REAL INCOME, ECONOMIC WELL-BEING AND THE QUALITY OF LIFE
Michael E. Burns and Pauline Halchuk
University of South Australia
CEA 36 TH ANNUAL MEETINGS
University of Calgary
30 May – 2 June 2002
This is a report of work in progress and is not for quotation without the permission of the
authors.
2
Introduction
Researchers in many fields, including economics, psychology and sociology, would see as a
key objective of their efforts an increased understanding of human behaviour which in tur n
would better enable the enhancement of individual and community well-being through
economic and social policy. This widespread agreement as to the desirability of increasing
well-being is matched by equally widespread uncertainty and sometimes rank disagreement
as to how such well-being might be measured.
This paper seeks to contribute to the
volumous and still growing literature exploring how the causes of well-being might be
identified and how levels of well-being might be measured, at least in a comparative sense.
The approach adopted here is to both recognise the broad-based multi-dimensional nature of
well-being and to explore unashamedly how far the application of the economists optimising
methodology can go in yielding insights into its measurement. Of particular concern are the
questions as to how far the arbitrariness of many existing measures can be overcome, which
arguments should or should not appear in these measures and how should they be ‘priced’,
and finally, how much extra mileage can be obtained from consideration of an explicitly
multi-period modelling framework.
The layout of the paper is quite straightforward. In Section II, a brief overview is provided of
some of the key research directions that have been taken in the study of well-being. In
Section III the theory of intertemporal welfare measurement and the construction of index
numbers is briefly summarised. Insights are obtained into the weights that derive from the
optimisation procedure as well into the logical coexistence of multiple indicators of wellbeing. In Section IV the application of this theory is discussed at somewhat greater length
with regard to the cases where variables (such as intermediate goods) are not arguments of
the utility function but appear in constraints, and where arguments of the utility function are
either rationed or may not appear at all in the constraints. In Section V, we examine an
alternative surplus focussed approach to deriving indices of well-being and note the
implications of such an alternative measure for questions of inequality. In the final and
largely discursive Section VI we return to the specification of the intertemporal optimising
problem and briefly examine alternative approaches to the end-point problem (death), to the
treatment of changes in life expectancy, and how to take into account cross-country
differences in life expectancy. It is noted how, by taking account of changing expectations, it
is entirely plausible that recent economic growth may have been accompanied by feelings of
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reduced well-being.
The role of memory in well-being is also briefly touched upon.
Although a number of potentially useful insights are identified at various points in the paper,
much of what is presented here may be more useful in raising interesting questions than it is
in providing precise answers.
.
II.
Research Directions in the Study of Well-being and the Quality of Life
In the context of the present paper it is useful to identify two broad strands of the literature
addressing questions of the measurement of real income, economic well-being and the quality
of life. The first has its origins within the discipline of economics while the second is
associated with multi-disciplinary studies that often have strong roots in the behavioural
sciences. A major integrating force with regard to the latter group is the International Society
of Quality of Life Studies (ISQOLS). We shall discuss first the latter broad-based strand of
research.
While much of the focus of ISQOLS might be described as the study of subjective well-being
(SWB) or of happiness, the breadth of research undertaken under their umbrella reflects
recognition of the many and varied factors that contribute to individual’s feeling of
satisfaction with life. Some idea of this breadth si given by the number and nature of the
different research tracks featured at the recent fourth international conference of the ISQOLS,
held in Washington in December 2001. Specific tracks were organized addressing quality of
life (QOL) research in relation to:
•
different units of analysis, dealing with QOL studies of individuals, families, cities,
and countries.
•
specific life domains, for example, dealing with environmental well-being, economic
well-being, work well-being, health well-being, housing and neighborhood wellbeing, consumer well-being, and financial well-being.
•
specific populations, such as women, children, adolescents, the disabled, and the
elderly.
•
country-specific QOL studies, focusing on QOL studies targeting Western Europe,
Eastern Europe, North America, South America, Australia/New Zealand, Asia Pacific,
and Africa.
•
specific societal institutions such as education, business, media, tourism, public
health, and labor.
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4
•
methodological and philosophical issues in QOL research, including discussion and
analysis of problems and solutions in the measurement of subjective well being,
qualitative research and QOL studies, and QOL research and ethics.
While the descriptions of some of these research areas is indicative of what economists might
term a ‘partial equilibrium’ approach, a substantial literature recently surveyed by Diener and
Biswas-Diener (2001) also explores the interface between economics and the behavioural
sciences.
Particularly in the last two decades, investigation of the relationship between
income or wealth and subjective well-being or happiness has revealed a number of
provocative associations. Thus, while there have been identified large correlations between
wealth and SWB across nations the relationship is much weaker within nations and in a
number of studies apparent economic growth has been accompanied by either weak growth
or negative movements in SWB.
This raises a challenge to those who would develop
comprehensive measures of changes or indices of well-being, whether from an economic
base or otherwise, to develop measures that are consistent with correlations such as these.
How far an economic-based of index of well-being can actually go in capturing the totality of
impacts upon SWB is unclear, especially in light of the range of associations identified in the
literature surveyed by Diener and Biswas-Diener.
These associations include the lower
levels of SWB experienced by those who prize material possessions (unless they are rich) and
the increased risk among the poor to experience severe unhappiness-causing events. In
addition the poor experience: heavier prison sentences; poorer mental health; higher rates of
infant mortality; greater likelihood of being the victims of violent crimes; a greater number of
stressful life events; and, greater likelihood that their children will drop out of education and
that their daughters will become pregnant in their teens.
Other associations noted, such as those between education and happiness or between selfperceptions of happiness and employment success emphasise the intertemporal nature of
SWB as well as some of the difficulty in determining causality. Economists have of course
contributed in a number of related areas. In the ‘consumer as a pleasure machine’ discussions
in Fisher and Shell (1969), the possibility that education and training enable a consumer to
extract more utility from a given consumption activity offers one possible basis for an
education-happiness link
The connections between education and earning and between
education and health have been widely explored while associations between happiness or
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5
satisfaction and economic parameters have been addressed by a number of economists, as in
the work of Clark and Oswald (1994, 1996) with regard to the impacts of inflation and
comparative incomes on happiness and satisfaction. More recently the paper by Helliwell
(2002) offers a compelling demonstration of why and how economists might embrace a
broader perspective of well-being.
In essence, of course, this is where the main economic strand of the ‘well-being’ literature
has been going over at least the last three decades. In fairness, concerns with what is meant
by real income and interest in having a broad-based index of satisfaction have been at least
implicit in economic considerations for a very long time. This was apparent in Ulmer (1949)
who acknowledged the much earlier interests expressed in 1707 by the Bishop of Ely as to
the “…..relative difference in money income that would provide for a student of the
University of Oxford ‘the same Ease and Favour.’..” at that time as compared to 260 years
earlier. Various contributions to the Essays in Honour of J. R. Hicks edited by Wolfe (1969)
clearly attribute broad-based views of real income and economic well-being to Hicks
although it should be admitted that these concerns were often to be found within what were
fundamentally theoretical advances in our understanding of consumer demand and index
number theory. In a similar vein both the Samuelson and Swamy (1974) and Burns (1977)
theoretical index number papers acknowledge these historical concerns of the Bishop of Ely
while Burns (1979) explores some of the ways in which the traditional welfare measures can
be obtained in more general specifications of the utility maximisation model.
In practice, however, perhaps the major stream of economic advances in the development of
more comprehensive measures of well-being have flowed from the literature associated with
the inadequacies of indicators such as GDP or GNP per capita as an indicator of economic
well-being.
Many would see the starting point of this literature as the path-breaking
contribution of Nordhaus and Tobin (1973) in their development of The Measure of
Economic Welfare (MEW).
The MEW expands on the GDP by making two major
adjustments. First, the MEW reclassifies some products from final goods to intermediate in
order to account for defensive expenditures and second, the MEW includes non-market
flows, such as household labour. The starting point for the calculation of the MEW is the
personal consumption expenditure and the following adjustments are made:
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•
Subtract private instrumental expenditures that represent personal outlays for activities
such as commuting to work, banking, and legal services. These are considered
regrettables.
•
Subtract expenditure on consumer durable goods.
•
Subtract private spending on health and education. These are instead included as an
investment
•
Add services of consumer capital.
•
Add the value of leisure that adds to economic welf are (uses the opportunity cost of
work).
•
Add the value of non-market activities by using an imputed value of the services derived
from unpaid housework, parenting, and volunteer activities.
•
Subtract a disamenity correction value for the estimated higher costs of urban dwelling.
The Canadian measure uses the aggregate of urban disamenity elements estimated for the
GPI, which includes the cost of crime, automobile accidents and the cost of pollution. The
American version measures the difference between the urban and rural wage rates.
•
Add government spending of public current spending that is deemed to generate economic
welfare. (Nordhaus and Tobin assert that there are only two services that satisfy this
requirement, the postal services and recreation outlays.)
•
Add services of government capital by using an imputed value of services from the stock
of public capital that generates economic welfare.
The cumulative total of all these adjustments is the actual measure of economic welfare, and
may be related to a concept of ‘total consumption’. All of the variables are equally weighted.
From these beginnings development quickly flowed, in the form of seminal analytical
contribution to the measurement of economic growth by Usher (1980), and importantly, in
the contribution of Osberg (1985) which laid the foundation for The Index of Economic WellBeing (IEWB), since developed and refined in numerous studies by Lars Osberg and Andrew
Sharpe for the Centre for the Study of Living Standards (CSLS).
The IEWB is an
aggregation of four main categories with difference weights attached reflecting the
differences in their relative contributions to economic well-being. The four categories include
the effective per capital consumption flows, the net societal accumulation of stocks of
productive resources, poverty and inequality, and finally insecurity.
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Other indices of well-being or economic development have been proposed, including the
Genuine Progress Indicator (GPI) and the Human Development Index (HDI) used by the
United Nations Development Programme. The GPI is quite similar to the MEW developed by
the American policy institute Redefining Progress and came to the attention of the public in
1986 when the Atlantic Monthly published the article “If GDP is Up, Why is America
Down?” The HDI is based upon GDP per capita but also takes into account literacy and life
expectancy but with aggregation in most cases based upon scaling procedures that are aimed
at reflecting human needs and diminishing marginal utility of consumption (Desai, 1991). In
most of the research referred to the weights applied to different arguments of the index of
well-being have been largely arbitrary but more recently Dowrick, Dunlop and Quiggin
(2001) have developed a ‘true’ comparison of living standards approach where the weight are
determined by revealed preference from actual observed behaviour. In this work a utility
consistent index is derived taking into account both consumption and life expectancy as well
as building in an endogenous link between food and health consumption and life expectancy.
III
Theory
The literature on well-being discussed above offers many different indices of well-being, in
almost all cases with arbitrarily imposed weights. This raises some interesting questions. If
individuals are supposed to be able to consistently rank alternative combinations of the
arguments in the respective indices, can these different indices be consistent with each other?
Again, if individuals can exercise some choice over values of these arguments of any index
number and choose rationally in these face of one or more constraints, are not at least some of
the weights determined by this constrained optimisation process? Both of these questions can
be at least partially answered using the traditional tools of economic analysis.
The derivation of welfare measures such as consumers' surplus and index numbers, and of
their properties, occupies an extensive literature. Discussions of these measures and their
properties for a wide range of optimising problems can be found in Samuelson and Swamy
(1974), Burns (1977, 1979), Phlips (1983) and Diewert (1980, 1990). The treatment here
follows most closely that of Burns (1979),
Data availability suggests that a discrete time rather than continuous time representation of
the optimisation problem is appropriate. In general form we have
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(1)
Max U(…xit.…) s.t Sk(…xit…; … k it…) =0 ∀ i = 1……n; t = 1……T; k = 1……K
where for simplicity we may denotes the sets of xit and k it more simply by x and k.
Here xit is the quantity of the ith 'consumption' undertaken in the tt h period while S k is one of K
constraints defining relationship between elements of the x and k. These relationships would
include an intertemporal budget condition, time constraints and specific consumption pattern
limitations as appropriate. Any future price or quantity must, by definition, be an expected
value while discounting of future 'consumption' is accommodated within the utility function.
The period over which optimisation takes place is from the present time until expected death.
Within this framework it may easily be derived that:
(2)
dU = Σ λk Σ
∂Sk
∂S
dx = - Σ λkΣ k dk
∂x
∂k
which indicates that welfare changes may be evaluated either in terms of weighted changes in
the arguments of the utility functions or in terms of weighted changes in the constraint
parameters. Monetary measures of the utility change would be obtained by dividing (2) by
the λ associated with the budget constraint, which without loss of generality can be assumed
to be the first constraint. For small changes dU/λ1 would yield measures of the CV, EV or
change in Marshallian surplus, there being negligible difference between these measures in
this case. For large changes either the CV, EV or a Divisia chain measure would be used,
ambiguities arising for all the well-understood problems of path dependence (Burns 1977).
Returning attention to ‘small change’ case, even if only a single constraint changes, and
suppose that is due to changes in current and expected prices, p it, in the intertemporal budget
condition, the measure involving changes in the arguments of the utility function retains the
complex weights suggested in (2).
This result is unaffected by substitution between
constraints to reduce the overall numbers of constraints, as is illustrated within the simple
two-constraint allocation of time model due to Becker (1965) where the substitution of the
time constraint into the budget constraint yields the result
(3)
dU/λ = Σ(pi + wti)dx i
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What this simple illustration reminds us is that additional constraints to the budget constraint
effectively bring about a divergence between the simple money price, pi , and the true
opportunity cost of consuming a particular good, xi. This insight invites us to re-write (3) in
its general form (based upon (2)) as:
(4)
dU/λ1 = Σpi* dxi where pi* = Σ
λ k ∂S k
λ1 ∂xi
where p i* clearly reflects the ‘full price’ or opportunity cost of consuming a unit of xi.
Equation (3) also reminds us that sometimes, as in the Becker case, substitutions among
constraints may actually simplify some of these ‘full price’ expressions by solving out some
of the Lagrangean ratio terms.
Of course, even in the intertemporal multi-const raint model, it follows from (2) that if only a
single price change in the budget constraint, all other constraints remaining unchanged, then a
much simpler measure of the welfare change is possible in terms of weighted changes in the
constraint parameters, in this case by the usual measure
(5)
dU/λ1 = -xidpi
Bearing in mind the general message that sometimes measures of a welfare change may
sometimes be more simply expressed in terms of constraint parameter changes, it is useful
now to return to (4) and notes that our money measure of a well-being change can be rewritten as:
(6)
dU/λ1 = Σp i* dxi = Σ(pi*xi)
dxi
xi
Within this framework it is clear that the relative weights attached to the arguments of the
utility function are given by the ‘expenditure proportions’, calculated on the basis of the ‘full
price’ or opportunity costs of consumption. In the construction of an index of real income or
well-being there would be no attempt to provide a measure of a level of well-being, but rather
a proportionate measure would be obtained, comparing well-being to some base period. In
the simple single-period single -constraint convention would be that (6) is divided through by
the sum of the expenditures. As will be discussed further below, it is an interesting question
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10
in its own right as to what is the appropriate denominator in our general index of well-being,
but following convention the index would be derived as
(7)
1+
∂ U / λ1
Y*
= 1+ Σ
( pi * xi ) dxi
Y*
xi
where Y* = Σ pi*xi
which expression may be loosely interpreted as one plus the percentage change in the present
value of the utility associated with current and expected future consumptions.
Suppose one was concerned with how the well-being of a representative long-lived individual
might change over a sequence of years, as suggested abovea Divisia -type measure can be
derived as the product of the sequence of terms of the form
T
(8)
[1 + ∂U t / λ1t ]
∏
t =1
As noted sbove, such a measure embodies all the well-known ambiguity problems associated
with the path dependence issue. Having said this, as numerous authors have noted, many
Divisia type indices are likely to yield measures that can be bounded by indices based upon
the Hicksian CV and EV measures of a change in well-being.
The analytical approach adopted here is clearly a potential useful source of insight into the
what values the weights of different arguments of an index might take, weights that would
clear differ from individual to individual according to their different ‘full’ expenditure
proportions. This approach also offers some insights into the question of how many of the
different types and forms of well-being index can sensibly coexist. At least it raises a number
of relevant questions.
First there is clearly an issue as to whether a particular index does reflect an underlying
preference function, and relatedly whether individuals or groups can be regarded as
attempting to optimise in some sense subject to one more binding constraints. There seem to
be two levels of answer here. On the one hand the literature on separability, neatly
summarised in Phlips (1983), seems to suggest that the arguments of an all-embracing wellbeing function might be separable into sub-groups so that some aspects of well-being
optimisation might be possible on a group-by-group basis. On this basis, it might make sense
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11
to consider separately for a given individual an index of economic well-being, an index of
psychological well-being, an index of health well-being and so on. We might then logically
be able to consider separately policies or actions to increase these different dimensions of
well-being, but this would seem to at least require that the conditions for weak separability be
satisfied, that the marginal rates of substitution between arguments of one group be
independent of the levels of arguments in other groups. If we believe, for example, that the
marginal rates of substitution between goods or services would depend upon aspects of
health-wellbeing, these conditions would not hold.
There may be other reasons that make inconsistent the co-existence of multiple indices or
sub-indices of well-being. Much of the separability literature appears to focus on a single constraint world. If instead we accept that we live in a multi-constraint world and that the
constraints may be of an economic, legal or cultural nature, it becomes much less clear that
the usual separability rules are going to be much help.
IV
Application
As in many areas of enquiry and endeavour the statement of theory is a great deal simpler
than the matter of putting the theory into practice. With regard to the measurement of
well-being and as indicated above, this realisation is certainly not new and as discussed in
Section II above, many of the pitfalls were identified in the cited earlier work by Nordhaus
and Tobin, Usher and have been considered more recently at length in the various
contributions by Osberg and Sharpe.
What should be included in the Utility Function?
Matters would be a great deal simpler if the xi above corresponded, at some acceptable degree
of aggregation, to the categories of final goods and services usually contained in a country's
national income accounts. Even though future prices and quantities would still have to be
estimated, the accounts themselves would still provide some kind of statistical base from
which the estimations could be made. As has been made abundantly clear, there are many
difficulties with using the national accounts as a measure of valued consumptions.
As indicated in the discussion of the authors cited above there is a general problem in the
interpretation of expenditure data. Many of the market activities undertaken by consumers,
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12
including those involving final goods and services, are means to an end rather than the end
itself. This is so, even in the single period context.
It has been argued that activities such as essential travel, whether to work, school or shops,
should be omitted from considerations but there are dangers in adopting an ad hoc approach.
A superior analytical alternative is to set up the optimising problem so that the roles of
different consumption activities are clearly specified. Using the standard single-period
optimising problem as an example, suppose that x1 does not yield utility directly but that a
certain amount must be consumed to facilitate consumption of other goods. Let the
'facilitation' relationship be described by:
(9)
x1 = g(a, x 2…… x n)
where a is a shift parameter. In this case the optimising problem would be
n
(10)
Max U(x 2……x n ) s.t. M -
∑ pixi = 0 and
x1 - g( a, x2…… xn) = 0,
i =1
By substitution this reduces to a simple Lagrangean specification
(11)
L = U(x2……x n ) + λ (M – p1. g(a, x2…… xn ) -
n
p ixi)
∑
i =2
which, by standard manipulation of the optimisation conditions yields
(12)
Ui = λ (pi + p 1 ∂g )
∂ xi
(i = 2……n)
so that
(13)
dU/ λ = (Σ ∂U dxi)/ λ =
∂xi
(p1 ∂g + pi ).dxi [ = Σpi*dxi in the sense of Equaton(4)]
∂xi
n
∑
i =2
n
= p1 ∑
i =2
∂g
dxi +
∂xi
n
n
pidxi = ∑ p idxi
∑
i =2
i =1
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- p1
∂g
.da
∂a
13
In other words, providing the facilitation function does not change, the money measure of a
change in well-being and the associated index of well-being can be written in terms of the
price-weighted quantity changes summed over all goods, not just those included in the utility
function.
If, however, the facilitation function changes, so that more x1 is required to
facilitate consumption of given quantities of the remaining goods, then a cost is imposed.
This cost is measured by the final term in (13) which, on the margin, would be the
price-weighted enforced qua ntity change in x1 (necessary to maintain other consumptions).
Of interest, and perhaps contrary to intuition, using a money metric based upon the standard
price-weighted quantity changes of only those goods included in the utility function would
give an incorrect evaluation. If only those goods are included, they must be weighted by the
‘full’ prices or opportunity costs that take into account the constraint relating x1 to the
quantities of other goods consumed. This assumes, of course, that the quantities of x are
chosen optimally, taking into account this additional constraint.
When arguments of the objective function are rationed or do not appear in the constraints
As indicated above situations will also arise when variables that should be arguments of the
objective function are not the subject of choice by the individual. There are at least two
reasons why this may be so. First the variables may be of a public good (or bad) nature that
the individual ‘consumes’ in externally imposed quantities without any budgetary
implications.
Second, the variables may take quantity-constrained values and the
implications of these constraints may have been substituted into the objective function and
budget constraint, so that the maximisation problem is reduced to choosing the values of the
unconstrained goods xi in order to
(14)
Maximise
U(x1 … xi…x n ; z1… zj …z k) s.t. M -
k
n
j=1
i=1
∑ pjzj - ∑ pixi = 0
where pj may take the value zero for a publicly provided good or other good that has no
budgetary implications.
Both the solution for this problem and the determination of the
appropriate shadow prices for the zj can be obtained directly from the approach suggested in
Neary and Roberts (1980). This involves consideration of a maximisation problem that
would have yielded the same ‘choices’ of the xi and zj in the absence of quantity constraints
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14
(15)
Maximise
U(x ; z) s.t. [M +
k
k
k
or
Maximise
k
n
pj*zj - ∑ pjzj] - ∑ p j*zj - ∑ p ixi = 0
∑
j=1
j=1
j =1
i=1
U(x ; z) s.t. M* -
n
pj*zj - ∑ pixi = 0
∑
j=1
i =1
where the p*j M* are what Neary and Roberts termed virtual prices and income. In this
situation it is easily shown that our money measure of a change in well-being is given by
(16)
dU/ λ =
n
∑
i =1
k
pidxi + ∑ pj*dz j
j=1
In other words, the determination of the appropriate changes in well-being and in the
associated index numbers requires ‘only’ knowledge (or, more reasonably, estimates) of these
virtual prices. While the Neary and Roberts analysis usefully reminds us of what the shadow
price of quantity-constrained ‘free’ goods should, it is perhaps more pertinent to note that this
result (as would be true for model with quantity constraints) is just a further special case of
(4) above.
V
A Review of the Role of Surplus in the Construction of an Index of Well-being
So far we followed the convention of using expenditure as the denominator in converting the
money measure of a change in well-being into an index based upon a ‘proportionate’ change
in the money measure. There are a number of reasons why a review of this practice appears
justified. First, the money measure of a change in well-being is itself a measure of a change
in surplus. Second, an individual only achieves an increase in utility from an activity that
generates an increase in surplus – at the most basic level, individuals will not undertake the
labour that yields access to consumption unless the benefits from consumption outweigh the
disutility associated with that labour. Third, there is a research interest in the equality of
well-being, both specifically in the context of questions of national well-being as well as in
its own right, and because alternative indices of individual well-being may offer different
pictures of the degree of inequality in a particular society.
In this context, however, there is a further issue that merits review and that is to do with the
well-understood characteristic of surplus-based measures, that marginal variations vary with
income. This point can be made more clearly with the aid of a simple illustrative example.
DRAFT VERSION ONLY: MAY 2002
15
Consider the following variation to the standard multiplicative utility function example,
where the choice problem is to
n
(17)
Max.
U=
∑ αi.log x i
s.t xi = 0 or ≥ 1 ∀ i ;
i =1
n
∑ αi = 1; and M i =1
n
p ixi = 0
∑
i =1
The assumption here is that there are some indivisibilities in consumption, although these
minimum units of quantity can be almost as small as we desire. We will however ignore the
effects of indivisibilities for all quantities greater than one and therefore assume the following
‘continuous case’ demand relations are applicable
(18)
xi = α.M/pi
where xi ≥ 1 ∀ i
For simplicity of exposition we shall assume all goods are consumed and note that within the
framework described here the willingness-to-pay for the first unit may simply be given
simply by
(19)
WTPi (1) = αiM = pixi ∀ i
It is instructive now to obtain a measure of the consumer surplus associated with
consumption of the ith good, by allowing for (19) and evaluating the area between the
demand curve and the ‘price line’ by integration of the inverse demand curve as follows
x
(20)
CSi = (WTPi (1) = p ixi) +
∫1 α iM/xi
- (Spending on ith good, p ixi )
= αi.[M. log(xi ) - M. log(1 )] = αiM log(x i )
In this case, summing the consumers surplus across the i goods we there have exactly
(21)
Σ CS i = Σαi.M. log(xi ) = M.Σαi log(xi ) = M.U
The fact that the individual’s ‘aggregate’ consumer surplus in this case is related directly both
to the level of money income and to a measure of utility both reminds us of well-known
limitations in the use of consumer surplus in interpersonal comparisons and is suggestive that
proportionate changes in aggregate surplus may offer a useful alternative basis for an index of
DRAFT VERSION ONLY: MAY 2002
16
well-being. How far the flavour of this result extends to more complex utility functions is the
subject of ongoing research.
Why is all this relevant? For the simple reason that such a measure may present a very
different view of distributional variations in well-being or changes in well-being than
traditional measures. Why might this different view emerge? Possibly, and this is quite
untested, because the difference between the disutility associated with earning access to
additional units of a commoditiy and the marginal valuations of the units so obtained may be
relatively greater for low income than high income individuals.
VI
Intertemporal Optimising Behaviour, Expectations and Happiness
In this final and largely discursive section we briefly consider a number of issues that appear
to be at least partially illuminated by using the type of analysis outlined above. The
intertemporal approach itself immediately highlights the relevance of issues such as the
connections between different types of current consumption and future consumption
possibilities. These considerations lead naturally to the issue of life expectancy. Then again,
as we indicated in our brief survey of research directions, a broad strand of the literature has
been especially concerned with SWB and happiness while a related literature has explored
relations between happiness and income or wealth. In particular observations have been
made of increases in income or wealth being associated with reduced happiness or wellbeing, while overall there appears to be some positive correlation between happiness and
income. In a number of ways the approach suggested above appears to generate results
entirely consistent with the kinds of observation described above.
Life Expectancy
An issue that must be confronted concerns the fact that life is finite and that in general older
persons expect to live for a shorter period than younger people. As Usher noted “One of the
ways we are becoming better off is that we live longer" (p233). It was indicated above that
our general model of utility maximisation can certainly embody intertemporal considerations.
Consumption in different periods can quite simply be related to different x’s while the budget
constraint can easily be expressed in an intertemporal form.
As a first approximation it might be assumed that current and expected future utility only
extends to the expected time of death and that no further pleasure is anticipated after death.
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For those to whom such an assumption is offensive, similar conclusions as reached could
probably be derived from an alternative assumption that undiscounted pleasure after death is
anticipated but that acceleration of death would be heavily penalised. A consequence of
either such an approach is that increased life expectancy will in general lead to increased
well-being as measured.
Within an intertemporal framework one particular issue has been the subject of lively debate
between Usher and Williamson (1984) as well as receiving attention in the recent research by
Dowrick, Dunlop and Quiggin (1994, 2001). How do we take account of consumptions in
one period that increase life expectancy and therefore future consumption? While the analysis
above offers some insights here, further complications that could arise are that life-enhancing
activities may be enjoyable in their own right or previously discussed possibility that some
activities may also lead to increased utility from certain future activities.
A relevant point here is clearly whether an individual knows that an activity will increase life
expectancy.
If this is not known then no special problems arise.
Similarly, if the
implications of consumption of a particular type are understood but neither current nor future
utility is affected in the manner described above, analysis similar to that of the previous
section would appear to be appropriate and similar conclusions follow. An early treatment
dealing with the 'constant consumption over time' case can be found in Hughes (1978),
Cross Country Comparisons
The approach adopted here offers two ways of putting a measure on differences between the
rates of change of well-being across countries. The first yields a weak test of convergence by
comparing rates of growth of well-being as indicated by the Divisia-type measures. Since,
unlike Dowrick et al, no attempt is made to formally benchmark living standards between
countries, the approach here never formally suggests which country has the higher living
standard at any point in time.
A second possibility suggested by the approach adopted above concerns how one might take
into account the impact upon national well-being of changes in life expectancy. As an
alternative to quite simply reporting changes in the mortality tables one could proceed in the
following manner. Changes in an intertemporal measure of well-being flowing directly from
increased life-expectancy are calculated for a number of represent individuals in different
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countries, say aged 10, 20, 30, 40, 50, 60, 70 etc. These changes incorporate increases due to
the impact of utility now being obtained over a longer period of time, but because of the
discounting effects the impacts will obviously differ according to the age of the individual
concerned. When the rates for individuals are obtained, a weighted figure is then derived for
each country taking into account the age distributions in question.
A clear implication of the proposed approach is the importance of life expectancy, and of the
relevance of this to the issue of convergence. A question raised by some is whether separate
account really needs to be taken of factors such as diet, health provision, crime, fear and other
quality of life indicators. The reason for the question is that increased life expectancy may
itself be a good measure of the degrees of quality of life improvement due to such other
factors and indeed, this is the approach adopted by Dowrick et al (2001).
In reality data limitations will prevent consideration of many of the interesting questions
tossed up by theory, especially with regard to the measurement of changes in well-being over
long periods of time. Consumption, hours of work, government spending and possibly
investment may often be the only data series that extend back over periods much in excess of
a hundred years. Certainly there have been increases in the availability of historical data of
reasonable quality, such as that for the United Kingdom due to Mitchell (1988) and more
recent cross-country series such as those presented in Williamson (1995).
Happiness and Expectations
Leaving aside the problems associated with what goods and services to include, there are
some further predictions that would flow from the intertemporal optimising methodology.
One of the more interesting is the obvious conclusion that an individual's perception may be
that their well-being is decreasing even though the conventional income per capita measure
suggests an increase. This would arise in situations not unlike those experienced in many
countries over the last decade or so, when expected real rates of growth have been regularly
revised downward. As an example, assuming a 5% discount rate, a fall in the expected
growth rate from 3% to 2% would reduce the present value of a steady income stream by
around 30% even though current growth remains positive.
Notice however, that this entirely plausible explanation does require recognition that wellbeing does depend upon both our current situation and our expected future. Once behaviour is
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viewed within a proper intertemporal framework a related observation from the behavioural
research, relating optimism to happiness, also becomes completely unsurprising.
Happiness and Memory
Once one accepts the intertemporal choice framework as being the natural and appropriate
model, a whole set of interesting questions are thrown up. These include ideas discussed at
various points above, many of which are not historically new. They include the roles of
education, training, medical expenditures and the like in increasing access to future
consumption, both through increased earning capacity and through increased life expectancy.
The notion of individuals achieving increased efficiency as a ‘pleasure machine’ and
associated notion regarding the question of tastes changing also present interesting challenges
to those who would measure changes in well-being.
The interesting things about all of the examples above is that they are all forward-looking,
although it is true that depending upon ones view point there can also be the backward–
looking element in the sense that consumption in the current period is related to the choice of
activities in the past. There is, however, a further variant on this theme that to our knowledge
has not been widely explored. This involves the role of memory as a source of later utility.
While a natural response to the suggestion that this should be allowed for might be that the
utility function has now become so general as to be of limited use, this would not be how the
business world has perceived the role of memory. A range of products have been developed
which are valued because they complementary to memories, such as cameras, souvenirs,
nostalgia in all forms, novels and films produced for baby-boomers.
This immediately yields a further reason, to add to all the others, as to why the poor, in
general, may be less happy than the rich. The chances that the poor should have such a rich
array of enjoyable experiences to relive (and obtain utility from) as the rich, are presumably
not high. Of course, one says this with care, as it may be that the warmth of a secure and
loving environment in ones childhoods, which may be largely independent of family income,
carries a very high weight in an overall index of well-being. In which case the role of
memory might be in explaining why the distribution of properly measured well-being in is far
narrower than the distribution of wealth. In either case the role of memory is important.
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