an SWO may be weak (i.e. broadly accepted) or
strong (i.e. controversial).
23. SWO possibilities are limited by informational requirements that pertain to the
measurability and comparability of households’ utility.
24. There are four possible measurability assumptions: ordinal scale measurability;
cardinal scale measurability; ratio scale measurability; and, absolute scale
measurability.
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25. There are three possible comparability assumptions: non-comparability; partial
comparability; and, full comparability.
26. The Arrow Possibility Theorem states that if household utility is measurable on
an ordinal scale and utility is non-comparable across households the only possible
SWO is a dictatorship. That is, social orderings must coincide with the
preferences of some arbitrary household in the economy regardless of the
preferences of the others.
27. Other forms of the SWF are feasible depending on the measurability and
comparability assumptions one is prepared to make. Such SWOs include:
Bergsonian SWO; Bernouilli-Nash SWO; generalised Bernouilli-Nash SWO;
generalised utilitarian SWO; positional dictatorship (e.g. maximin, maximax);
positional lexicographic SWO (e.g. leximin, leximax); and, utilitarian SWO.
28. Markets fail, so that the conditions for the first fundamental theorem of welfare
economics to hold are not met for the following reasons: non-competitive
behaviour; externalities resulting from a lack of property rights; externalities
resulting from jointness in consumption and production, including public goods;
and, informational externalities.
29. Governments intervene to address such market failures. Additionally
governments intervene for the following reasons: the theory of second best
suggests that governments should intervene even in unconstrained sectors of the
economy if a market failure occurs elsewhere in the economy; to provide the
institutional and legal framework under which the market operates; to redistribute
income; and, to provide merit goods and limit/ban provision of demerit goods.
30. 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.
31. 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.
32. Public goods have two related features: non-excludability, which means that my
consumption of the good does not exclude your consumption of it; and, nonrivalry, which means that my consumption of the good does not decrease the
amount of it left for you.
33. The level of provision of pure public goods is Pareto optimal when the sum of the
marginal rates of substitution (MRS) of private goods (Pr) for public goods (Pu)
across all households in the economy is equal to the marginal rate of
transformation (MRT). In other words:  MRS Pr,Pu  MRTPr,Pu
34. To construct the aggregate demand curve for public goods we add the demand
curves for individual households vertically. Vertical summation is appropriate
because a pure public good is necessarily provided in the same amount to all
individuals.
35. Operationally a Pareto optimal allocation of public goods can be achieved using
the Lindahl equilibrium. The Lindahl equilibrium states that a Pareto optimal
provision of public goods can be achieved at the output level where the aggregate
level of demand equals the aggregate level of supply, as above. In the Lindahl
equilibrium all households enjoy the same provision of the public good, but they
differ in the (tax) prices that they pay for the good, where the tax price is
determined according to the marginal willingness to pay of each household.
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36. Public choice is the study of the political mechanisms and institutions that
explain government and individual behaviour. It can be defined simply as the
economic study of non-market decision-making.
37. In a democratic economy, decisions made by the government about the
desirability of social states are made in three stages: 1. Households vote for
elected representatives (politicians); 2. Politicians vote for the desirability of
social states (e.g. a particular allocation of government expenditure); and, 3.
Bureaucrats, who work for administrative agencies, act on the outcome of the
vote by the politicians (e.g. they spend their specific allocation of government
expenditure).
38. Politicians face two problems: how do they ascertain the views of their
constituents? (This is the problem of preference revelation); and, how do they
reconcile differing views across constituents? (This is the problem of aggregating
preferences).
39. One way of addressing these problems is through voting. Perhaps the most
widely employed rule for decision-making in a democracy is majority voting,
which says that in a choice between two alternatives, the alternative that receives
the majority of the votes (i.e. 50% + 1) wins.
40. There are three factors that will influence an individual voter’s attitudes towards
a particular level of public provision: the voter’s attitudes towards the good; the
voter’s income; and, the nature of the tax system.
41. The median voter is the voter for whom the number of voters who prefer a higher
level of provision is exactly equal to the number of voters who prefer a lower
level of provision. The majority-voting level of provision is the level that is most
preferred by the median voter.
42. There are a number of problems with the majority voting equilibrium: A majority
voting equilibrium may not exist; and, the majority voting equilibrium, if it does
exist, may not be Pareto optimal.
43. Government intervention may not be desirable for two reasons: the government
requires some means of addressing the problem of preference revelation and the
problem of aggregating preferences; and, there may be government failures,
where, even if governments do possess some means of revealing and aggregating
preferences government intervention is still undesirable on the grounds that it is
Pareto inferior (or at best Pareto indifferent) to no government intervention.
44. The empirical application of welfare economics is the study of applied welfare
economics.
45. We can construct two measures of welfare change using a money metric: the
compensating variation (CV) and the equivalent variation (EV)
46. The CV of a move from state 0 to state 1 is defined as the amount of income
(positive or negative) that the household would pay in state 1 in order to leave it
as well off as it was in state 0 (= the maximum amount the household would pay
to secure the change).
47. The EV of a move from state 0 to state 1 is defined as the amount of income
(positive or negative) that the household would accept in state 0 in order to leave
it as well off as it would be in state 1 (= the minimum payment the household
would accept to forego the change).
48. A change in social welfare from state 0 to state 1 is given by: W =
H
 a v CV ,
j1
j
j
j
where aj, is the welfare weight that society attributes to each household j in the
economy and vj, is the marginal utility of income of household j.
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49. Social cost-benefit analyses in practice usually estimate W 
n
 CV
j1
j
z
 C where
CVjz is the CV pertaining only to the increase in health status z obtained by the n
individuals who receive the health care programme and C includes: all direct
medical and health care costs; medical and health care costs associated with any
adverse effects of the health care programme; savings in medical and health care
costs arising from the prevention or alleviation of disease caused by the health
care programme; and, medical and health care costs incurred from treating
diseases that would not have occurred if the patient had not lived longer as a
result of the health care programme.
50. In a social cost-benefit analysis the appropriate decision rule is the net present
T
B  Ct
value (NPV), given by NPV   t
, where r is the (one-period) social
t
t 0 (1  r )
time preference rate.
51. In cost-effectiveness analyses typically the desirability of a project is described in
terms of a ratio of incremental costs to incremental benefits. Such an incremental
C
cost-effectiveness ratio (ICER) may take the following form: ICER =
.
( z1  z 0 )T
C
1
 , where 1/g is the
52. The proposed project should be implemented if
( z1  z 0 ) T g
critical cost-effectiveness ratio.
Acknowledgement: These notes are closely based upon those initially developed for this course by
Stephen Morris. I am grateful to Steve for allowing the use of his teaching materials.
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