On shadow prices for the measurement of sustainability

The objective of this research is to discuss the direction of the bias of the existing estimates of genuine savings also known as adjusted net savings.

Such estimates rely on observed prices and quantities of investment and natural resource extraction. This has two consequences: first, it causes an overestimation of the shadow price of productive natural resources; second, it leads to omitting the depreciation of environmental services and amenities.

We use simple numerical models to determine the path of optimal development under different assumptions. We find that the existing estimates of genuine savings are likely to be biased upward for countries with high levels of pollution, and biased downward for natural resource extracting countries.

On the Use of Shadow Prices for Sustainable Well-Being Measurement

This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Average rather than marginal extraction costs are considered, as information on the latter is unavailable. To simplify the notation, in what follows we omit the subscript t. If the production function is not separable in K and R, this does not necessarily hold, as the marginal product of R can grow even if the amount of extraction grows, if the stock of physical capital K is higher than in the first period.

Asheim, G. Green national accounting for welfare and sustainability: A taxonomy of assumptions and results. Scottish Journal of Political Economy, 50 2— Can NNP be used for welfare comparisons?

Environment and Development Economics, 12 111— Justifying, characterising and indicating sustainability. Dordrecht: Springer. Google Scholar. Atkinson, G. Savings, growth and the resource curse hypothesis.A shadow price is a monetary value assigned to currently unknowable or difficult-to-calculate costs in the absence of correct market prices.

It is based on the willingness to pay principle — the most accurate measure of the value of a good or service is what people are willing to give up in order to get it. A shadow price is often calculated based on certain assumptions, and so it is subjective and somewhat inaccurate. The origin of these costs is typically costs that are external to a market or an unwillingness to recalculate a system to account for marginal production. For example, consider a firm that already has a factory full of equipment and staff.

They might estimate the shadow price for a few more units of production as simply the cost of the overtime. In this way, some goods and services have near zero shadow prices, for example information goods. Less formally, a shadow price can be thought of as the cost of decisions made at the margin without consideration for the total cost.

Although shadow pricing may be inaccurate, it is still often used in cost-benefit analyses. For example, before defining a project, businesses and governments may want to weigh the costs and benefits of the project to decide whether the project is worthwhile. While tangible costs and benefits such as the cost of labor are easy to quantify, intangible costs and benefits such as the number of hours saved is much more difficult to quantify.

In this case, business owners and policymakers turn to shadow pricing to determine what these intangibles are.

LSBF - ACCA F5: Lecture on Linear Programming -- Shadow Prices

There are usually many tools to estimate monetary values of these intangibles. They include contingent valuationrevealed preferencesand hedonic pricing. In constrained optimization in economicsthe shadow price is the change, per infinitesimal unit of the constraint, in the optimal value of the objective function of an optimization problem obtained by relaxing the constraint. If the objective function is utilityit is the marginal utility of relaxing the constraint. If the objective function is costit is the marginal cost of strengthening the constraint.

In a business application, a shadow price is the maximum price that management is willing to pay for an extra unit of a given limited resource. In advance of adequate regulation or market pricing for some commodity items, conservative organizations will place on their balance sheets a value they believe to be an accurate reflection of the value of those items to their operations.

on shadow prices for the measurement of sustainability

This is common for companies with a large carbon footprint or water footprint. More formally, the shadow price is the value of the Lagrange multiplier at the optimal solution, which means that it is the infinitesimal change in the objective function arising from an infinitesimal change in the constraint.

This follows from the fact that at the optimal solution the gradient of the objective function is a linear combination of the constraint function gradients with the weights equal to the Lagrange multipliers. Each constraint in an optimization problem has a shadow price or dual variable.

Shadow pricing is frequently used to figure out the monetary values of intangibles and hard to quantify factors during cost-benefit analyses. In the context of public economicsshadow pricing is very useful for governments and policymakers to evaluate whether a public project should be pursued.The concept of sustainability has become increasingly popular in international and domestic debate on social progress; it is also a key dimension of the Treasury wellbeing framework.

However, confusion surrounds the concept, its measurement and its application in decision-making. Defined as maintaining or increasing wellbeing between generations, sustainability requires a focus on aggregate stocks of capital. Key features of the sustainability problem are uncertainty about the future, thresholds and substitutability between capital stocks. It is these issues, rather than theoretical paradigms, that are of practical importance to decision-makers.

An assumption that future generations will be always better off has permeated economic thinking since the work of Adam Smith and David Hume. It has been used to justify arguments that society need only worry about today because the future will take care of itself. Such arguments hold only if actions today do not harm future generations; however, this cannot be known with certainty. It is possible that future generations can be made worse off by inheriting fewer resources from the current generation than they need to match our standard of living Anand and Sen In recent years, calls for inclusion of sustainability principles within policy-making and alternatives to Gross Domestic Product GDP as a measure of social progress have also increased.

If there are reasons to consider future generations, how should this be conceptualised, measured and implemented? A large literature on intergenerational equity and sustainable development has sought to answer these questions, with significant contributions from the fields of economics, philosophy and environmental science. In economics, it has been part of the economic growth literature since the work of Frank Ramsey Ramsey The related theories of Hotelling and Hartwick are also standard elements of many natural resource management textbooks and are embedded in efforts to measure and apply sustainability concepts.

However, techniques and policy prescriptions derived from this literature are based on particular theoretical models of economic development whose underlying assumptions greatly simplify reality. Applying them without appreciating the consequences of these assumptions — or being aware of the range of alternatives — can lead to false confidence that we understand and are able to manage the impacts of our actions on future generations.

This paper distils the economics literature on sustainability and intergenerational equity concepts and offers insights relevant to their practical application in policy-making.

After reviewing the assumption that future generations will always be better off, it offers a simple but broad definition of sustainability that addresses confusion about the concept. Different theoretical constructs for sustainability are then briefly presented and their assumptions contrasted. The consequences of these assumptions for sustainability measurement are explored, revealing complex implications for discounting.

The fact that information about the future is lacking is a common theme throughout, and underpins concluding suggestions for improving decision-making in the face of uncertainty. Historical trends in wellbeing and projections about the future state of the world can inform a sense of whether future generations will be better off, notwithstanding the significant data gaps associated with each.

Angus Maddison attempted to infer historical trends in wellbeing by drawing disparate and patchy data on the lives of past generations into a measure of GDP per capita, as shown in Chart 1. While GDP is an incomplete measure of wellbeing in that, among other things, it inadequately measures contributions from the environmental and social spheres, it can nevertheless provide some insight.

Chart 1.

on shadow prices for the measurement of sustainability

GDP per capita appears to have remained at relatively low levels for many centuries, below even levels in the poorest African countries today, before growing rapidly following the industrial revolution. In the first one and a half millennia AD, life was short and marked by disease and famines. Average life expectancy at birth was 24 years in Roman Egypt during the first two centuries AD, and also in Medieval England Maddisoncompared with 80 — 90 years in developed economies today CIA During the World Wars and Great Depression of the 20th Century, the wellbeing of affected countries declined.

However, these events did not last for a generation and wellbeing as measured by GDP per capita resumed its growth during the periods of reconstruction that followed. Since the end of the Second World War, average world GDP per capita has more than tripled, driven by strong growth in developed economies and, more recently, Asia Maddison Living standards in developing countries remain much lower than those of the developed world, but they are still increasing.

Higher incomes have been accompanied by better health, education, longevity, environmental amenity particularly in advanced economiesand reductions in working hours and absolute poverty. Average world GDP per capita is currently around eleven times that ofwhile the world population has grown nearly sixfold.

on shadow prices for the measurement of sustainability

While the Maddison dataset suggests increasing wellbeing over time, there have been periods where the wellbeing of successor generations has decreased. For example, wellbeing in Europe declined between the first and tenth centuries, following the fall of the Western Roman Empire. Looking forward, it cannot simply be taken for granted that the current growth in living standards can be maintained for future generations.

The current economic turmoil in Europe risks creating persistent negative impacts on the wellbeing of some European countries that could be felt on a generational timescale. Productivity growth in developed economies has also been undergoing a decline since the s; potentially reducing the momentum that has driven increasing living standards in recent times TED This paper tries to answer the following research question: can multidimensional concepts like well-being or sustainability be measured by using a single metric such as shadow prices?

The defence of shadow prices is generally based on the pragmatic argument that different dimensions economic, social, environmental,… cannot be aggregated when measured by means of different metrics, thus a common measurement rod has to be found, that is shadow prices have to be used. Here the following conclusions are drawn: 1 The choice of shadow prices is not neutral, in fact implicit assumptions such as that substitutability is always desirable need to be accepted.

This means that the use of shadow prices is not consistent with a simple measurement objective but with a precise weltanschauung.

In the framework of sustainable well-being measurement, this may give rise to counterintuitive results, such as that the loss of an important well-being component is not perceived since its physical scarcity is compensated by its increase in monetary value. Since incommensurability between different metrics does not imply incomparability, there is no obvious reason for not using multidimensional techniques to measure multidimensional concepts. This is a preview of subscription content, log in to check access.

Rent this article via DeepDyve. One obvious problem here is that many natural resources e. Thus one would need to find implicit or shadow prices in some way.

Even those prices that do exist may not be useful; they may be affected by market imperfections and taxes, and they may exclude externalities involved with the production and use of the resource. In terms of history of the economic thought, it is also worthy to remember that the issues concerning the nature, role and measurement of capital goods was the focus of the so-called Cambridge controversy Harcourt Although the term capital was referred to artificial capital, the results can be extended to natural capital too, if money valuation is used, in particular the problem of circularity among the quantity of capital, its monetary value and the rate of interest.

The Many Definitions of Shadow Price

In terms of history of the economic thought, it is worthy to remember that indeed shadow prices were invented as a solution to the debate on economic calculus in a socialist economy.

Hayek, replying to Neurath wrote Neurathp. Kantorovich found a possible solution to this dilemma by inventing shadow prices see also Karmiloff, for an overview of shadow prices use in the former Soviet Union.

Indeed, weak sustainability is simply a different statement of the so called Hartwick-Solow rule Hartwick; Solow Solow ab, stating that in order to have a stream of constant level of consumption per capita to infinity, society should invest all the current returns from the utilisation of the flows from the stock of exhaustible resources.

These authors generally recognise that even if the production technologies of an economy can potentially yield increases in output commensurate with increases in inputs, overall output will be constrained by limited supplies of resources growth theory with exhaustible resources. But these limits can be overcome by technological progress : if the rate of technological progress is high enough to offset the decline in the per capita quantity of natural resource services available, output per worker can rise indefinitely.

A stronger statement is the claim of weak sustainability: even in the absence of any technological progress exhaustible resources do not pose a fundamental problem if reproducible artificial capital is sufficiently substitutable for natural resources.In the strictest sense, a shadow price is any price that is not a market price. A price that is not based on actual market exchanges must then be calculated or mathematically derived from otherwise indirect data. Shadow prices can be derived for anything from a resource to a good or service.

But this is just the tip of the iceberg. While economists tend to be committed to markets as a means of valuation, the lack of a market price is not necessarily a limitation of their research. Such goods might include the intangible like clean air. While the most basic understanding of the term shadow price relates simply to the lack of a market price for some resource, good, or service, the meanings of the term as derived from its real-world uses relay a more complicated story.

In the world of investments, shadow price can refer to the actual market values of a money market fund, which essentially refers to securities that are accounted for based on amortized cost rather than a value assigned by the market.

This definition carries less weight in the world of economics. More relevant to the study of economics, another definition of shadow price denotes it as a proxy value of a good or intangible asset that is most often defined by what must be given up to gain an extra unit of the good or asset. Last, but not least, shadow prices can also be utilized to derive an inclusive value of the impact of a project, whether it be a benefit or costs, using stated preferences, making the process an extremely subjective one.

In the study of economics, shadow prices are most often used in cost-benefit analyses in which some elements or variables cannot be otherwise quantified by a market price. In order to fully analyze the situation, each variable must be assigned a value, but it is important to note that the calculation of shadow prices in this context is an inexact science.

In the context of a maximization problem with a constraint or constrained optimizationthe shadow price on the constraint is the amount that the objective function of the maximization would increase by if the constraint were relaxed by one unit. In other words, the shadow price is the marginal utility of relaxing the constant or conversely, the marginal cost of strengthening the constraint.

In its most formal mathematical optimization setting, the shadow price is the value of a Lagrange multiplier at the optimal solution.

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On the Use of Shadow Prices for Sustainable Well-Being Measurement

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Frey, Bruno S, Dasgupta, Partha, Pearce, David W. Rabinowicz, Wlodek, A critical appraisal ," Ecological EconomicsElsevier, vol. More about this item Keywords Weak sustainability ; Commensurability ; Multi-criteria evaluation ; Statistics Access and download statistics Corrections All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions.

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On shadow prices for the measurement of sustainability

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