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Leslie Lipper
Resource Economist
Leslie Lipper is a Staff Economist in the Economic and Social Department, Agriculture and Economic Development Analysis Division of the Food and Agriculture Organization of the United Nations.

1. Introduction

Soil degradation is a major global environmental problem, causing widespread and serious impacts on water quality, biodiversity and the emission of climate changing greenhouse gases. The chemical and physical deterioration of soils also has major implications for agricultural productivity. According to a recent study, nearly 40 percent of the world's agricultural land experiences serious productivity impacts due to soil degradation, with rates up to 75 percent for some regions. (IFPRI, 2000) Yet a primary cause of soil degradation is the depletion of soils which results from the farming systems chosen by the farmers. Decisions such as where and when to produce, the types of techniques used - particularly in land preparation - and the level and timing of inputs, all affect the biophysical quality of the soil, and the extent to which it is depleted, conserved or augmented. Thus, although society and farmers themselves may benefit from higher levels of soil quality, it has proven difficult to achieve the changes in farm management practices necessary to reach this goal. This seeming contradiction raises one of the key questions addressed in this paper: How do farmers make decisions about the management of the soil resources under their control? What incentives are they responding to, and what constraints do they encounter in this process?

Although soil degradation is generated by farmers of all income levels, taking a closer look at poor producers in particular is warranted because of the impact of poverty on farmers' production decisions, and because of the potentially important role of improved soil management in poverty alleviation. Agricultural production is the most important source of income to a majority of the world's rural poor, who currently number around 800 million. Through its effect on agricultural productivity, the quality of their soil resources has a major impact on the capacity of poor farmers to achieve food security. Improvement of soil resources thus in many cases represents an important avenue for improving incomes among the world's poorest inhabitants. However, the condition of poverty engenders a different set of incentives and constraints in terms of making the farm production decisions necessary to attain such improvements. How the condition of poverty has an impact on farmers' soil management decisions, then, is the second main question analysed in this paper.

Understanding the incentives and constraints under which farmers are operating in making their production decisions is an important requirement for formulating effective policies to promote improved soil management, as well as other natural resources under farmers' control.

The paper is organized as follows: in section 2.1, a brief introduction to the major issues of analysing natural capital assets in an investment framework is given, followed by a discussion of the key determinants of investment behaviour and the role of environmental externalities in investment analysis. In section 2.2, a detailed analysis of the costs associated with soil degradation from the farmers' perspective is given, including the impacts on average productivity and the variance of agricultural yields. In section 3, the key determinants of soil investment incentives and constraints among poor farmers are examined. In section 3.1, an analysis of the distribution of natural capital endowments by wealth class is made, followed by an assessment of the importance of natural capital assets in general, and soil capital assets in particular for the incomes of poor agricultural producers. In section 3.2, the property rights regimes governing access to land resources among poor farmers are assessed in the light of their impacts on investment behaviour. In section 3.3, the access of poor farmers to financial capital and its influence on investment behaviour through impacts on investment capacity, risk and insurance capacity and discount rates is discussed. In section 4, the analyses made in sections 2 and 3 are used in a discussion of the implications for policy-making for both improved environmental management and poverty alleviation. In section 5 the paper concludes with an agenda for research needs which were identified throughout the course of the analyses presented.

2. Natural resources in agricultural production
2.1 Natural resources as a capital asset in the investment portfolio

Capital is a stock of real goods with the potential to produce a flow of benefits or utilities in the future (Hicks, 1939). Natural capital, then, is the stock of goods derived directly from nature that have the potential to contribute to the long-term economic productivity and welfare of societies. (Barbier, 1998) It includes raw materials such as timber, water and soil, as well as environmental services such as waste assimilation and watershed maintenance. In addition, natural capital provides utilities through the provision of aesthetic and recreational services.

As with financial capital, natural capital is measured in stocks and flows, although in physical rather than monetary units. Natural capital stock and flow values may be converted to monetary units with the application of resource prices to the physical quantities, although this exercise is often problematic due to imperfections in resource markets that lead to distorted prices. Adjustments to market prices to reflect the true opportunity costs of resource use to society are therefore necessary, but difficult to assess and often controversial.

Natural capital stocks are commonly divided into renewable and exhaustible categories. The former is defined as "a plant or animal population with the capacity for reproduction and growth at a significant rate when viewed from man's economic time scale" (Conrad and Clark, 1996) These include fish populations, forests and, under certain circumstances, soil fertility. Such resources are capable of regenerating themselves - as long as the environment in which they are nurtured is favourable (Dasgupta and Heal, 1979). Upsets in this nurturing environment may lead to a loss of regeneration capacity and thus the exhaustion of the resource. Exhaustible resources on the other hand, are those which are limited in quantity and not producible in any economically relevant time frame (Fisher, 1981). Extraction of one unit of this resource results in a decrease in the total stock of the resource by exactly the same amount. Natural resources that fall into this category include hydrocarbons, groundwater from aquifers and minerals.

The distinction is important, as it drives the "optimal" rate of investment, when viewed from the neo-classical economic point of view. In the case of exhaustible resources the key factors determining the optimal depletion path are the cost of "harvesting" the resource, its price and the discount rate. For renewable resources, the natural rate of regeneration enters into the calculation. Human intervention can change the natural rate of regeneration through capital investments augmenting the stocks, as well as through depletion, which adds another dimension of complexity in determining economically optimal patterns of use.

Economists have traditionally approached the analysis of natural resource use and allocation over time as an investment decision. However, in the application of capital investment analysis to systems that include natural capital it is necessary to recognize that there are fundamental ways in which natural capital differs from financial capital. The first is that natural capital provides services to humans (and other life forms) other than providing raw materials in the production process. Natural capital provides waste assimilation services as well as other ecosystem functions which provide utilities such as recreation, health, cultural and aesthetic services, as well as the maintenance of essential climatic and ecological cycles and functions. (Barbier, 1989; 1998) These additional functions of natural capital must be considered when assessing the use and savings of natural capital.

Another unique characteristic of natural capital is that it is produced and maintained within a complex web of biological and physical relationships that are defined as ecosystems (e.g. the "nurturing environment" mentioned above). Ecosystems are "communities of organisms in which internal interactions among the organisms determine behaviour more than do external biological events" (Holling, 1986). Ecosystems occur at various scales - from microscopic to global, depending on the type of behaviour that is being analysed. Often there is a high degree of linkage between the functions of various species within an ecosystem, so that disturbances to one member of the community lead to impacts throughout the system, which in turn may impact the ability of the system to maintain its functions.

Ecosystems are characterized by their degree of biological diversity and resilience. The two are linked; higher levels of biodiversity generally give rise to a higher degree of resilience (Odum, 1953; De Leo and Levin, 1997) Resilience is defined as "the ability of the ecosystem to maintain its characteristic patterns and rates of process in response to the variability inherent in its climate regimes (Walker, 1992). The impacts of depleting one or more natural capital assets on the various ecosystems in which it is embodied vary tremendously across resource and ecosystem types.

By its very nature, the analysis of natural resource investment and management requires an intertemporal dimension, as resource flows are dynamic. Changes in the stocks of renewable and non-renewable resources in the current time period have implications for the future flows of the resource. Thus the use of natural resources must be considered as a trade-off over time periods. For non-renewable resources, current consumption of the resource may result in higher marginal costs of extraction for future users, e.g. depletion of a groundwater aquifer resulting in higher pumping costs to future users of the well. With non-renewable resources, tracing the changes in the stock of the resource over time is often a simple matter of accounting for the amounts withdrawn or added to initial stocks. However, with renewable resources, the natural regenerative process of the resource and its relationship with the initial stocks must be considered, as well as the harvest rates over time (Taylor and Howitt, 1993). In some cases this may be a quantity change over time (e.g. fish population levels) while in others it may be a quality change over time (e.g. soil fertility).

An additional feature of natural capital that is critical to consider in an investment analysis is the fact that investments are partially or entirely irreversible (Dixit and Pindyck, 1994). This is true of most capital investments: sunk costs are generally irretrievable. However, in the case of investment strategies involving natural capital, a larger dimension is involved, due to the embeddedness of natural capital within an ecosystem. Changes in the level of natural capital stocks can result in changes in entire ecosystems and thus their ability to provide ecological services. This is clearly the case with the depletion of an exhaustible resource, but may also occur with renewable resources, when the patterns of use exceed the capacity of the system to renew itself. In such cases the resilience of the ecosystem is driven below a threshold resulting in a major transformation of the system - and the loss of some of its characteristics and functions.

2.2 Incentives for investment

2.2.1 Time preferences and investment

In the course of managing agricultural production and the natural resources involved therein, farmers constantly make decisions about the relative merits of various investment and depletion options regarding their natural capital assets. These decisions are made under uncertainty: the farmer does not know what future market and production conditions will be, and in many cases does not know how his/her actions may be manifested in environmental outcomes. According to orthodox economic theory, if farmers are "rational", e.g. motivated by profit, their decisions will be based on an implicit or explicit calculation and comparison of the expected stream of benefits and costs associated with the activity over time. An important determinant of the decision will be the rate at which the decision-maker trades off current for future consumption, or the discount rate. If the discounted difference between costs and benefits, e.g. the net present value, of the investment being considered is positive, then it should be undertaken.

Even in this relatively simple framework for analysing investment incentives there are several complicated issues to be resolved. One key issue is how people's discount rates are determined, and the implications of the rate for investment decisions related to natural capital use. Another major issue is how the presence of uncertainty and risk affects the investment decision. These issues are discussed below.

Discounting is the most common way in which economists account for the time dimension of investments. The discount rate is an indicator of the trade-off between present and future consumption. Often, the interest rate on capital is used as an inverse indicator of the discount rate, as it is a market-determined price for the exchange of goods or services across time. The choice of discount rate has an important impact on the analysis of incentives for investment, because the costs and benefits associated with management are incurred at various points in time and the discount rate determines how this temporal distribution has an impact on the desirability of the investment. For example, a high discount rate indicates a preference for present over future consumption, and thus disincentives to adopt management strategies that result in delayed returns.

The implications of how discount rates have an impact on incentives for sustainable natural resource use are quite controversial. Some argue that because of the bias against investments with delayed returns, high discount rates universally work against sustainable natural resource management, and thus decision-makers with higher discount rates are more likely to be engaged in environmentally degrading activities.

Norgaard and Howarth (1992) provide an interesting perspective on the relationship between discount rates and sustainable resource management. First of all, they point out that a high discount rate could result in environmentally beneficial outcomes as they make capital investment projects which may have negative environmental impacts - such as a dams - less attractive. Secondly, they argue that the transfer of resources to future generations should rightly be considered as an equity issue, and not one of efficiency. The discount rate is a way of determining efficient resource allocation over time, given the fact that goods and services have a time value associated with them. Given a time value of money that investors are faced with, e.g. interest rate on capital, it is appropriate to discount when looking at the efficiency of investments from the current generation's point of view. This decision is fundamentally different from a decision on resource allocations which is based upon equity considerations. In this latter case, a decision-maker may choose to bequeath resources to future generations in order to achieve a desired level of income or natural resource distribution. Norgaard and Howarth (1992) distinguish between these two types of resource allocation decisions, but make an important link between them: resource allocations made between current and future generations based upon equity considerations will change the efficiency prices which current generation investors face. The desire to transfer assets to future generations based on equity considerations has an impact on the allocation of resources over time and, thus, the investors' discount rate.

Estimating the discount rate among decision-makers is often problematic. It is quite tricky to estimate the rate at which individuals value future versus current consumption, and market-derived indicators, such as the interest rate, are often subject to distortions, limiting their ability to reflect true preferences. Individual investor's discount rates may change over the course of their life: younger people may be more willing to wait for future consumption than the elderly whose time horizon is shorter. Discount rates may vary across different types of investments, if the fungibility of assets held by the household is constrained. Another issue is that the rate at which individuals trade off present and future consumption is usually assumed to be different from that of groups or society, so the discount rate applied under a joint investment scheme may be quite different from that of a private investor. The institutional arrangements under which this type of collective investment is undertaken will also have a major impact on an individual's discount rate.

2.2.1 Investment under uncertainty

The presence of risk has a significant impact on the choice of investment and natural resource management strategies (Dixit and Pindyck, 1994; Dasgupta and Heal, 1979). It is necessary to consider both the nature of the risks encountered as well as the attitude of the decision-makers towards risk and their capacity to insure against risks, in order to capture the impacts on investment behaviour.

Risk arises from the presence of uncertainty and can be categorized by several different features: their frequency, the intensity of the impact they create, the degree to which they are experienced on an individual versus a collective basis, and the degree to which they are correlated over time (FAO, 2000). These characteristics are an important determinant of the ability of decision-makers to cope with risk, either through ex-ante insurance schemes, or ex-post consumption smoothing mechanisms. Either of these may have significant impacts on investment decision-making.

Producers' attitudes towards risk, and the degree to which they are averse to being exposed to risk have an impact on the types of investments they are willing to undertake. Results from theoretical and empirical studies indicate that producers who are more risk averse will allocate resources to activities that are less risky (e.g. lower variability of returns) but which have a lower average return (Roe and Graham-Tomasi, 1986; Rosenzweig and Binswanger, 1993).

Risk aversion not only affects the composition of the portfolio of activities undertaken, but also the production levels within activities. Theoretically, risk averse producers may be expected to produce less when exposed to risk (Sandmo, 1973). However, the impacts of risk on investment decision-making can be quite different if the consumption and production decisions of the decision-maker are linked. Many small-scale agricultural producers are both consumers and producers of agricultural production, making the consumption and production decisions non-separable. Sadoulet and de Janvry (1995) note that risk-averse producers may actually increase production of a risky commodity if they are net buyers of the commodity. Grepperud (1997a) points out that it is necessary to know how inputs affect production risk, and distinguish production from market uncertainties, in order to determine how risk will impact farmers' soil management choices.

Risk preferences vary among populations also due to the fact that people have different perceptions of the probability of an event occurring, which may be due to differing degrees of information available to each. These differences in risk perceptions and preferences give rise to the possibility of trading between individuals for insurance services or for commodities with differing degrees of risk associated with them. However, in order for such markets to be efficient in coordinating decisions involving time and uncertainty, they would have to include all commodities at every date, and in every possible state, or contingent commodities (Arrow and Debreu, 1954). Under such conditions the presence of risk would not affect investment decisions, as managers could efficiently insure against it. Since a complete set of contingent commodity markets clearly does not exist, and the ability of individuals to insure against risk is not perfect, risk preferences do enter into the investment decision (Fisher, 1981).

In addition to the issues raised in a standard investment analysis framework, the impact of irreversibility on the incentives to make investments is an important aspect that needs to be considered in the context of natural resource management. Frequently, indeed usually, the potential future value of holding a natural resource stock is uncertain, especially if all of the services it does and may provide are included into the calculation. The presence of this uncertainty results in a cost associated with irreversible investments or depletions (e.g. negative investments) The combination of irreversibility of investment with the uncertainty over the value of future losses results in an "option value" of waiting for more complete information before any irreversible action is taken.

There are two important aspects of irreversibility that may have an impact on a farmer's investment decision under conditions of uncertainty. In the first case, irreversibility arises from a lack of investment or depletion of the resources, which results in irreversible loss, which can be true for renewable resources as well as exhaustible ones. In this situation, there is a value associated with investments that result in the avoidance of an irreversible loss (e.g. extinction), with the result that investments are more attractive to the decision-maker.1 In the second type of example, the investment represents a "sunk cost" which is irreversible from the farmer's point of view - he or she cannot recover the capital that went into such an investment (Dixit and Pindyck, 1994). In this situation, there is a positive value to waiting to accumulate more information before making such an investment, particularly in the case where liquidation of productive assets is a form of insurance employed by the producer.

The impact of irreversibility thus has two opposing effects on farmer's investment incentives: on the one hand a positive incentive to avoid irreversible loss of natural capital services, and on the other a negative incentive for an immediate commitment of scarce investment capital that cannot be recovered. The relative weight of these two effects will depend on the extent to which an irretrievable loss of natural capital services is experienced as a private cost to the farmer, rather than an externality (see section 3 for discussion on externalities), and the degree to which the farmer prefers to keep liquid assets versus sunk capital assets.

2.2.3 Externalities and investment incentives

Many of the impacts generated by the investment or disinvestments of farmers in natural capital are realized in the form of externalities. When an agricultural producer takes an action that results in costs (benefits) that are borne by others, an externality is generated. Examples include the siltation of downstream waterways with eroded soils from upstream producers, the pollution of water sources from agricultural chemical runoff, the loss of biodiversity associated with land clearing for agriculture and the generation of greenhouse gases which contribute to global climate change arising from the loss of biomass associated with some types of agricultural production. Externalities can occur over both space and time, e.g. between current and future generations or between individuals and groups distributed over space.

External costs and benefits arising from agricultural production are distinguished from private ones - whose impact is felt by the agent taking the management decision. The distinction is quite important, as it implies that the full value of the action is not considered in the decision-making process, thereby resulting in a suboptimal2 amount of resource depletion or investment. Externalities are an important form of market failure, and their existence implies that a strict reliance on market forces will not yield an efficient allocation of resources. For this reason, some sort of intervention is required in order to correct the market failure and in order to reach a more efficient allocation of resources. Correcting the market failures associated with externalities will result in an increase in social welfare, as resource investment and depletion decisions will be taken in accordance with the true social values of the resources in question.

One of the primary reasons for the generation of negative environmental externalities through agricultural production (and other sectors) is ill-defined property rights to the resources or environmental services. If property rights were well defined and enforced, the owners would have the incentive to make investments whose future values can be expected to accrue to them. In addition, the presence of a well-defined property rights structure creates the possibility of trading among owners, e.g. a market for the goods, and thus an efficient allocation of resources could be obtained. There are several reasons for the lack of a well-defined property regime with regard to natural resources and environmental services. One main issue is that it is often difficult to quantify the resource, due to a lack of technical understanding of the good, as well as heterogeneity in the distribution of the resource over space and time. In many cases, natural resources require collective action among claimants under common property or private property regimes, which is difficult to achieve, due to high transactions costs and socio-economic pressures such as population growth and land use changes which create conflict rather than cooperation. In some cases, the environmental good or service in question has a public good nature, which means that exclusion of access is not possible, thereby reducing the incentives of any one claimant to invest in its provision.

From the perspective of analysing investment behaviour, the critical feature of all types of externalities generated through agricultural production choices is that they do not enter the investment decision-making process of the producer. However, it is also important to recognize that, in many cases, the same actions which generate negative environmental externalities also result in some impacts on the producers themselves, and to this extent the costs will be considered in investment and production decision-making. Assuming the producer is a profit maximizer, decisions on investing or depleting in natural capital will then be guided by their impact on the total profit making capacity of the producer. It is therefore important to understand the relationship between natural capital and agricultural production outcomes, in order to understand the rationale of producers' investment and production decisions.

It is also important to understand that when market failures are present, the production and investment choices made by farmers will not lead to a socially optimal allocation of natural capital and, in order to reach this goal, it will be necessary for some sort of intervention. In recent years considerable interest has been raised in programmes and policies which will provide incentives to agricultural producers to adopt practices which will generate local or global environmental benefits. One such example is the Global Environment Facility which supports projects that provide incentives to agricultural producers to adopt land use practices that conserve biodiversity, protect watersheds and reduce greenhouse gas emissions. The Clean Development Mechanism which is being negotiated under the Kyoto Protocol is a potential example of a market based mechanism for transfer payments to land users for the adoption of practices which generate carbon sequestration benefits. On a more local scale, power-generating facilities may pay upstream farmers to adopt practices that reduce erosion, in order to obtain higher hydropower generation capacity.

These transfer mechanisms have a tremendous capacity for generating both on-farm and external production and environmental benefits. However, it is critical to have a clear understanding of the farm level perspective on the benefits provided by natural capital, as well as the costs of investment and the various types of market and non-market barriers that farmers face when contemplating investments in natural resources in order to design effective strategies for improving the welfare of farmers as well as others in local, global or future communities.

2.3 Natural capital in agricultural production: farm level income and insurance services

For any agricultural producer, natural resources play a key role in the production process. Agricultural production is a process of transforming natural resources into a form that is usable to humankind through the application of labour and capital inputs. The stock of natural capital available to the farmer at any one point in time will have an impact on the rate at which this transformation occurs, e.g. the productivity of the system. Conversely, the nature of the agricultural production practices employed - including the investment decisions made by the producer, has an impact on the stock of natural capital and thus future flows of natural capital and agricultural production outcomes reliant upon such flows.

Natural capital can thus be thought of as an input to agricultural production, alongside the more commonly thought of inputs such as labour, financial capital and technology (El Serafy, 1990). Elements of natural capital which are most relevant in the context of agricultural production include soil quality (slope, texture, composition) climate (amount and timing of rainfall, solar radiation, wind), water resources (availability, quality) and land cover (amount and type of vegetation).

In this section the analysis is focused on the relationship between the management of soil resources and three key benefits which are derived from soil natural capital: the level of productivity, the stability of production and the efficiency of input use. Agricultural production levels are one of the major determinants of rural incomes. Production variance determines the degree of production risk producers face, which is also a critical determinant of consumption levels, as well as investment strategies. Input efficiency is an important determinant of production costs and thus net returns to production. While there are many other benefits which farmers may consider in making their soil management decisions, these three aspects are the major determinants of the financial and risk benefits associated with soil investments and thus encompass a major portion of the potential benefits from the farmers' perspective.

2.3.1 Relationship between soil resources and average agricultural productivity levels

Lal (1994) has identified the following processes which are included in soil degradation: accelerated erosion and desertification, compaction and hard setting, acidification, decline in soil organic matter content and biodiversity, and depletion in soil fertility. These processes result in changes in soils which in turn have an impact on yields through changes in soil nutrient content, water-holding capacity (WHC), organic matter content (SOM), soil reactivity, topsoil depth, salinity and biomass (Scherr, 1999).

Soil degradation effects on agricultural productivity are manifested through their impacts on both the average and variance of yield, as well as the total factor productivity of agricultural production. These impacts are translated into economic costs in the form of loss of income (or consumption), increased income (or consumption) risk, and increased costs of production. Several studies have been conducted in an attempt to quantify these costs under varying circumstances. Their results have indicated that these can be quite substantial.

The impact of soil degradation on agricultural productivity is a dynamic process that is highly heterogeneous across time and space. In addition, the impacts vary by type of degradation: the impact of soil erosion on agricultural yields is different than that of salinization. The fact that soil degradation impacts are so highly site and time specific is one reason that it is difficult to assess the economic implications in a generalized fashion. In addition, the fact that humans can influence both the occurrence and impacts of various forms of degradation also makes it difficult to assess the economic implications of the process (Erenstein, 1999).

To illustrate the impact of land degradation on agricultural yields, the case of soil erosion can be taken. Soil erosion is caused by water and wind action leading to a loss of soil from the uppermost land layers. Oldeman, Hakkeling and Sombroek (1990) estimated that approximately 83% of the land degradation in developing countries is caused by water and wind induced soil erosion. Erosion can result in the physical deterioration of the soil and/or induce chemical deficiencies and toxicities, which in turn impact agricultural crop yields (FAO, 1999a).

Yadav and Scherr (1995) summarize over 40 studies at a global, regional and local scale of analysis on the impacts of erosion on agricultural production. The estimates of impacts are reported in terms of yield declines as well as economic values. Yield declines range from 0.04 percent per annum to 100 percent (e.g. land goes out of production). In terms of economic costs, estimates range from US$26 000 million annually on a global scale (UNEP, 1991) to 5-10 percemt of GNP for developing countries annually (Bishop and Allen, 1989; Pearce and Warford, 1994). At a farmer level, estimates of losses of between 0.4 to 8 percent of agricultural gross product have been made. (Bojo, 1991; Norse and Saigal, 1992) Several different methodologies and assumptions are used in the calculation of both the yield and economic impacts of degradation among these studies, so their results are not directly comparable.

Erosivity and erodibility
The relationship between soil erosion and agricultural yields can be divided into two separate components: the rate at which erosion occurs over time, e.g. the susceptibility of the soil to erosion as measured by tonnes of soil loss per year, and the relationship between the level of erosion and productivity measured in tonnes of crop yield loss per unit erosion. The first is a function of two groups of factors: forces that generate erosion and forces that resist erosion (Lal, 1990). Forces that generate erosion include climate and topography; specifically the amount and distribution of rainfall and wind velocity and the steepness and length of slope. Collectively these are referred to as the erosivity of the soil (Lal, 1990). The forces that resist erosion include the degree of land cover as well as several characteristics of the soil including its texture, structure, water retention capacity and transmission properties (Lal, 1990). Taken together this latter group of characteristics may be referred to as the erodibility or resilience of the soil (Lal, 1990; FAO, 1999a).

In the tropics there is some evidence that soils exhibit high rates of erosivity and low rates of erodibility (Erenstein, 1999). One major factor is that rainfall patterns in the tropics tend to have sharp and intensive peaks in distribution that is highly erosive (Lal, 1990) Tropical soils are generally considered less resilient to erosion, because they are more highly weathered (Lal, 1984). For example, Alfisols that are widespread in arid and semi-arid areas of South Asia and sub-Saharan Africa have extremely poor soil structure and are highly prone to accelerated erosion (Lal and Stewart, 1995). However, Lal (1990) makes clear that it is not possible to generalize that in the tropics there is a higher rate of erosion occurring over time than is the case in temperate regions.

The negative relationship between the level of erosion and impact on crop yields is generally expected to be stronger in the tropics than in temperate zones (Lal, 1987, 1990; Erenstein, 1999). Soil erosion causes more severe quality changes in tropical soils due to their low inherent fertility, concentration of plant available nutrients or organic matter in the topmost layers of the soil, and subsoils unfavourable for edaphic life forms and lacking effective root volume (Lal, 1987). However, as Sanchez and Logan (1992) point out, it is important to disaggregate specific elements of tropical soil characteristics in order to illustrate the distribution of soil chemical properties relating to fragility throughout the tropics, rather than simply assume tropical soils are universally infertile and fragile.

Extent of erosion
The degree to which the soil has already experienced human-induced or natural degradation is clearly an important determinant of the current yield impacts of degradation, as well as potential returns to reversing or continuing along the path of erosion3 (FAO, 1999a). That is, one needs to know not only what the shape of the function mapping erosion over time looks like, but at which point on the function the farmer currently finds himself or herself. There is a fairly high probability that a land user will be operating on degraded land. In the Global Assessment of Soil Degradation study, Oldeman, Hakkeling and Sombroek (1990) found that 23 percent of all lands in agriculture, pasture or forestry were degraded to some extent. The regional distribution of the GLASOD findings on land degradation is shown in Table 14.

In Table 2, the degree to which erosion is the cause of land degradation by region according to the 1990 GLASOD estimates is shown, together with the distribution of the severity by three categories. These categories are somewhat anecdotal, and tied specifically to the economic costs associated with the level of degradation. For example, lightly degraded soils are those that experience only a small degree of productivity decrease and for which restoration to full productivity is possible through management modifications (Oldeman, Hakkeling and Sombroek, 1990). In contrast, moderately degraded soils have greatly reduced productivity, and require major improvements beyond the means of local farmers in developing countries for restoration to full productivity (Oldeman, Hakkeling and Sombroek, 1990)

The costs of erosion to a farmer in terms of foregone output, then, depend upon the following four factors: (i) the resilience of the soil; (ii) the degree of erosion risk present (e.g. the erosivity); (iii) the degree to which erosion levels impact yields (the sensitivity); and (iv) the degree to which erosion and land degradation are already present. In essence, one needs to know the shape of the functions relating yields to level of erosion as well as erosion over time and the point at which the farmer or land user finds himself/herself on this latter curve, in order to determine the costs of land degradation and potential benefits from reversal to the farmer.

Considerable research on the rate of erosion over time on varying soil types and under varying production conditions has been done. In general, with no technological change intervening, the function is non-linear and convex to the origin: erosion increases over time at an increasing rate (Lal, 1987).

Relationship between erosion and yields
Research on the nature of the relationship between erosion levels and yields is less common because of difficulty in measurement due to the large number of variables involved as well as the interactions between them (Lal, 1990; Erenstein, 1999). Recent research by FAO (1999a) has indicated that for a wide variety of soil types, there is a negative exponential, or logarithmic relationship between level of erosion and yields. The implications of this finding are that the highest returns in terms of crop yields to reversing or decreasing soil erosion will be realized on less-eroded soils. This relationship was found to be fairly robust for the humid and subhumid tropics, but less so for semi-arid areas, where water availability becomes the main constraint to productivity.

In order to get a sense of how the resilience and sensitivity of the soil to erosion interact to impact farm level incentives and constraints in managing the land base, a simple matrix as shown in Table 3 can be used. In addition to the two dimensions of resilience and sensitivity, a time dimension is included in the impact assessment in order to give a general sense of how the implications vary at different point estimates on the erosion and productivity functions.

For example, a farmer with soils of low resilience and low sensitivity may have little or no evidence of any yield-related impacts if they are at low levels of cumulative soil erosion. However, the impacts would be quite different further down the road of erosion on the same soils, as the cumulative impact of the erosion is finally manifested as a dramatic drop in yields.

The factors represented in each of the squares of the matrix may be considered collectively as the farmer's current endowment or stock of soil natural capital. Given this initial stock of soil natural capital, farm management decisions can have an impact on the future flows of the capital; by influencing both the rate of erosion over time and the yield impacts from a given level of erosion. For example, adopting crop rotation or tillage practices that keep soils covered at times of high rainfall or wind occurrence reduces the rate of erosion. Cultivating sloping lands on a vertical rather than horizontal contour increases erosion. In Table 4, the farm management decision of how much cover to maintain on the land and its impact on the soil erosion rates for varying soil types and slopes can clearly be seen. The degree of land cover can be determined by several different management decisions including crop choice (e.g. perennials versus annual), crop sequencing/rotations, or tillage practice (e.g. conservation tillage versus conventional tillage).

Aside from having an impact on the rate at which erosion occurs, farm management decisions can also influence how much yield loss is experienced at varying levels of erosion. This can be accomplished through the use of inputs that directly mitigate for the impacts of erosion on crop productivity. The farmer is essentially substituting some form of manufactured capital for the natural capital of the soil, although the degree to which substitution is attainable is quite variable.

Erosion has an impact on crop yields through changes in soil chemical characteristics and/or changes in soil physical or structural characteristics (FAO, 1999a; Lal, 1990). One of the most widespread examples of the former is the loss of soil nutrients through leaching associated with erosion. The highest concentration of nutrients necessary for plant growth is found in the uppermost layers of the soil, so the loss of this layer results in a decrease in soil nutrient reserve. The situation is even more serious on soils with low levels of natural fertility, as is the case in much of the tropics (Sanchez and Logan, 1992).

Erosion also causes the loss of a buffer layer of organic material, exposing soils to aluminium toxicity and acidification which can cause sudden and severe yield decreases (FAO, 1999a; Lal, 1990). Through the removal of clay content and organic matter, erosion may result in a decreased capacity of the soil to provide phosphorus in a form usable to plants (e.g. increase phosphorus fixation). In terms of structural impacts, soil erosion can increase the bulk density of the soil, making it more difficult for water to penetrate to rooting depths and for plant shoots to emerge, either by the removal or organic matter and colloids that create spaces between soil particles or by exposing highly compacted subsurface layers (FAO, 1999a).

Are soils natural capital and manufactured capital substitutes or complements?
Farmers can mitigate the chemical or physical consequences of erosion by substituting for the services lost through the erosion process, or correcting for the chemical and physical constraints erosion leads to. The application of fertilizers to replenish lost nutrients is the most common example of substitution. Correcting acidity through the addition of lime is an example of a corrective action.

However, soil natural capital provides a wide array of services in conjunction with other components of the ecosystems it is embedded within, so even if substitution for one aspect of the services provided by soil capital is attainable, there may still be a decrease in other ecosystem services. The decline in these linked services may result in a decrease in the productivity of manufactured inputs, with the result that under some circumstances, soil natural capital and human applied manufactured capital are complements, rather than substitutes5. In the case of chemical fertilizers, for example, the loss of soil quality through degradation processes may result in a decline in the yield response to chemical fertilizers, e.g. the marginal productivity of chemical fertilizer declines with declining soil natural capital.

The question of the extent to which manufactured forms of capital can substitute for natural capital is quite controversial and lies at the heart of the debate on sustainable natural resource management. Weak sustainability is defined as the maintenance of an aggregate level of the capital stock, be it composed of natural or human-made capital. In contrast, strong sustainability requires the maintenance of natural capital stock (Erenstein, 1999). The difference between the two positions is essentially a difference in the assumption of substitutability between natural and manufactured forms of capital. Proponents of weak sustainability assume a high degree, while those of strong sustainability think of natural and manufactured capital as complements.

Whether or not soil natural capital and manufactured capital are substitutes or complements is a critical determinant of the impacts of soil erosion on productivity and thus farm decision-making. Essentially, if they are complements then the loss of soil natural capital is higher, because it results in both a loss in productivity directly associated with its own loss, as well as a decrease in productivity in manufactured inputs. Deriving parameters that describe under which conditions natural capital and manufactured capital are substitutes or complements is an important area for future research.

In several economic models of optimal soil management the results are dependent upon the critical assumption of complementarity between natural and manufactured inputs. Goetz (1997) constructed a dynamic model of soil management in which he distinguished between the case of soil depth and fertilizer as substitutes and one as complements. He hypothesized that the two would be complements at low levels of soil depth where depth is the limiting factor, but substitutes at high levels of soil depth due to a lower marginal accretion in the yield as the soil increases. The results of his analysis indicate that which of these cases holds true is a critical determinant of the steady state soil stock, as well as the impact of changes in crop prices or the discount rate on the optimal level of soil depth. In his dynamic models of optimal soil management, Clarke (1992) assumes that soil natural capital and manufactured inputs are complements but notes that "the relationship between commodity price changes and viable soil conservation strategies depends crucially on the complementarity/substitutability relationships between the inputs". La France (1992) and Barbier (1998) assume a complementary relationship between soil stock and cultivation and Grepperud (1997b) side-steps the question by defining the inputs to the production function in relation to their impact on soil quality or erosion, rather than including an explicit term for soil natural capital in the production function.

In an empirical study, Walker and Young (1986) found that, with fertilizer inputs, higher yields were obtained on fields with lower levels of erosion, indicating a complementary relationship between soil natural capital and chemical fertilizer. They analysed the impacts of erosion on crop yields in the Palouse area in Idaho and Washington States in the United States that had experienced both high rates of erosion and increasing yields.6 The authors concluded that the complementary relationship between inputs is highest in situations where unfavourable subsoils underlie topsoil horizons. A greater degree of substitution would be found between chemical fertilizers and eroded soils in cases where a greater degree of homogeneity exists between surface and subsoil quality.

Since technological change itself is a complement to soil natural capital, any assessment of the impacts of soil quality decline must consider the difference between yields obtainable under the new technology with and without the presence of erosion, rather than yields before and after the adoption of the technology, which is often the case among farmers. According to the authors of the study, soil conservation practices were not widely adopted in the area because of the producer's belief that yield-enhancing technology compensated for lost topsoil.

2.3.2 Impact of erosion on crop yield variability

Another major concern of farmers is the variability of crop yields over time. Yield fluctuations arise primarily due to climatic factors or pest and disease incidence. Fluctuations in yields create production risk, which generates costs to risk averse farmers seeking to insure themselves. The absence of facilities to store produce over time, together with poor market development and low incomes, means that farmers are often directly dependent on the current year's harvest for their food supply. Variations in yields can have quite dire consequences for rural populations and therefore yield variability enters production decision-making as a source of risk, in some cases quite intensely.

One of the biggest sources of variability in yields is uncertain rainfall. The inability of crops to obtain sufficient water during critical periods in the growth process results in significantly lowered or no yields at all. In much of the world, most farmers are dependent on rainfall for their source of crop water. Water is made available to plants through transport through the soil medium into the plant roots. The capacity of the soil to store water that can be made available to the plant over the growing season is thus an important feature for mitigating uncertain rainfall patterns. This capacity, known as the soil water holding capacity (WHC). Under undegraded conditions, soils vary naturally in their WHC, with heavier soils with higher clay content exhibiting higher levels generally than lighter, sandy soils.

The process of degradation can reduce the soils' WHC. The loss of soil topsoil layers through erosion may have a negative impact on soil moisture retention capacity and increased infiltration rates (Bishop and Allen, 1989). Colacicco, Osborn and Alt (1989) state that soil erosion may increase the variability of production regardless of its effect on average yields. Moyo (1998) found that soil erosion in Zimbabwe resulted in reduced soil organic matter and clay content, which caused a drop in fertility, an increase in bulk density and a reduced storage capacity of plant available water, particularly with the sandy soils in Zimbabwe's communal areas. His research was carried out in the semi-arid region of southern Zimbabwe that is characterized by erratic and unreliable rainfall between and within season. The results indicated that there were no significant yield differences in years of high rainfall, but under poor rainfall conditions yields varied significantly, with plots treated with mulch ripping showing much higher yields in the poor rainfall year (Moyo, 1998).

To what extent can farmers substitute manufactured inputs to substitute for the lost services of the soil in terms of yield variability? In the case of rainfall uncertainty, one obvious measure that could be taken is the supply of irrigation water to substitute for lost water availability in the soil. However, as in the case of declining average yield levels, the adoption of such mitigating measures in the presence of continuing soil degradation results in a decreased productivity of irrigation water - for example, soil quality and irrigation are complements rather than substitutes. Under degradation that leads to decreased infiltration rates and lower moisture retention rates, higher and more frequent irrigation rates are required to obtain a given level of water delivery to a plant. Under degradation, irrigation efficiencies (e.g. the degree of water used by the plant divided by the total amount of water applied) decline, thus the costs of irrigation are higher. If the fixed capital costs of constructing and maintaining an irrigation system are considered as well as the variable costs of delivering the water each season, the returns to using irrigation as a substitute for services lost through soil degradation are even lower.

The implication of these findings is that the cost of soil degradation to farmers is higher than just loss in average yields, particularly in rainfed areas that experience uncertain rainfall patterns. Under these conditions, investments in soil conservation which result in reduced yield variability may be quite attractive to farmers, even if they do not increase average yields. The critical determinants of the decision to adopt soil conservation measures in this case are the degree of exposure to risk arising from the degradation and the farmer's attitude towards risk on the one hand, as well as the relative costs and returns to soil conservation and technologies which mitigate the impacts of yield variability.

2.3.3 Costs of soil conserving and mitigating inputs

In the previous two sections the major impacts of soil degradation, and specifically erosion, on farm production costs and the strategies which the farmer can adopt to address these were outlined. Broadly, farmers can opt for one of four strategies: (i) do nothing; (ii) take measures to slow the rate of erosion; (iii) take measures to mitigate the negative impacts of erosion on crop yields and variability; and (iv) adopt a combination of (ii) and (iii). The strategy the farmer adopts will depend on the magnitude and type of costs associated with degradation, and how these compare with the costs associated with adopting any one of these four strategies. It is to the analysis of these latter costs that this section is devoted.

A key concept necessary to understanding the costs of soil management strategies from the farm perspective is that of opportunity costs, which is simply the value foregone by employing a resource in one use, rather than an alternative use. This means consideration of what the farmer is giving up in adopting a particular course of action, which may involve financial costs such as payments for inputs or loss of livestock feed supplies, as well as non-market costs, such as the loss of leisure or a loss of insurance capacity. As financial constraints are a key barrier to the adoption of any farm management strategy, it is essential to consider the strict financial implications associated with any course of action; however, in order to have a full understanding of the incentives and constraints of the farmer in making investment decisions on soil natural capital, it is necessary to consider other non-financial costs as well.

Taking each of the key factors of production in turn, a broad description of the types of opportunity costs associated with each, if they were to be employed in any one of the four strategies outlined above, can be outlined. For example, in the case of the first strategy, the cost to the farmer of doing nothing in the face of soil degradation associated with erosion is the loss of production value associated with the degradation - the loss of yields, input efficiency or crop yield stability which is due to the degradation. As described in the previous section, the magnitude of this loss will vary considerably, depending on the rate of erosion, the rate of yield loss or stability loss associated with erosion, and the current level of erosion. In some cases this loss may be rather small, and less than the costs to the farmer of adopting any measures to reverse the process, in which case the farmer has no incentive to take any action; the opportunity cost of the foregone production is less than the cost of preventing its loss.

Now take the case where erosion does result in substantial production costs and assume that the costs associated with slowing or reversing the erosion process are less than the foregone production losses. Ostensibly the farmer has a financial incentive to adopt erosion control. However, if the erosion control measure involves the use of investment funds in the current time frame in order to achieve a positive impact on production in a future time frame, the farmer is essentially giving up the use of this capital in the present - foregoing the current use of capital. The way in which this trade-off of current capital for future capital is viewed depends on the discount rate of the farmer, as well as the expected future payoff. A high discount rate, which implies that current consumption is weighted more heavily than future consumption, will result in a high opportunity cost of investment funds to the farmer.

Another type of opportunity cost that a fixed capital investment for erosion control might involve is that of insurance capacity. By making an "irreversible" capital investment in erosion control, the liquidity of the asset portfolio of the farmer is lowered. To the extent that asset liquidity serves as an insurance mechanism that allows for a rapid access to funds in the case of shocks, tying up funds in an illiquid investment implies foregoing an insurance benefit.

The opportunity costs associated with labour are also a critical determinant of farmers' soil management strategies. Adopting erosion control or mitigation measures may require more labour, or a more arduous type of labour, or a labour requirement at a specific seasonal time. In adopting such a measure the farmer may be giving up the opportunity to work off-farm - and thus the wages associated with such employment. Alternatively, the farmer may be foregoing leisure, or less physically demanding types of labour7, or the ability to work on other crop activities on farm. Any of these may constitute a significant cost to the farmer, and thus a disincentive to adopt the strategy in question. Under these conditions, farmers are unlikely to invest at a socially optimal level in avoiding soil erosion.

Empirical literature on adoption

The opportunity costs of other forms of natural capital are another key consideration determining the incentives of farmers to invest in soil natural capital. That is, if natural capital is employed for the purposes of preserving or augmenting soil natural capital, what alternative uses are foregone? One important example in this category is the use of crop residues as a mechanism for returning biomass to the soil, as well as providing erosion-reducing groundcover. Crop residues may be used for livestock feed or fuel purposes; however, in this case the loss of these uses constitutes a significant opportunity cost to the farmer, particularly where alternative sources of fuel and feed are scarce and expensive.

Given this framework for assessing the costs associated with the various options for soil management, an assessment can be made of the empirical literature on experiences with the adoption of soil erosion and mitigation practices on farm. Traditionally, measures designed to decrease soil erosion, have been primarily focused on engineering approaches, for example the construction of physical barriers such as terraces or bunds to impede the movement of the soil. Such measures tend to require a large fixed capital investment and/or a high input of labour. The impacts or benefits of these barriers tend to be realized only after a substantial length of time. In addition, in many cases the adoption of such technologies leads to a decrease in crop output, due to a loss of area in production. The combination of a high fixed cost up front and delayed and reduced benefits make this sort of investment unattractive in many cases to farmers.

Lutz, Pagiola and Reiche (1994) reviewed cost benefit analyses for nine soil conservation projects in Central America and found that the measures with the highest economic return were the low cost and quick returning ones, in areas where erosion had appreciabe impacts on productivity. In one case, the adoption of soil conservation led to a decline in long-term returns to agriculture, due to the loss of land in production to diversion ditches and the limited impacts of erosion on productivity. Barbier (1998) found that the high labour cost for the construction of bench terraces to stop erosion in the uplands of Java made the adoption of this measure unattractive to farmers. This implied a loss of foregone income from the labour that could be used in alternative income-generation activities, as well as a loss of land for production.

In Honduras, Carcamo et al. (1994) distinguished between the on-farm versus externality benefits of adopting various measures that impact soil degradation rates, growing various crops with varying land cover services, the use of alternative tillage practices, and the construction of soil erosion control devices. They concluded that in order to achieve socially optimal levels of soil degradation both a reduction in farmer income and an increase in the degree of production risk the farmer is exposed to will occur, which implies a need for subsidies or transfer payments to farmers in order to achieve the desired level of degradation control.

Hwang et al. (1994) conducted research on farmer incentives for erosion control among small-holders on steeply sloping lands in the Dominican Republic and found that large-scale reduction in soil loss can only be achieved at the expense of significant declines in farm income. Even where soil erosion control measures result in increased production, the impact of erosion control adoption on production risk may make them unattractive to farmers (Day et al., 1992; Grepperud 1997a).

More recently attention has become focused on biological measures of soil erosion control, such as cover crops and mulching. The attractiveness of these measures as compared with engineering approaches are a lower initial investment requirement, less loss of cropping area, and the realization of benefits other than just erosion control, such as fertility enhancement, soil structure improvement and weed control. However, they too involve costs to the farmer. Erenstein (1999) gives great detail on the costs which may be involved with the adoption of crop residue mulching over conventional systems, including increased seeding, fertilization and weeding costs, losses in input productivity and loss of livestock grazing. He also makes the point that even in cases when adoption of a mulching technology results in an overall reduction in labour requirement, the timing of the labour input may shift and conflict with other activities and therefore not be a viable option for farmers (Erenstein, 1999; FAO, 1999b).

The costs of adopting substitution and correction approaches to erosion-induced productivity loss are those of obtaining and applying the inputs. In general these types of measures tend to fall into the category of operating rather than fixed costs - e.g. they occur on an annual or seasonal basis and their impacts are generally realized within the same production cycle. For this reason, as well as their generally lower costs as a percentage of overall production costs, mitigation measures are often more attractive to farmers than erosion control measures. They do not involve a high rate of foregone current use of capital, they allow some flexibility in terms of ability to respond to shocks, and they exhibit short-term and visible results. The problem is, of course, that the effectiveness of mitigation strategies will decline with increasing soil erosion, although this is not always recognized by the farmer. The example described in section 2 of the farmers in the Palouse area of Idaho is one illustration of this situation. Although high rates of erosion were experienced, increasing yields associated with fertilizer inputs masked the problem from the farmers' perspective, and made the adoption of erosion control practices seem unnecessary. Here, the true costs of erosion to the farmers was the foregone production and fertilizer efficiency they could have obtained with decreased erosion, however either these costs were less than the costs of controlling the erosion, or the farmers were unaware of the losses they were accruing, and therefore no erosion control was adopted.

This leads us to a final consideration in the analysis of farmers' soil investment incentives: the degree to which the costs of disinvestment or depletion are recognized as such by the farmer. Obviously, where no cost is recognized, there will be no incentive to take action. Particularly in cases where erosion results in a slowly accumulating impact, which only after some continued stress reaches a critical threshold at which significant production impacts are realized, it is difficult for farmers' to perceive the benefits of erosion control investments. Unfortunately, in many such cases reaching such a critical threshold implies irreversible damage or prohibitively high costs to reverse the process. In such cases, educational efforts among the farmers on the potential impacts of their actions may be necessary.

2.4 Conclusions

Natural capital in general, and soil natural capital specifically, play a critical role in providing farm income through agricultural production, as well as insurance services by reducing production variability. Farmers have an initial endowment of natural capital, which includes the degree to which the resources are resilient to degradation processes, the degree to which they are exposed to natural processes that cause degradation and the degree to which the resource has already experienced some level of degradation. The level of natural capital endowment is one of the major determinants of the costs of degradation on-farm, and thus the resource management decisions that farmers make. Aside from the costs experienced by farmers, the degradation of natural capital assets may result in external costs, which are borne by others at a watershed, regional or global scale of impact, or by future generations. Although these costs can be quite substantial and in some cases irreversible, they do not enter into the decision-making calculations of the farmers, who are assumed to make decisions on natural capital use solely based upon the impacts felt on-farm, given the constraints they are operating under.

Farmers can make conservation investments that reverse or decrease the level of degradation of natural capital, or they can adopt measures that mitigate the impacts of degradation on the average and variance of crop production levels. Mitigation measures may substitute for one or more of the services provided by natural capital, but since natural capital provides a wide array of inter-linked services, the substitution between natural and manufactured forms of capital is often limited. Instead natural capital and manufactured capital are often complements, so that the loss of natural capital results in a decline in the effectiveness of manufactured capital inputs to agricultural production.

Due to the time requirements for natural capital regeneration, investments in the reversal or decrease of natural capital depletion often exhibit delayed returns. In the case of soil, traditional measures to reverse degradation have required large fixed capital investments for engineering-based solutions. In addition, such measures often resulted in lower farm production levels, due to a loss of land under production. In contrast, mitigation measures are often experienced as operating costs, which require a lower level of investment on a more frequent basis, and whose results are often more readily realized than in the case of natural capital investments. More recently, greater attention has been focused on biological forms of soil degradation control, which require less fixed capital outlay, and which may exhibit a shorter turn around time for results. However, even these measures may result in higher on-farm costs in terms of foregone production, loss of alternative sources of labour income, livestock feed or fuel sources, and reduced input productivity.

The initial endowment of natural capital is a key determinant of the on-farm losses in productivity and increased yield variance associated with continued degradation, as well as the returns to investment in reversal or mitigation in terms of crop output. The relative prices of conservation and mitigation measures, as compared with the value of production obtained are also critical factors. Finally, in the case of yield variability, the farmers' attitude towards risk is a critical determinant of the optimal natural resource management strategy. These are the issues that are covered in the following section of the paper.

1 This is assuming, of course, that the decision-maker is aware that depletion can lead to irreversible damage and that the damage impacts his or her utility - e.g. that they care about it.

2 Suboptimal is used here with reference to the concept of Pareto efficiency. A Pareto efficient allocation of goods and services in an economy implies that there is no other feasible allocation that would be preferred by all agents in the economy. It is important to note that this criterion is focused on the efficiency of resource allocation, rather than equity considerations and that other objective criteria for optimality are possible (and likely) in any given society.

3 What is critical here is the degree to which erosion has caused a decrease in the depth of the top layer of soil and how different (and less productive) the underlying lower layers are.

4 Includes land under crop cultivation, forestry and woodland, and pasture.

5 The terms "complements" and "substitutes" are used in the Edgeworth sense, such that for a production function with two arguments: Q=f(x,s) where fxs< 0, the inputs are substitutes and for fxs> 0 they are complements.

6 Over four decades preceding 1986 wheat yields in the Palouse area had increased by 25 bushels per acre (approximately 1630 kg/hectare). Over the same period between 9.5 and 14 tonnes of soil per year were estimated to have been lost to erosion.

7 This is a particularly important consideration among malnourished populations, as physically demanding labour requires more caloric expenditure.

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