National accounts can be adjusted to reflect depletion of natural capital.  There are various ways to do it, none simple.

Gross National Product (GNP), as is very well known, has many limitations as an economic measure.  One is implicit in the word ‘gross’.  Whatever its merits as a measure of economic activity, the fact that GNP makes no allowance for depletion of capital renders it unsuitable for use in assessing either economic or environmental sustainability.  A natural step, therefore, is to focus in addition on a measure which does take into account depletion of assets, that is, Net National Product (NNP).  But how exactly is NNP to be defined?  Here I will consider five possibilities.  First however a few preliminaries.

I shall address NNP at a high level, ignoring ignore various secondary considerations that exercise statisticians in measuring economic aggregates.  There will be no mention for example of imports and exports, inventories, government services, or taxes and subsidies.  My aim is to focus on key issues regarding NNP in the context of sustainability. 

National economic statistics often highlight Gross Domestic Product (GDP). GDP is a territorial concept: it includes all the output produced within a country, regardless of who owns the means of production or who receives the income from its sale.  GNP, by contrast, also includes the output of foreign investments owned by a country’s residents, but excludes that of inward investments by residents of other countries.  A similar distinction may be made between Net Domestic Product (NDP) and Net National Product (NNP), although when we are concerned with natural capital that no one owns, we can hardly do other than include it on a territorial basis.  Here I shall focus on the latter simply because it is that – sometimes termed Green NNP – which features most often in the literature on sustainability. 

All the aforementioned economic aggregates are flow concepts.  They are typically calculated for a period, often a year, sometimes a month or quarter, although often we are less interested in their magnitude than in the percentage change from one period to another.  However, a flow can also be expressed mathematically as an instantaneous rate, and for some purposes, especially when concerned with long-term sustainability, it can be helpful to do so.  There is a well-defined relationship between the two approaches using elementary calculus. 

GDP and GNP are typically expressed in monetary units derived from market prices.  When considering a series of periods, adjustments are made for changes in the price level relative to a chosen base period.  NNP has also been expressed in monetary terms, but it can also be convenient to use alternative units as will be discussed below. 

For our purposes we can represent GNP and NNP by the following formulae:

GNP  =  Σp_jC_j + Σq_kI_k …… (F1)

NNP  =  Σp_jC_j + Σq_kΔK_k ……  (F2)

where the C_j are quantities of consumption goods, and the p_j and q_k are the unit values of consumption goods and capital goods respectively.  The difference between these formulae is in their treatment of capital goods: for GNP we include only gross investment I_k, while for NNP we include net changes ΔK_k. All five of our NNP concepts exemplify formula (F2).  They differ only in the scope of the capital goods included and the bases of the unit values.

The aggregate capital term in formula (F2), Σq_kΔK_k, may be either positive or negative.  If it is positive, then the capital stock has increased, albeit with the important caveat that reductions in some capital goods may have been more than offset by increases in others.  That is a situation which, if continued in future periods, may be consistent with long term sustainability.  If it is negative, however, then the capital stock has been depleted and, other things remaining equal, the reduction in capital stock will reduce the productive capacity of the economy, which will not be sustainable in the long term. Looking at this another way, a plausible condition for the possibility of sustainability is:

Σq_kΔK_k >=  0  …… (F3)

from which, using (F2) above, we may infer:

Σp_jC_j <=  NNP …… (F4)

From inequality (F4) we can see a potential significant role for NNP: it could perhaps sets an upper limit on how much can be consumed in an economy, consistently with its long term sustainability. However, the condition will not do as it stands.  Other things are unlikely to remain equal.  Technological progress may make the depleted stock of capital more productive.  A change in the relative prices of different capital goods could switch (F3) and therefore (F4) from true to false or vice versa.  And most fundamentally, the significance of NNP must depend on how it is defined.

1. Conventional NNP

Most countries prepare national accounts broadly in accordance with the System of National Accounts (SNA), an international standard endorsed by the UN and other bodies.  The SNA specifies, among other things, what kinds of assets are to be included, how they are to be valued, and how depreciation and depletion are to be assessed.  Conventional NNP is a convenient term for NNP calculated according to these principles.  For the US in 2025, for example, GNP was 30,846 (billion US$), capital consumption 5,055, and NNP 25,791 (1).

In respect of natural capital, the SNA states that “not all environmental resources qualify as economic assets” (2).  It specifies two conditions for such resources to qualify.  They must be owned, and they must be capable, currently or in the near future, of yielding economic benefits to the owner (3).  These definitions exclude quite a lot of natural capital, not only those fisheries, forests and minerals which are not subject to ownership rights, but also owned biological and mineral resources which are not currently capable of yielding economic benefits to the owner but which may eventually become so following technological progress or changes in relative prices.  Also excluded are the atmosphere, the high seas, and ecosystem assets (4).

Within the SNA framework’s treatment of owned natural resources, no value is attributed to benefits accruing to parties other than the owner (5).  A forest, for example, is treated primarily as a source of timber for sale by the owner.  Sales of other forest products would also be relevant, as would income from charges, if any, for recreational access.  But other ecosystem services generating benefits to society but no income to the owner, of which more below, have no bearing on its treatment in conventional national accounts.

These relatively narrow definitions limit the issues to be addressed in asessing NNP, largely avoiding any need for contentious valuation techniques such as we will consider below.  The main issues arising relate to allocations over time, such as the spread of depreciation over the life of a produced asset, and the pattern of growth of an owned renewable resource.  The scope of judgement required is much less than for the other NNP concepts we will now consider.  Conventional NNP is relatively easily measurable; its limitation is that it invites a focus on what is measurable rather than what is really important in assessing long term sustainability.

2. NNP With Natural Resources at Known Market Value

For this NNP concept we drop the requirement that only owned assets are to be included.  In addition to those assets included in conventional NNP, we consider all unowned assets within the area of a country’s jurisdiction, including its maritime Exclusive Economic Zone, whether owned or not. But such unowned assets are included in NNP only if their values can be estimated with reasonable certainty by reference to actual market prices. 

The simplest application of this concept is to non-renewable natural resources such as minerals.  Suppose the underground stock of a certain mineral, not owned by anyone, has been depleted in a period by X tonnes, and its market price is P per tonne.  Whether the mineral is sold directly to consumers or to manufacturers producing other goods for sale to consumers, the value PX will be included within consumption.  With conventional NNP, that is all; there is no adjustment to reflect the depletion of the stock of mineral.  With this NNP concept, however, the value PX is also deducted within the capital account. 

In a straightforward case, the deduction from capital will exactly offset the addition to consumption, so that the overall effect on NNP will be nil.  But if we are concerned with sustainability, that is surely the result we want?  To count the consumption but ignore the depletion yields a figure which, whatever its other merits, is of no relevance in assessing sustainability.  Of course matters are usually not quite so straightforward.  Perhaps, after extraction, the minerals are processed in a way which adds value, so that the addition to consumption is more than PX.  Perhaps they are used in the production of capital rather than consumer goods, so that the depletion of the mineral is offset by the extra capital goods.  In such cases the overall effect on NNP will not be nil.  But the principle remains: the depletion of the mineral should be recognised within NNP.

For a renewable natural resource such as a forest or fishery the calculation must also allow for the natural regeneration of the resource.  Suppose the harvest of timber or fish is X tonnes while the natural growth is Y tonnes, and the market price is Q per tonne.  Then we can include in NNP a deduction of Q(X – Y) or, if the natural growth exceeds the harvest, an addition of Q(Y – X).  Again, that surely gives a more meaningful figure than if we ignore both the harvesting and the natural regeneration?

That may seem fairly simple, but further thought suggests various possible complications.  What should we do if the market price of a resource changes during a period?  The change might be because of a shift in demand, as for example when a new technology creates a demand for a mineral that was of little use before, or renders a previously vital mineral redundant.  (An interesting thought experiment would be to consider how such an NNP concept would have applied to early human development during the transitions from stone tools to bronze and then iron.)  A change in the price might also be due to a change in supply, with the price of a resource rising as it is depleted, becoming scarcer and perhaps more difficult to extract.

One approach would be to apply the average price over the period to the change in stock.  But where the price of a resource either rises sharply or falls sharply because of a new technology, to focus on the change in stock would be to ignore the elephant in the room.  In those circumstances, the quantity of most interest is surely the consequent change in value of the whole stock of the resource?  Arguably, the quantity to be included in NNP for a period should be:

(Closing stock x Closing price) – (Opening stock x Opening price)  …… (F5)

If however a price change is a consequence of depletion of a resource, then such an approach would surely be inappropriate?  To see this, consider a scenario in which the relevant elasticities result in a price increase that exactly offsets the effect on total stock value of the depletion, so that formula (F5) equals zero.  In respect of depletion of that resource, therefore, there would be no deduction within NNP, despite this being just the sort of situation in which we would expect a deduction if NNP to be of use in assessing sustainability.

A further complication for renewable resources is that a focus on tonnes of natural growth within a single period is arguably too narrow.  Suppose many trees have been planted during the period, in a location where they can be expected to grow well in future years.  That is surely a relevant consideration in assessing sustainability?  But young trees take time to become established: a plot of tree growth over time typically shows an S-shaped curve (6), so that the additional tonnes in the first year are negligible.  Similarly, a fish re-stocking project may have a modest effect on stocks, measured in tonnes, in the first year, and much larger effects in subsequent years in which the new fish have had time to mature and reproduce. 

The application of this NNP concept is thus far less straightforward than it may initially appear.

3. NNP Including Non-Market Values of Natural Resources

Our second concept, though broader than the first, still ignores the very broad class of values unrelated to, or only indirectly related to, market prices.  Forests, for example, can provide benefits for which there is rarely a market price, including flood control, air and water purification, carbon sequestration, support for biodiversity, and recreational opportunities.  The value of such benefits can often be assessed using various techniques of non-market environmental valuation, including revealed preference and stated preference methods, and also integrated approaches such as the DICE model (7), with broadly the former more relevant to localized benefits and the latter for contributions to global benefits such as carbon sequestration to mitigate climate change.

Other examples of natural resources providing non-market benefits include grassland (livestock feed, biodiversity, recreation), wetlands (flood control, water purification, carbon sinks, biodiversity, recreation), mangroves and reefs (coastal protection) and insects (crop pollination).  Our third NNP concept, therefore, includes deductions for depletion not only of natural resources having a market value but also of those which can be valued only via non-market valuation techniques. 

This concept is, in a sense, comprehensive: it takes account of all losses of natural resources, whether or not they are owned, and whether or not they have a market value.  It is however very far from simple.  Since it includes all the same deductions as the second concept, it shares all its complications.  There are also new complications arising from the greater range of assets and benefits to be considered and the use of non-market valuation techniques.  Collection of the quantity and variety of data required would be extremely demanding.  In the case of forests, tonnage may be a good basis for assessing their benefits as a source of timber and via carbon sequestration, but assessment of their other benefits including flood control, biodiversity and recreation is likely to require different data.  Assessing the benefits of grassland and wetlands may require data on seasonal changes as well as annual aggregates.  The pollination benefits of insects will depend on the mix of species as well as the overall population.  These are just a few examples. 

In some cases the benefits of natural resources are partly or even wholly offset by harms they cause.  Forests in cold or dry locations can be so slow-growing that the climate benefit from their carbon sequestration is offset by the climate harm from their low albedo and consequent high absorption of heat from sunlight (8).  In locations where flooding is not a risk, trees can also absorb so much water that river flows become insufficient to meet the needs of downstream agriculture and wildlife.  Forests can also cause harm through fire risk when near  human settlements, and by providing habitats for predators when near grazing livestock.  Wetlands are a source of methane, a powerful greenhouse gas, and can be a breeding-ground for pests and disease vectors including Anopheles, the mosquito which transmits malaria.  Insect populations may include a mix of beneficial and harmful species.  Deductions for depletion of natural resources need to take account of reductions in such harms as well as lost benefits.

Non-market valuation techniques are complicated to apply and yield, at best, only approximate estimates of value.  In some cases they are contentious: there are wide differences of opinion among economists as to the usefulness of stated preference studies (9) and regarding the appropriate rate of discounting of future benefits to be used in integrated approaches (10).

In many case, the benefits and costs of ecosystem services are context-dependent.  A couple of examples will illustrate what this means.  Suppose we estimate that a year’s growth of a forest has sequestered so many tonnes of carbon dioxide. To value that sequestration (as one component of the overall change in value of the forest) we might use an estimate of the social cost of carbon.  But the social cost of carbon is not fixed: it depends on a whole range of variables including the degree to which households around the world have adopted air-conditioning and its cost and efficiency.  Suppose also we estimate that the forest growth has reduced river flow by so much, and estimate the cost (as another component of the overall change in value of the forest) in terms of reduced harvests to downstream farmers.  But such reduced harvests again depend on a whole range of variables including crop selection, in particular the availability and degree of adoption of drought-resistant varieties. 

One implication of context-dependency is that the data requirements for estimation of changes in the value of a natural resource can be very large.  Another is that a change in context during a year will affect not only the value of that year’s change in the resource: it also affects the value of the whole stock of the resource.  If more households adopt efficient air conditioners, for example, then (other things being equal) the value of the carbon sequestered by a forest in previous years is diminshed.

My conclusion that the application of the second NNP concept is complex thus applies even more strongly to this third concept.

4. NNP based on Shadow Prices within a Forecast to Infinity

This NNP concept is radically different from any of the three we have considered, although it still fits the pattern of formula (F2) above, suitably interpreted.  My presentation here is based on an influential paper by Dasgupta & Maler (2000) (11). 

In order to calculate this NNP concept we first need to consider what Dasgupta & Maler term social well-being or social welfare.  This is not social welfare as most people would understand it, referring to the well-being of a society at a particular time.  It is intertemporal social welfare, calculated from the present into an indefinite future: mathematically, the discounted present value of the stream of social utility from now to infinity. Expressing utility as an instantaneous rate enables this to be conveniently formulated in terms of integral calculus. 

The stream of utility depends in turn on the progress of the economy.  Dasgupta & Maler define an economic programme in terms of seven variables including consumption, labour and man-made capital.  The other four variables all relate to natural resources: their stock, their rate of use in production, expenditure to enhance the stock (including mineral exploration and pollution clean-up), and a variable related to the stream of such expenditure to date  (12).  All seven variables are aggregates: the model does not distinguish between different consumption or capital goods.  Furthermore, the consumption and man-made capital goods are one and the same, an “all-purpose, non-deteriorating durable good” (13).  These unrealistic assumptions can perhaps be defended as useful for purposes of exposition, facilitating a focus on key properties of the model. 

The rates of change of the stocks of man-made capital and of natural resources are assumed determined by the other variables.  Looking at it another way, changes are assumed not to depend on calendar time (14).  I take this to mean that, for example, use of natural capital could change pro rata to its total stock, but not in response to a change in some exogenous variable such as population or technology.

What economic programme an economy will follow will depend on the initial stocks of capital and resources, the institutional structure and the behaviour of various agents.  But suppose we have information and assumptions about all that, so that we can make a forecast of an economic programme from the present to infinity.  We can then calculate social welfare, defined as above.  Call this W_t, where t is the present time.

The key idea of this NNP concept is to take the current unit value of capital to be the marginal increase in this W_t that would result from one extra unit of initial stock of capital.  Similarly, the unit value of the natural resource is the marginal increase in W_t from one extra unit of resource.  Dasgupta & Maler refer to the unit values determined in this way as “accounting prices” (15), although ‘shadow prices’ is perhaps a more familiar term.  But leaving the terminology aside, what this means is that unit values are determined without any reference to market prices.  Another consequence is that those values are expressed in units of utility.

For consistency with the above, NNP must be expressed as an instantaneous rate measured in utility units.  Adapting slightly our formula (F2) above, we can write it as:

NNP_t =  p_tC_t + q_KΔK_t + q_RΔR_t …… (F6)

Here C_t is the instantaneous rate of consumption and ΔK_t and ΔR_t are the instantaneous rates of change in capital and resources, all at time t.  q_K and q_R are the shadow prices per unit of capital and resources, derived as above.  p_t is the marginal utility of consumption.  This is admittedly a simplification of NNP as defined by Dasgupta & Maler, who also include for example a component for leisure (16), but I think it captures its essence.

Dasgupta & Maler present this NNP concept as “properly defined” (17), seeming to imply that their definition is the correct one.  I can see no basis for that claim: it is just one more possible definition, quite an ingenious one, but like others with both merits and limitations and, to be fair, they do attempt to set out both.  Their analysis leads to the conclusion that NNP, so defined, is unsuitable for use in comparing social welfare over time or between countries.  They also show that in general it lacks a property that has sometimes been claimed for green NNP, that of being equal to constant-equivalent utility, that is, to the constant rate of utility which, if sustained forever, would have the same discounted present value as the varying stream of utility implied by the forecast economic programme (18).  This claim appears to have been first made by Weitzman in 1976 (19), and was included in Nature’s Numbers (1999), a report by a panel of US experts, where it was described as “the output-sustainability correspondence principle” (20).  It was because the claim has had a degree of influence among economists and perhaps others that Dasgupta & Maler were at pains to show that, on their definition of NNP, it does not hold. 

So what are the merits of this NNP concept?  One is that in principle it can be calculated for any economic programme to infinity.  Unlike some other economists who have formulated such programmes, Dasgupta & Maler do not rely on an assumption that the programme is optimal.  A second merit is that shadow prices calculated as above are inherently forward-looking.  Subject to the reliability of the underlying forecast economic programme, they take account of the welfare effects from the present to infinity of extra units of capital or resource.  They give full weight, for example, to the future benefits from newly planted trees that may grow only slowly at first.  In that respect this NNP concept goes beyond the valuation techniques of our third NNP concept above.  A further merit claimed by Dasgupta & Maler is that this NNP concept can be used to evaluate short-term (that is, temporary) economic policy reforms.  Specifically, such a reform increases intertemporal social welfare if and only if it results in an increase in NNP (21).

It is instructive to consider what would be involved in using this property to evaluate a policy reform.  We would need to calculate what we may call NNP₀, based on an economic programme without the reform, and also NNP₁, based on an economic programme with the reform, and then compare the two.  Each economic programme would cover the whole period from the present to infinity, and each would require a comprehensive forecast.  Even if the policy reform is temporary and on a modest scale, it would be naïve to assume that the programme supporting NNP₁ would differ only marginally from that supporting NNP₀ (recall the ’butterfly effect’ (22)).

This exemplifies a general difficulty with this NNP concept.  Any estimate of NNP is completely dependent on  the underlying forecast economic programme, and any conclusions that may be drawn from such estimates rest on the dubious foundations of forecasts from the present to infinity.  We simply do not have the information that would be needed to make such forecasts (23).  Moreover, if we did have that information, we would surely want to draw conclusions about policy reforms or sustainability directly from the forecasts, rather than taking the extra step of calculating NNP estimates? 

Further difficulties with this NNP concept are its dependency on assumptions about the form of the utility function and the discount rate to be applied to future utility.  Dasgupta & Maler are able to avoid making assumptions on these matters because their paper is at a highly theoretical level.  Any attempt actually to calculate NNP for a particular economy would require specific assumptions, which would inevitably be contentious. 

Finally, an odd feature of Dasgupta & Maler’s presentation is their characterisation of the single consumption and capital good as non-deteriorating.  Since depreciation of man-made capital is the main difference between GDP and conventional NNP, it seems rather surprising that any attempt to define a more comprehensive NNP concept should exclude this important aspect of economic reality.

5. NNP tailored to Equal Constant-equivalent Utility

We have seen that the concept of constant-equivalent utility (CEU), defined above, has been of interest to a number of economists interested in sustainability.  Although the fourth NNP concept is not in general equal to CEU, a slightly different NNP concept does have this property in at least a large class of cases.

We retain the framework of a forecast to infinity with unit values of assets calculated as shadow prices.  We generalise from Dasgupta & Maler’s specification to allow depreciation of the capital asset.  But we impose one restriction. The utility function must be linear.  Thus we rule out any utility function exhibiting diminishing (or increasing) marginal utility.  That assumption was implicit in Weitzman’s paper, which did not use the term ‘utility’ but took intertemporal welfare to be the discounted present value of the stream of future consumption (24).  But it lessens the interest of this NNP concept, for it is generally considered that diminishing marginal utility is evidenced by many people’s behaviour and therefore that, at the level of a whole economy, continuing growth exhibits diminishing returns to aggregate utility.

It is worth noting that we do not require that the underlying forecast be based on an optimal programme.  That is significant because Weitzman’s presentation of the equality between NNP and CEU did limit itself to the case of optimality (25).

A proof of this proposition, with an exact characterisation of the conditions under which it holds, is beyond the scope of this post.  Those wishing to explore the topic further are referred to Asheim (2003) (26).  What I offer below is a numerical illustration.

We follow Dasgupta & Maler in assuming a single capital and consumption good, but specify that capital K depreciates at an instantaneous rate 0.1K. There is a single renewable natural resource, with natural growth of the stock S at a rate 0.2S.  The initial stocks of capital and the natural resource are respectively K₀ = 1000 and S₀ = 100.  Output Y of the single good is determined by a Cobb-Douglas production function Y = K^0.5R^0.5 where R is the rate of use of the single natural resource. Labour input and technology are assumed constant so are not represented in the function.  Utility U is the simplest possible linear function of consumption, that is, U = C.  The discount rate is assumed to be 5%.

The time path of the economy within this framework is determined by two decisions: use of the natural resource is at a fixed rate, R = 10, and consumption is equal to output, C = Y.  These decisions are fairly obviously sub-optimal: the natural growth of the resource would sustain a fixed rate of use of 0.2 x 100 = 20, while holding consumption to less than 0.9Y would allow growth rather than depletion of the capital stock.  The point of the illustration, however, is to show that NNP is equal to CEU despite the absence of optimality. 

From the above we can infer the equation of motion of capital:

dK/dt  =  Y – C – 0.1K  =  – 0.1K …… (F7)

Given also the initial stock K₀ = 1000, it can be shown that (27) the time path of capital is:

K_t =  1000e^-0.1t …… (F8)

With use of the resource fixed at R = 10, the time path of output is:

Y_t =  (1000e^-0.1t)^0.5(10)^0.5 =  100e^-0.05t …… (F9)

Given that U = C = Y together with the 5% discount rate, the time path of discounted utility is:

U_t =  (100e^-0.05t)e^-0.05t =  100e^-0.1t …… (F10)

We now need social welfare W₀, the present value of the stream of discounted utility from the present to infinity at the above rate.  Using integral calculus, it can be shown that this is:

W₀ =  1000 …… (F11)

The next step is to find the accounting price of capital q_K.  We rework formulae (F8) to (F11) on the assumption of one extra initial unit of capital, that is, if K₀ = 1001.  So in (F8) and (F9) we replace 1000 by 1001, and in (F10) we replace 100 by 1001^0.510^0.5 = 10010^0.5 which is almost exactly 100.05.  In (F11), 1000 then becomes 1000.5.  The accounting price is then the difference between the new and original values of V₀:

q_K =  W₀(K₀ = 1001) – W₀(K₀ = 1000)  =  1000.5 – 1000  =  0.5 …… (F12)

In principle the accounting price of the resource q_R requires a similar calculation.  But given our specific assumptions, with the natural growth of the resource exceeding the rate of use, it is apparent that an extra initial unit of resource would make no difference to W₀.  So we have simply q_R = 0.

We can now calculate NNP at time t = 0 by applying formula (F6) which for convenience is shown again below:

NNP_t =  p_tC_t + q_KΔK_t + q_RΔR_t …… (F6)

Given U = C, the marginal utility of consumption p₀ is 1.  Consumption C₀, which equals output, is 100 (from (9) above).  The rate of change of capital ΔK₀ is -0.1K₀ (from (7)) which is -0.1(1000) = -100.  Since q_R = 0, so does q_RΔR₀.  So we have:

NNP₀ =  1(100) + 0.5(-100) + 0  =  100 – 50  =  50 …… (F13) 

What about constant-equivalent utility CEU?  Suppose CEU = x.  To find the value of x, we need to set the discounted present value from the present to infinity of a stream of utility at rate x equal to V₀ = 1000, the discount rate being 5%.  Using integral calculus it can be shown that:

CEU₀ =  x  =  0.05(1000)  =  50 …… (F14)

So we have shown that:

NNP₀ = CEU₀ = 50 …… (F15)

Note that CEU is at most times either less or more than actual utility.  From (9) above we can infer that U₀ = Y₀ = 100, but that U_t falls gradually over time, passing 50 at around t = 15 and falling below 1 around t = 90. 

Given the possibility of such large differences at particular times between CEU and actual utility, it must surely be concluded that CEU is of limited relevance in assessing sustainability?  The most that can be claimed for it can be stated as follows (28):

Let CEU* be calculated on the basis of an optimal programme from the present to infinity. Then if the present rate of utility U₀ exceeds CEU*, or equivalently exceeds NNP calculated on the basis of the same programme, it cannot be indefinitely sustainable.

Why is this so?  Simply because if a rate equal to U₀ could be sustained indefinitely, it would imply that the programme was not optimal.  This seems to be the best we can do in developing what we described in our preliminaries as a potential significant role for NNP into a valid sustainability criterion.

But this result is of limited significance for two reasons.  One is the enormous difficulty of determining, for a real economy with all its complexities, whether a forecast is optimal.  The other is that it tells us nothing about sustainability when U₀ is less than U*. Perhaps for example CEU at any rate equal to U₀ or greater would require an initial period in which utility is less than U₀ while building the capital stock to support higher levels of utility in the long term.

This fifth NNP concept thus has three major limitations.  It shares with the fourth concept all the difficulties implicit in reliance on forecasts from the present to infinity.  It requires the unrealistic assumption of a linear utility function.  And its apparent advantage, that it can make NNP equal to CEU turns out to be of very limited significance.

Conclusion

It is not the intention of this post to advocate for any one of these NNP concepts. Each one has its limitations.  I will not go so far as to say that none of them should ever be used, but it can be inferred from the above analysis that all but conventional NNP are extremely challenging to estimate and all, including conventional NNP, have considerable potential to mislead.  The well-known limitations of Gross National Product (GDP) should not lead anyone to the view that NNP, however defined, constitutes a simple and meaningful alternative as a measure of either welfare or sustainability.  Any use of NNP should be undertaken with full awareness of and transparency about the limitations of the particular concept used.

Notes & References

1. Federal Bank of St Louis, Table 1.7.5 (2025) https://fred.stlouisfed.org/release/tables?rid=53&eid=41999&od=# Accessed 14/10/2026 (figures may be subject to revision)
2. UN Statistics Division, System of National Accounts 2025 https://unstats.un.org/unsd/nationalaccount/sna2025.asp Click towards top right on “System of National Accounts 2025 (Pre edit version) in searchable PDF format”, para 11.183
3. As (2) above, paras 11.184-5
4. As (2) above, para 11.22
5. As (2) above, para 35.33
6. Lowry Z (2021)  How fast do forests grow?  https://thetimberlandinvestor.com/how-fast-do-forests-grow/
7. Wikipedia – DICE model  https://en.wikipedia.org/wiki/DICE_model See also (10) below, section headed Integrated-Assessment Modelling p 442 ff.
8. Hasler N, Williams C A, et al (2024) Accounting for albedo change to identify climate-positive tree cover restoration  Nature Communications 15, Article 2275 (2024)  https://www.nature.com/articles/s41467-024-46577-1
9. See for example the symposium on contingent valuation in: Journal of Economic Perspectives Fall 2012 pp 3-56  https://www.aeaweb.org/issues/288
10. Nordhaus W D (2018) Nobel Prize Lecture  https://www.nobelprize.org/uploads/2018/10/nordhaus-lecture.pdf section headed The Conundrum of Discounting pp 455-6
11. Dasgupta P & Maler K-G (2000) Net National Product, Wealth and Social Well-Being  Environment and Development Economics 5 (2000) pp 69-93  https://www.cambridge.org/core/journals/environment-and-development-economics/article/abs/net-national-product-wealth-and-social-wellbeing/8819C6F796223EF600E7F5C339491944
12. As (11) above, pp 73-4.  Re the variable (denoted Z) related to past expenditure (which I do not find very clearly presented), see top of p 74.
13. As (11) above, p 73
14. As (11) above, p 75
15. As (11) above, p 77
16. As (11) above, p 79 Formula 23a
17. As (11) above, Abstract and p 89
18. As (11) above, Abstract and p 81
19. Weitzman M L (1976) On the welfare significance of national product in a dynamic economy  The Quarterly Journal of Economics 90(1) Feb 1976 pp 156-162  https://academic.oup.com/qje/article-abstract/90/1/156/1860289 Abstract
20. Nordhaus W D & Kokkelenberg (ed) (1999)    Nature’s Numbers https://www.nationalacademies.org/read/6374/chapter/1 Ch 2 p 36 & App A p 187-8
21. As (11) above, p 80 Proposition 1
22. Wikipedia – Butterfly Effect https://en.wikipedia.org/wiki/Butterfly_effect
23. While this point may be considered obvious, an articulation in a peer-reviewed source may be found in Smulders S (2012) An arrow in the Achilles’ heel of sustainability and wealth accounting  Environment and Development Economics 17(3) June 2012 pp 368-372  https://www.cambridge.org/core/journals/environment-and-development-economics/article/abs/an-arrow-in-the-achilles-heel-of-sustainability-and-wealth-accounting/CC1CEEC0296CFD27D65A460F572880AD See especially section headed Shadow Prices p 369-70
24. As (19) above, p 159 Formula (7)
25. As (19) above.  The last sentence on p 158 and the first on p159 make clear that the programme (“trajectory”) under consideration is optimal.
26. Asheim G (2003) Green national accounting for welfare and sustainability: a taxonomy of assumptions and results  Scottish Journal of Political Economy 50(2) May 2003 pp 113-130  https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9485.5002001 see especially pp 121-2
27. Mathematical workings supporting this and other points presented with the words “it can be shown that” may be found in the supplementary material downloadable below.
28. This is a succinct statement of a proposition which I previously presented in this post.  A closely related proposition may be found in Asheim G (2000) Green national accounting: how and why?  Environment and Development Economics 5(2000) pp 25-48 https://www.cambridge.org/core/journals/environment-and-development-economics/article/abs/green-national-accounting-why-and-how/191DC044A09A7BB6BFED4A9B5AA92AC9 p 39 Proposition 8