Economic analysis of sustainability.∗

Chapter 1 of “Justifying, Characterizing and Indicating Sustainability”.

Geir B. Asheim†

January 31, 2007

∗I thank Jack Pezzey and Bertil Tungodden for helpful comments.

†Department of Economics, University of Oslo, P.O. Box 1095 Blindern, NO-0317 Oslo, Norway

(e-mail: g.b.asheim@econ.uio.no).

Twenty years ago the notion of ‘sustainable development’ was introduced into

the political agenda by the World Commission on Environment and Development

through its report (WCED, 1987), also called the Brundtland Report. The Report

does not give a precise definition of ‘sustainable development’. The quotation that is

usually taken as a point of departure is the following: “Sustainable development is a

development that meets the needs of the present without compromising the ability of

future generations to meet their own needs” (WCED, 1987, p. 43). The Brundtland

Report looks at sustainability both as a requirement for intragenerational justice

and as a requirement for intergenerational justice.

In the contributions included in this book I (and my co-authors) limit the discus-

sion by considering sustainability to be a requirement for intergenerational justice.

The included articles present models where an infinite number of generations follows

in sequence, and where distributional issues within each generation are not explicitly

considered. In all but one chapter, population is assumed to be constant. In such a

context sustainability requires that we, as the current generation, not use more than

our fair share of the resource base. More precisely, we should manage the resource

base such that the wellbeing that we ensure ourselves can potentially be shared by

all future generations.

The notion ‘wellbeing’ includes everything that influences the situation in which

people live. Hence, it includes much more than material consumption. It is intended

to capture the importance of health, culture, and nature. There are two important

restrictions, though: Wellbeing does not include the welfare that people derive from

their children’s consumption. Likewise, only nature’s instrumental value (i.e. recog-

nized value to humans) is included in the wellbeing, not its intrinsic value (i.e. value

in its own right regardless of human experience); i.e., an anthropocentric perspective

is taken. The general rationale behind these restrictions is that there is an argu-

ment to be made in favor of distinguishing the concept of justice applied in a society

from the forces that are instrumental in attaining it. In the present context this

means that it may be desirable to separate the definition of sustainability from the

forces that can motivate our generation to act in accordance with the requirement

of sustainability.

To approach a formal sustainability definition, I follow Pezzey (1997, p. 451) in

saying that development is sustained if the stream of wellbeing is non-decreasing.

Using this term we can then define the concept of sustainable development as follows:

1

Definition 1 A generation’s management of the resource base at some point in

time is sustainable if it constitutes the first part of a feasible sustained develop-

ment. A stream of wellbeing develops in a sustainable manner if each generation’s

management of the resource base is sustainable.

The idea of defining sustainability in this way corresponds closely to what is usually

meant by sustainability, which “basically gets at the issue of whether or not future

generations will be at least as well off as the present generation” (Krautkraemer,

1998, p. 2091). This is not the place to present a survey of the abundance of sustain-

ability definitions; it suffices to stay that the above definition is closely related to the

definition of sustainability proposed by Pezzey (1997). Note that sustainability in

the sense of Definition 1 does not preclude that a generation makes a large sacrifice

to the benefit of future generations, so that its own wellbeing is lower than that of

its predecessor. Hence, sustainable development is a wider concept than sustained

development: While sustained development implies sustainable development, the

converse implication does not hold.

Economic theories of natural and environmental resources usually seek to answer

the following question: How can an efficient management of natural and environ-

mental resources be achieved? The objective is to get the real economy to imitate a

perfect market economy through internalizing external effects and to promote eco-

nomic efficiency through regulating the use of natural and environmental resources

when such internalization is not feasible. Traditionally, many economists have held

the view that, in a perfect market economy, posterity will be made better off due to

accumulation of manmade capital (including accumulation of knowledge). To the

extent that the depletion of natural resources and the degradation of environmental

resources have been explicitly taken into account, these economists have claimed

that, due to rising resource prices and technological progress, new reserves will be

added to existing resources and substitutes to these resources will be made avail-

able. A classic reference for this point of view is Barnett and Morse (1963) (see also

Nordhaus, 1974).

However, in general, this view cannot be defended. At any time the present gen-

eration determines how the resource base is being managed. Given our technological

capacities, it is possible to exploit the resource base to our own advantage—at the

expense of the wellbeing of future generations. That economic efficiency does not

2

necessarily lead to intergenerational fairness was forcefully argued by Talbot Page

(1977) in his book Conservation and Economic Efficiency. He illustrated the issue

by the following analogy: If someone suggested that the ocean fisheries in the Pacific

should be regulated by giving full rights to the entire resource stock to Japan for

one year, to the United States for the next, to Russia for the third year, and so

forth, it would be natural to claim that the country that came first would exploit

the resources to too large an extent. This skepticism would be especially great if the

harvest methods were technologically advanced. Still, if we abstract from the fact

that generations overlap, this is the way a perfect market economy (without market

failure of any kind) allocates natural and environmental resources between the gen-

erations: Future generations’ wellbeing depends on the altruism that we extend to

them as well as our limited capacity to exploit stocks of natural and environmental

resources to our own advantage.

This leads to the following conclusions:

• Generational conflicts will not necessarily be solved in a perfect market econ-

omy. Distributional problems arise because the present generation through its

capital and resource management policy determines the endowment of future

generations.

• A requirement for sustainability, if binding, is a requirement for a more fair

intergenerational distribution. It is not a requirement for an efficient manage-

ment of natural and environmental resources.

Page (1977) contains another analogy—of a sailing ship—which nicely illustrates

this distinction: Sustainability corresponds to setting the rudder according to the

destination, while efficiency corresponds to balancing the sails according to the wind.

The two issues are related: How the rudder is set influences how the sails will have

to be balanced. However, if we care about where we will end up, it is not sufficient

to concentrate all attention on how the sails are balanced.

In the collection of articles included in this book, I (and my co-authors) subject

sustainable development to economic analysis by posing three questions.

(1) Justifying sustainability: From a normative perspective, why is it desirable

for our generation to contribute to the implementation of sustainable develop-

ment? In the analogy of a sailing ship: Why does sustainability correspond

3

to a right destination?

(2) Characterizing sustainability: If sustainable development is implemented,

what does it look like? How do we describe the situation if we are heading for

the right destination?

(3) Indicating sustainability: If we would like to implement sustainable devel-

opment, how can we tell whether development is in fact sustainable? How to

detect if we are off course?

This book consists of three parts corresponding to the three questions posed

above; each part consisting of 6 articles. In the following three sections of the

introduction I give a guide to each part. I also provide an up-to-date but selective

survey of relevant literature and their relation to the included articles.

1 Justifying sustainability

Generations have conflicting interests in the management of the resource base: If the

current generation increases its own wellbeing by exploiting natural resources and

degrading the quality of the natural environment, without making sufficient com-

pensating investments in manmade capital, then the interests of future generations

are undermined.

Can social choice theory guide us in the normative question on how such an

intergenerational conflict should be resolved if all generations gathered behind a veil

of ignorance (Vickrey, 1945; Harsanyi, 1953; Rawls, 1971), not knowing in what se-

quence they would be appear? What kind of criterion for intergenerational justice

would we recommend if we did not know to what generation we belonged and con-

sidered intergenerational distribution from an anonymous perspective? Would we

in such a hypothetical situation argue for sustainable development, thus giving this

concept a normative foundation?

When seeking a normative foundation for sustainability, one must impose some

self-evident condition (or axiom) ruling out present behavior that leads to inequitable

consequences for future generations. A commonly suggested equity condition is

Weak Anonymity (WA). This condition ensures equal treatment of all generations

by requiring that a permutation of the wellbeing of two (or a finite number of)

4

generations not change the social evaluation of the stream. In the intergenerational

context WA implies that it is not justifiable to discriminate against a generation

only because it appears at a later stage on the time axis.

However, equal treatment can be achieved by treating all generations equally

poorly. Therefore, one must also impose some condition that leads to efficiency,

thus ruling out such wasteful policies. A commonly suggested efficiency condition

is Strong Pareto (SP). This condition ensures sensitivity to interests of any one

generation by requiring that a stream of wellbeing is socially preferred to another if

it at least one generation is better off and no generation is worse off.

When applied to a reflexive and transitive binary relation, the combination of

WA and SP is often referred to as the Suppes-Sen grading principle (Suppes, 1966;

Sen, 1970).

In Chapter 3 (which reproduces Asheim et al., 2001), Wolfgang Buchholz, Bertil

Tungodden and I show that the Suppes-Sen grading principle rules out any unsus-

tainable development if the technology is productive. The intuition is simple: Sup-

pose one generation’s wellbeing is higher than the next. If the excess wellbeing of the

first generation were shifted to the second, then by WA the resulting stream would

be equally good in social evaluation. However, since the technology is productive,

such an investment of the excess wellbeing of the first generation will actually have

a positive net return, meaning that the second generation will end up with a higher

wellbeing than what the first generation had in the original situation. Hence, by

SP, there exists a feasible transfer from one generation to the next that leads to a

socially preferred stream whenever the first generation has a higher wellbeing than

the second. This means that only efficient and non-decreasing streams of well-being

can be admissible in social evaluation under WA and SP. Such streams correspond

to sustained—and hence, sustainable—development.

Even after ruling out streams that are not efficient and non-decreasing, the fol-

lowing problem remains: How to resolve intergenerational conflicts that go beyond

the sustainability question? In Chapter 4 (which reproduces Asheim and Tun-

godden, 2004), Bertil Tungodden and I address this problem by imposing further

conditions on the social evaluations of wellbeing streams. We first impose (two ver-

sions of) a preference continuity axiom that establishes a link to the standard finite

setting of distributive justice, by transforming the comparison of any two infinite

streams to an infinite number of comparisons of streams each containing a finite

5

number of generations. We may then supplement WA and SP with well-known

equity conditions from the traditional literature on distributive justice.

One such condition is Hammond Equity, giving absolute priority to genera-

tion i if generation i is worse off than generation j, in comparisons between two

streams where all generations but i and j have the same wellbeing. When added to

our other conditions, this results in lexicographic maximin (or ‘leximin’ ) extended

by an overtaking procedure to an infinite number of generations. Leximin gives

absolute priority to the worst-off generation, but takes in a lexicographic manner

into account the wellbeing of better-off generations to resolve ties between alterna-

tives. Under this criterion of intergenerational justice an efficient and completely

egalitarian stream is the unique optimum if such a stream exists.

Another condition applied in the traditional literature is 2-Generational Unit

Comparability, which also considers comparisons between two streams where all

generations but i and j have the same wellbeing. It requires that there there be a car-

dinal scale of instantaneous utility, along which wellbeing is measured, so that social

evaluation not change if there is a constant addition to the wellbeing of generation i

in both alternatives and a (possibly different) constant addition to the wellbeing of

generation j in both alternatives. When included, this leads to undiscounted utili-

tarianism extended by an overtaking procedure to an infinite number of generations.

Undiscounted utilitarianism maximizes the sum of wellbeing and entails that any

admissible stream is efficient and increasing in productive technologies.1

Hence, both leximin and undiscounted utilitarianism satisfy WA as a condition

for equal treatment, while a commonly used criterion like discounted utilitarianism

does not. It has been suggested (see Asheim and Buchholz, 2003, p. 407, for ref-

erences) that the application of undiscounted utilitarianism imposes unacceptable

demands on the present generations, by requiring it to implement a very high saving

rate in productive economies. This in turn is used as an ethical justification for dis-

counting, as it protects the present generation from the excessive saving that seems

to be implied when future wellbeing is not discounted.

In Chapter 5 (which reproduces Asheim and Buchholz, 2003) Wolfgang Buch-

1Two recent contribution similar to ours, but not imposing our preference continuity axiom, are

forthcoming: Bossert et al. (2006) show the consequences of adding Hammond Equity (and this

condition only) to WA and SP, while Basu and Mitra (2006) show the consequences of adding

(only) a unit comparability condition similar to the one that we use.

6

holz and I question this justification of discounting by showing that undiscounted

utilitarianism has sufficient malleability within important classes of technologies.

Consider any efficient and non-decreasing stream of wellbeing. Then there exists

some cardinal scale of instantaneous utility, along which wellbeing is measured, so

that this stream is the unique optimum according to undiscounted utilitarianism

when this utility scale is used.2

However, if we seek to resolve the intergenerational conflicts that go beyond

the sustainability question, then this may not be an entirely attractive conclusion:

Even if we add to the Suppes-Sen principle conditions sufficient to characterize some

version of undiscounted utilitarianism, we need not limit the kinds of sustainable

development that may be deemed as an acceptable social choice.

The so-called Dasgupta-Heal-Solow (DHS) model of capital accumulation and

resource depletion (Dasgupta and Heal, 1974, 1979; Solow, 1974) is a useful testing

ground for different criteria for intergenerational justice.

• Even under assumptions that ensure that non-decreasing streams are feasible,

discounted utilitarianism forces wellbeing towards a zero consumption level

eventually, independently of how small the positive discount rate is. The

reason is that the capital productivity of the economy approaches zero as

an increasing stock of reproducible capital substitutes for dwindling resource

input. Hence, discounted utilitarianism seems not to respect the interests of

the future generations in this model.

• Undiscounted utilitarianism, on the other hand, leads to unbounded growth if

the function that maps wellbeing into instantaneous utility is strictly increasing

(cf. footnote 2), leading to unacceptable inequality: Why should we save for

the benefit of descendants infinitely better off than ourselves?

• Finally, leximin leads to a constant consumption stream, implying that well-

being at any point at time is at the maximal level compatible with sustainable

development. Such a stream may not be attractive: (a) If the economy is poor

2This result is subject a qualification of mathematical nature: We allow the function that maps

wellbeing into instantaneous utility to be constant beyond some level of wellbeing, while ensuring

that SP is satisfied by means of a lexicographic construction (see Asheim and Buchholz, 2003,

Appendix A, for details).

7

at the outset (i.e. has a small stock of manmade capital), it becomes locked

into poverty. The productive resources of the economy are managed in a sus-

tainable way, but development is not created. (b) If generations actually care

for their children, why should they not be allowed to save on their behalf?

In Chapter 6 (which reproduces Asheim, 1988) I analyze the DHS model and

ask whether there are criteria for intergenerational justice which (i) protect the dis-

tant generations against the grave consequences of discounting, (ii) do not lead to

unacceptable inequalities, and (iii) do not waste the possibilities for development.

Answers to this question can be provided by assuming that each generation’s dy-

namic welfare—according to its subjective preferences—is a convex combination of

its own wellbeing (measured along some cardinal scale of instantaneous utility) and

the dynamic welfare of its children. The term ‘subjective preferences’ is meant to

capture ‘selfish’ altruism, which motivates a generation to contribute to the welfare

of its children because it leads to increased welfare for the contributor. Note that the

subjective preferences are non-paternalistic (in the terminology of Ray, 1987) since

each generation respects the subjective preferences of its children, and thereby, takes

into account the wellbeing of all future generations. If each generation manages the

resource base in order to maximize its dynamic welfare, then the resulting stream

corresponds to a discounted utilitarian optimum. Hence, in the DHS model, this

leads to unacceptable outcomes for future generations.

However, if the criterion of intergenerational justice maximizes the dynamic wel-

fare of the generation that according to its subjective preferences is worst off, then—

as I show in Chapter 6—this leads to streams where wellbeing grows initially when

the economy is highly productive, followed by an eventual phase with constant well-

being, thereby protecting the distant generations against the grave consequences of

discounting. Thus, the possibilities for development are not wasted without leading

to unbounded inequalities, while at the same time the economy’s resource base is

managed in a sustainable manner. This criterion, which is due to Calvo (1978),

includes undiscounted utilitarianism and leximin as special cases since (i) if each

generation on the basis of its subjective preferences does not discount the welfare

of its children, then the criterion of intergenerational justice is of no importance

and we return to undiscounted utilitarianism, while on the other hand (ii) if every

generation discounts the welfare of its children heavily, then the criterion leads to a

8

completely egalitarian stream and no development occurs.

In Chapter 7 (which reproduces Asheim, 1991) I first give a justification of

sustainability, as an alternative to the one presented in Chapter 3.3 I postulate

that one stream is better than another if it has both less inequality (in terms of

Lorenz domination) and a larger sum of wellbeing (measured along some cardinal

scale of instantaneous utility). This amounts to a seemingly weak ethical restriction:

A feasible development is excluded if there exists another feasible development that

increases the total sum to be shared between the generations, and simultaneously,

shares it in a more egalitarian way. I show that a stream of wellbeing must be non-

decreasing in order to be an admissible social choice under this ethical restriction. I

then consider the consequences in the DHS model of each generation managing the

resource base in order to maximize its dynamic welfare, subject to the constraint that

wellbeing is non-decreasing. This turns out to produce the same kinds of streams as

in Chapter 6, where wellbeing grows initially when the economy is highly productive,

followed by an eventual phase with constant wellbeing.

Chapters 3–7 are introduced by Chapter 2 which reproduces Asheim (2005).

2 Characterizing sustainability

Human economic activity leads to the depletion of natural resources and the degra-

dation of environmental resources. Sustainable development requires that manmade

capital (both real and human) be accumulated in order to make up for the decreased

availability of natural capital.

Hartwick’s (1977) rule is a well-known characterization result for sustainable

development of a certain kind, namely development where wellbeing is held constant,

meaning that at all times wellbeing is held at the maximum level consistent with

sustainability. The rule assumes constant population and a stationary technology

and gives the following characterization: In a perfect market economy, wellbeing is

held constant indefinitely if the depletion of natural capital at any time corresponds

3The justification of sustainability provided in Chapter 7 requires that wellbeing is measured

along a cardinal scale of instantaneous utility and that both levels of and differences in such instan-

taneous utility are comparable between different generations. For the justification of sustainability

provided in Chapter 3, on the other hand, it is sufficient that wellbeing is measured along an ordinal

scale, and that levels of wellbeing are comparable between different generations.

9

in market value to the accumulation of manmade capital, i.e., the market value of

net investments is equal to zero.

Note that Hartwick’s rule does not entail that the total value of the capital stocks

is constant along a path where wellbeing is held constant. This would be the case

under the assumption of a constant interest rate. However, constant wellbeing and

a constant interest rate may be inconsistent in the sense that they cannot both be

realized. This is indeed the case in the DHS model of capital accumulation and

resource depletion, where the decreasing capital productivity (as an increasing stock

of reproducible capital substitutes for dwindling resource input) along the egalitarian

stream corresponds to a decreasing interest rate. If the interest rate decreases, then

the capital gains will be positive. In this case, constant wellbeing corresponds to

an increasing total value of the capital stocks. In Chapter 10 (which reproduces

Asheim, 1996) I explore the relation between capital gains and the interest rate along

an egalitarian path.

Hartwick’s rule holds both for an open (national) and a closed (global) economy.

However, particular problems arise when applying Hartwick’s rule for sustainabil-

ity in an open economy: The technology must then include the gains from trade

(see Svensson, 1986). This means that the assumption of a stationary technology

would necessitate that the relative international prices are constant. However, from

Hotelling’s (1931) rule it follows that from a resource-rich economy’s point of view,

the terms-of-trade facing future generations will be more favorable than the one

facing the present generation. This implies that a part of the capital gains on the

unexploited stocks of natural resources can be consumed at the present time with-

out conflicting with the sustainability requirement, thus lowering the required com-

pensating investments. Hence, sustainability for all countries require resource-rich

economies to invest less that their own resource rents, and resource-poor economies

to invest more. In Chapter 9 (which reproduces Asheim, 1986) I derive an analogue

to Hartwick’s rule for open economies and apply it to the DHS model. This analysis

is further developed in Chapter 10.

In Chapter 9 I also show how the combination of capital accumulation, resource

depletion, and a decreasing interest rate in the context of the DHS model have

consequences for how sustainable income is divided between three classes of peo-

ple: workers, capitalists, and resource owners. Resource owners use an increasing

resource price to offset their diminishing stocks and achieve constant consumption

10

while investing nothing. In contrast, the capitalists do all the investing. The reason

is the following: In order to achieve constant consumption they must accumulate

capital, so that the greater capital stock compensates for the decreasing rate of

return, as measured by the interest rate.

Assume constant population and a stationary technology within a general multi-

sector growth model, which may include natural and environmental resources. Hart-

wick’s rule states that if, along an efficient stream, the value of net investments (with

resource depletion included as negative components) is zero at each point in time,

then wellbeing is constant. This rule was established for a very general class of

models in an elegant and important piece of work by Dixit el al. (1980). Dixit el

al. also attempt to show the converse result: If wellbeing remains constant at the

maximum sustainable level, then the value of net investments is zero at each point

in time. However, they succeeded to do so only under additional (and perhaps

not very attactive) assumptions. In Chapter 11 (which reproduces Withagen and

Asheim, 1998) Cees Withagen and I give a direct and comprehensive proof of the

converse of Harwick’s rule in a general setting without having to make any additional

assumptions.4

Formally, the main result of Chapter 11 states that if a constant wellbeing stream

maximizes the sum of discounted wellbeing for some path of discount factors sup-

porting the wellbeing stream, then the value of net investments is equal to zero at all

times. In a critique of our work, Cairns and Yang (2000) argue that, in the context

of streams where wellbeing is held at the maximum level consistent with sustainabil-

ity, discounting “is contrived and inconsistent with the motivation of sustainability

analysis”. They thus suggest that in the DHS model—which is the basic model

in which Hartwick’s rule for sustainability was originally derived—falls outside the

realm for the main result in Chapter 11.

Chapter 12 (which is a corrected version of Withagen et al., 2003a)5 was orig-

inally written as a response to the critique presented by Cairns and Yang (2000).

4The necessity of Hartwick’s rule has subsequently been addressed by Mitra (2002) and Buchholz

et al. (2005).

5The main claim of the original version published as Withagen et al. (2003a) remains valid,

but its proof included incorrect components. By assuming that resource input is important in

production (Mitra, 1978, p. 121), meaning that its production elasticity is uniformly bounded away

from zero, we are able to present an amended version as Chapter 12.

11

In this paper, Cees Withagen, Wolfgang Buchholz and I supplement the analysis of

Chapter 11 by showing that any stream in the DHS model having the property that

the wellbeing of the worst-off generation is maximized satisfies the following: It has

constant consumption and maximizes the sum of discounted consumption for some

path of supporting discount factors. This means that the premise of our general

result on the converse of Hartwick’s rule is satisfied in the case of the DHS model.

The view presented by Cairns and Yang (2000) is based on a misunderstanding

that stems from confounding discounted utilitarianism as a primary ethical objective

with having supporting discount factors in a model where intergenerational equity

is the objective. In Chapter 13 (which reproduces Withagen et al., 2003b) Cees

Withagen, Wolfgang Buchholz and I clarify our approach further and relate it to

the concept of separating hyperplanes. Thus, we connect the characterization of

sustainability with the basic results of modern microeconomic theory, as originating

with Arrow (1951), Debreu (1951) and Arrow and Debreu (1951) in a general setting,

and with Malinvaud (1953) in the setting of dynamic infinite-horizon economies.

Chapters 9–13 are introduced by Chapter 8 which reproduces Asheim et al.

(2003). In this chapter, Wolfgang Buchholz, Cees Withagen and I shed light on

Hartwick’s rule, provide semantic clarifications, and investigates the implications

and relevance of this rule.

3 Indicating sustainability

The question which is posed in part III of this book—“how can we tell whether

development is in fact sustainable”—is often associated with a question posed by

Hicks (1946) in his book Value and Capital : What is the maximum that a population

of an economy can consume in a given period and still be as well off at the end of

the period as it was in the beginning? (cf. Hicks, 1946, p. 172). In an economy

with constant population and a stationary technology, this question can easily be

answered if there is only one aggregate capital good: Wellbeing does not exceed the

sustainable level if and only if the stock of the aggregate capital good is not reduced.

It is, however, a complicated task to answer this question in an economy with

heterogeneous capital. The reason is that if human economic activity depletes the

stocks of natural capital, then it is necessary to determine how much accumulation

of manmade capital is required to make up for the depletion. How can relative prices

12

be found that ‘correctly’ value the different kinds of capital? It is a natural point of

departure to investigate whether market prices—under the assumption of a perfect

market economy with constant population and a stationary technology—can be used

to determine the ‘correct’ relative price between natural and manmade capital: Does

it hold that wellbeing does not exceed the maximum sustainable level if the market

value of net investments is nonnegative, i.e., if the accumulation of manmade capital

at least compensates in market value for the depletion of natural capital? Is a non-

negative market value of net investments sufficient for sustainability?

By Hartwick’s (1977) rule, wellbeing is constant and at its maximum sustainable

level if the market value of net investments is equal to zero at all future times. In the

context of a competitive economy, Hartwick’s rule states that an intertemporal com-

petitive equilibrium leads to a completely egalitarian path if, at all times, the value

of depleted natural capital measured at competitive prices equals the reinvestment

in manmade capital. However, Hartwick’s rule does not entail that a competitive

economy that for the moment measured at competitive prices reinvests depleted

natural capital in manmade capital manages its stocks for natural and manmade

capital in a sustainable manner. For it is conceivable that such reinvestment is

achieved because the competitive prices of natural capital are low. This in turn can

be caused by the economy not being managed in a sustainable manner: If future

generations are poorer than we are, they will be unable to “bid” highly through the

intertemporal competitive equilibrium for the depletable natural capital we manage,

leading to low prices of such capital today.

Hence, although Hartwick’s rule implies that the economy follows an efficient

and egalitarian path if the market value of net investments is equal to zero at all

times, one cannot conclude that if the market value of net investments at some time

is equal to zero, then the wellbeing at that time is sustainable. I show this formally

in Chapter 15 (which reproduces Asheim, 1994) by means of a counterexample in

the context of the DHS model. Thus, since the value of net investments is not a

perfect indicator of sustainability even if the vector of net investments takes into

account the depletion of natural resources and the degradation of environmental

resources, it is likewise not possible to indicate sustainability by comparing the

value of consumption with comprehensive (or “green”) net national product (where

net national product is defined as the sum of the value of consumption and the value

of such a comprehensive vector of net investments).

13

The reason why this does not hold is that the relative price of manmade capital

in terms of natural capital in an intertemporal competitive equilibrium depends on

the entire future equilibrium path. Or in the words of Pezzey and Toman (2002) in

their discussion of my 1994 article:

“. . . changing an economy from unsustainability to sustainability changes all its

prices. Sustainability prices and sustainability itself are thus related in a circular

fashion: Without sustainability prices, we cannot know whether the economy is

currently sustainable; but without knowing whether the economy is currently

sustainable, currently observed prices tell us nothing definite about sustain-

ability. In particular, net national product . . . equals the maximum sustainable

level of consumption only if an economy is already at a constant consumption

path.”

These insights entail that only approximate indicators of sustainability can be de-

rived from observable market prices, even in an economy implementing an intertem-

poral competitive equilibrium without imperfections of any kind.

One approximate indicator of sustainability takes the following quotes from Hicks

(1946) as its point of departure. After considering the possibilities of changing

interest rates and changing prices, Hicks (1946) writes on p. 174:

“Income No. 3 must be defined as the maximum amount of money which the

individual can spend this week, and still be able to spend the same amount in

real terms in each ensuing week”.

Then, on p. 184:

“The standard stream corresponding to Income No. 3 is constant in real terms

. . . . We ask . . . how much he would be receiving if he were getting a standard

stream of the same present value as his actual expected receipts. This amount

is his income.”

In an economy where wellbeing depends on a single consumption good, this concept

of income can be defined as the constant level of consumption with the same present

value as the actual future stream of consumption. In Chapter 16 (which reproduces

Asheim, 1997) I show how comprehensive net national product must then be adjusted

for anticipated capital gains and interest rate effects in order to measure this kind of

14

Hicksian income. Unfortunately, this analysis is hard to generalize to the empirically

relevant case of multiple consumption goods.

However, the Hicksian question—what is the maximum that a population of an

economy can consume in a given period and still be as well off at the end of the

period as it was in the beginning—can be interpreted in an alternative manner. One

important alternative is to associate “as well off” with the level of dynamic welfare,

e.g., of the kind discussed in Section 1 of this chapter, entailing that dynamic welfare

corresponds to a discounted utilitarian welfare function. In this case it follows from

Weitzman (1976) (by combining his (10) with the equation prior to his (14)) that

dynamic welfare is improving if and only if the value of net investments is positive.

Although Weitzman (1976) appears to be the first to show formally that the

value of net investments has such welfare significance, his seminal paper emphasizes

the following related result: Increasing real net national product indicates welfare

improvement if the constant discounting of a utilitarian welfare function applies to

a single consumption good, or to a linearly homogenous aggregate of a vector of

consumption goods. Weitzman’s result is remarkable—as it means that changes in

the stock of forward looking welfare can be picked up by changes in the flow of the

value of current net product—but strong assumptions are invoked.

Fortunately, the assumptions can weakened as long as we stay within the setting

where national accounting is comprehensive so that the vector of net investments

takes into account the depletion of natural resources and the degradation of environ-

mental resources. The result that welfare improvement is indicated by (i) a positive

value of net investments and (ii) an increasing real net national product holds

• even if the constant discounting of a utilitarian welfare function does not apply

to a linearly homogenous aggregate of a vector of consumption goods. This is

shown by Martin Weitzman and me in Chapter 17 (which reproduces Asheim

and Weitzman, 2001) under the provision that net national product is deflated

by a consumer price index.6

• even if dynamic welfare does not correspond to a discounted utilitarian welfare

function. This is shown by Wolfgang Buchholz and me in Chapter 18 (which

6See Sefton and Weale (2006) for an analysis which demonstrates the importance of consumer

prices indices in the context of national accounting.

15

reproduces Asheim and Buchholz, 2004) under the provision that dynamic

welfare is maximized.

Chapter 18 also applies the DHS model of capital accumulation and resource deple-

tion to illustrate how a positive value of net investments and an increasing real net

national product can be used to indicate welfare improvement when the economy has

other objectives than discounted utilitarianism, e.g., objectives which incorporates

a concern for sustainability.

In practical applications, a host of different problems makes it hard to use the

indicators above for determining whether dynamic welfare is increasing.

The assumption that technology is stationary means that technological pro-

gress is captured by capital components that measure accumulated knowledge. The

change in these components must be included in the vector of net investments and

valued. How restrictive this assumption is, relates closely to a second problem,

namely that not all investment flows can be valued given the available price in-

formation. This applies not only to accumulated knowledge, but also to stocks of

natural and environmental capital. A third problem is related to the fact that our

capital and resource management does not have deterministic consequences.

Finally, if we allow for growth in population, then—even if we assume that an

aggregate capital good exists—it is inappropriate to require that the per capita cap-

ital stock be non-decreasing if the rate of population growth varies over time. If,

e.g., the present generation is half as large as all future generations (i.e. population

is constant beginning with the next generation), then sustainability does not require

that the present generation accumulates the stock of the aggregate capital stock to

a size twice as large as the one it inherited. Because this would leave the current

generation at a level of per capita wellbeing which is lower than that of later gen-

erations. In Chapter 19 (which reproduces Asheim, 2004) I discuss the meaning

of sustainability and welfare improvement under population growth and present a

general analysis of how to indicate welfare improvement with a changing population.

The analysis of Chapters 17–19 shows that a positive value of net investments

(appropriately adjusted if technology is not stationary or population is growing)

indicates welfare improvement. Returning to the discussion of Chapter 15, we recall

that a non-negative value of net investments is not a sufficient condition for sustain-

ability, entailing that increasing dynamic welfare does not ensure that wellbeing is

16

below the sustainable level. However, we have not addressed the question whether

it is a necessary condition: Does a decreasing dynamic welfare imply that wellbeing

exceeds the sustainable level? Pezzey (2004) demonstrates that this is indeed the

case under discounted utilitarianism, thereby showing that the welfare analysis of

Chapters 17 and 19 can be used as a one-sided sustainability test.

Chapters 15–19 are introduced by Chapter 14 which reproduces Asheim (2003).

In this chapter, I emphasize the role that different assumptions play for the various

results in welfare and sustainability accounting.

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