Pastoral strategies in sub-Saharan Africa : the economic and ecological sustainability of dryland range management

THE WORLD BANK ENVIRONMENT DEPARTMENT Pastoral Strategies in Sub-Saharan Africa: The Economic and Ecological Sustainability of Dryland Range Management Charles Perrings February 1993 Environment Working Paper No. 57 This paper has been prepared for internal use. The views and interpretations herein are those of the author(s) and should not be attributed to the World Bank, to its affiliated organizations or to any individual acting on their behalf. ACKNOWLEDGEMENTS Professor Charles Perrings is Head of the Department of Environmental Economics and Environmental Management at the University of York, UK. At the time this working paper was prepared, he was Professor in the Department of Economics at the University of California, Riverside. He would like to express his thanks to Brian Walker, John McIntire, John English and participants in a seminar at the World Bank, at which an earlier version of this paper was presented, for their helpful comments. The usual disclaimer applies. This study was made possible by a grant made to the World Bank by the Government of Norway for Sahelian studies. Departmental Working Papers are not formal publications of the World Bank. They present preliminary and unpolished results of country analysis or research that are circulated to encourage discussion and comment; citation and the use of such a paper should take account of its provisional character. The findings interpretations, and conclusions expressed in this paper are entirely those of the authors and should not be attributed in any manner to the World Bank, to its affiliated organization, or to members of its Board of Executive Directors or the countries they represent. Because of the informality and to present the results of research with the least possible delay, the typescript has not been prepared in accordance with the procedures appropriate to formal printed texts, and the World Bank accepts no responsibility for errors. ABSTRACT There has been considerable controversy in recent years over the question of whether the standard notions of 'carrying capacity' in the dryland range areas of Sub-Saharan Africa are relevant when considering policy towards traditional producers operating primarily in communal areas. This relates to changing ideas on the underlying ecological views of (i) the impact of alternative management regimes on the range ecosystem, and (ii) of the objectives of range management. These views have lead to a questioning of the position that the traditional "opportunistic" range management strategies are responsible for much of the rangeland degradation reported in the region. The paper reconsiders the economics of rangeland degradation in dryland economies in the light of the recent studies. Four sets of questions are posed. First, the paper asks what characterizes traditional range management strategies, and in what sense such strategies may be said to be opportunistic. Second, the paper asks what the ecological impacts of the choice of management strategy might be by identifying the level and variance of optimal grazing pressure under each strategy. Third, to put the opportunism of traditional range management strategies in some perspective, it considers the sensitivity of grazing pressure to change in the main elements of the economic environment: prices, incomes, and endowments. Fourth, it asks what implications this might have for environmental policy. The analysis presented in the report suggests that overgrazing is not due to the opportunistic nature of traditional range management strategies, but to the economi- and institutional conditions in which such strategies are worked out. Offtake is an increAsing function of the market value of animals sold, the fixed or quasi-fixed costs of rangeland access and the rate of discount, and is a decreasing function of the net benefits of livestock holdings. Given the range of benefits received by the traditional owner, and the non-marketed nature of some of them and, given the nature of the institutional arrangements under which access is secured (membership in a group which entails some costs), the results of the analysis of the impact of variations in the available policy variables are not always intuitive. The paper shows how recent trends in policy and economic parameters may have worked to provide incentives to traditional producers to increase, rather than decrease, their herd sizes, and discusses some ways in which the problem may be addressed. Pastoral Strategies In Sub-Saharan Africa: The Economic And Ecological Sustainability of Dryland Range Management Table of Contents Page 1 Introduction 1 2 The Wider Context 3 2.1 C'; ate 4 2.2 Th,. institutional environment 5 2.3 The market environment 7 3 Opportunistic Range Management Strategies 9 3.1 Equilibrium range succession and state-and-transition models 9 3.2 Elements of an opportunistic grazing model 12 3.3 Equilibrium versus opportunistic strategies 16 4 The Ecological Effects of Traditional Opportunistic Range Management Strategies 17 4.1 The general characteristics of traditional pastoralism 17 4.2 Ecological effects in model simulations 19 5 Polly Implications 26 5.1 Prices 27 5.2 Income and asset distribution 34 5.3 Restocking 37 6 Conclusions 39 Appendix 1 Optimal grazing pressure 43 Appendix 2 Simulation results 47 References 67 Pastoral Strategies In Sub-Saharan Africa: The Economic And Ecological Sustainability of Dryland Range Management 1 Introduction The conventional wisdom amongst environmental economists regarding the impact of different stocking strategies in the rangelands of Sub-Saharan Africa is that the traditional 'opportunistic' range management strategies are responsible for much of the rangeland degradation observed in the region. More particularly, it is argued that the traditional pattern - involving rapid herd growth on communal pastures in the wet phase of the rainfall cycle but sluggish destocking in the dry phase - has been a significant source of stress on rangeland. This has led to livestock densities in excess of the current ecologically sustainable carrying capacity of the range during dry periods, with adverse implications for the composition of biomass, the diversity of micro fauna and f1ora, and soil quantity and quality and, hence, agricultural productivity [cf Dixon et al, 1989; Pearce et al, 1990]. The effects of declining average rural productivity in the region are not in di3pute. There has been a long term deterioration in most indices of rural welfare. Between 1965 and 1985, average rural consumption and average nutrition levels both declined in Sub-Saharan Africa - daily per capita calorie supply falling by an average of nearly 20 per cent in Ethiopia, Sudan and Chad. Two groups of countnes in the region have been particularly severely affected: Senegal, Mauritania, Niger, Chad, Sudan, Somalia and Ethiopia in the Sudano-Sahelian region; and the Central African Republic, Zaire, Uganda, Zambia, and Tanzania in East ald Central Africa. Zambia aside, the economies of all these countries are dominated by agriculture, and most agriculture i3 pastoral. All recorded zero or negative average annual per capita GNP growth between 1965 and 1988. Indeed, the rural populations of the Sudano-Sahelian region remain the most deprived in the world by the UNDP's human development index [UNDP, 1992].1 What The human development index (HDI) is equal to one minus an avenge deprivation index, which is a simple average of three indicators: life expectancy, literacy, and GDP. On a scale in which Japan has an HDI of .996, tweny countries have an HDI of less that .3. All but three of those are in Sub-Saharan Africa. The eight most deprived countries in terms of this index are: Niger, Mali, Burkina Faso, Sierra Leone, Chad, Guinea, Somalia and Mauritania. *2 has been questioned in recent years In the range management and ecological literature is the link between traditional opportunistic range management and declining productivity. A number of studies have claimed that traditional opportunistic range management techniques are not only more productive than techniques based on equilibrium range succession models [Behnke, 1985; Westoby et al, 1989; Abel, 1990; Scoones, 1990], but do not lead to 'unacceptable' rates of range degradation [Biot, 1990; Abel, 1990; Scoones, 19911. This paper reconsiders the economics of rangeland degradation in dryland economies in the light of these studies. Four sets of questions are posed. First, the paper asks what characterizes traditional range management strategies, and in what sense such strategies may be said to be opportunistic. To do this it distinguishes between opportunistic and equilibrium range succession strategies, and considers the economic and ecological conditions under which one strategy dominates another (in the sense of generating an income flow of higher net present value). Second, the paper asks what the ecological impacts of choice of management strategy might be by identifying the level and variance of optimal grazing pressure under each strategy. Third, to put the opportunism of traditional range management strategies in some perspective, it considers the sensitivity of grazing pressure to change in the main elements of the economic environment: prices, incomes, and endowments. Fourth, it asks what implications this might have for environmental policy. One important set oi questions is not addressed in the paper, at least not directly. Although the paper considers the dynamics of rangeland management, it has nothing to say about optimal management strategy in an evolutionary state. That is, it abstracts from the problem of transition between states of nature. It is possible to determine the ecological sustainability of a particular stiategy in some state of nature, but it is not possible to say anything about the evolution of the state. It therefore ignores one aspect of the range ecology literature discussed above, and that is the optimal evolution or state-and-transition models of Westoby et al [1989]. .3 - The paper is in six sections. The following section identifies the major climatic, institutional and economic trends which give the context within which range management strategies have evolved. A third section approaches the construction of an opportunistic grazing model by reviewing the points at issue in the recent reappraisal of the range succession models. The same section sketches the elements of general grazing model, and distinguishes between opportunistic and equilbrium variants of the model. A derivation of the necessary conditions for optimality of the level of grazing pressure is offered in appendix 1. A fourth section considers the ecological impacts of strategy selection in terms of the ratio of optimal grazing pressure to ecologically sctainable grazing pressure. This section draws on model simulations reported in appendix 2. It also discusses the sensitivity of grazing pressure to variation in relative prices. Section 5 draws out the policy implications of the paper, and a final section offers some conclusions. 2. The Wider Context The immediate cause of range degradation in Sub-Saharan Africa is to be found in ecologically unsustainable levels of grazing pressure (stocking densities). The question prompted by the environmental economics literature is whether this reflecs an inherent weakness of traditional range management strategies. Historically, however, both the environment within which such strategies have been applied, and the strategies themselves have been changing. Indeed, the real question is not so much whether traditional range management strategies are inherently unsustainable, as whether the evolution of traditional strategies in response to changes in the institutional, economic and natural environments is sustainable. To approach the answer to this question, this section summarizes the environmental changes that have influened the evolution of traditional range management strategies. -4 2.1 Cimate The first of the exogenous trends that have influenced range management strategies is climatic, and its importance lies in the fact that it has reduced the carrying capacity of the range independently of the stocking decisions of pastoralists. Indeed, it has been argued that climatic factors have been the single most important cause of vegetation loss in rangelands [of Ellis and Swift, 1988].2 The driving force behind climatic change is generally believed to be the process of global warming. However, there is as yet no consensus on what is happening. The Sudano-Sahelian region has experienced an unusually large number of rainfall deficit years since the late 1960s. Moreover, the duration, intensity and extent of droughts in this period have been greater than that of droughts recorded earlier in the century [Snijders, 1986, Grouzis, 1990]. Streamflow has either collapsed or been severely disrupted in a number of rjor river and lacustral systems (the Senegal and the Niger systems and Lake Chad included). A similar story can be told of rainfall patterns in South-Central Africa. What is not clear is if the duration and intensity of drought in the region reflects a reduction in the mean level of rainfall, or simply an increase in climatic variability. The variance in rainfall has certainly been increasing, but the longer term implications of global warming for mean regional rainfall are not at all well understood. Different global circulation models are currently making diametrically opposite predictions in respect of mean rainfall in Sub-Saharan Africa. They are also making contradictory predictions in respect of soil moisture, although it has been argued that even if mean precipitation were to increase, higher temperatures would mean higher rates of evaporation and so increasing soil aridity [Parry, 1990]. 2 One minor qualification to this, is that economic activities may themselves have localized climatic effects. For example, direct vegetation due to arable or pastoral activity may increase surface albedo (reflectivity of solar radiation) so causing air to lose heat radiatively, to descend and to lose relative humidity [cf Charney, 1975]. -s - increasing soil aridity and increasing variation in rainfall have two important consequences for the ecological impacts of stocking decisions. First, increasing soil aridity lowers the mean carrying capacity of the range. Second, increasing variation in rainfall increases variation in carrying capacity. A fail in the mean and an increase in the variance of the maximum ecologically sustainable level of grazing pressure raises the risk of both economic and ecological failure. This trend turns out, as we shall see, to be an important element in the evolution of range management strategies. 2.2 The institutional environment A second important element in the recent evolution of traditional strategies is to be found in changes in the Institutional conditions of pastoral economies in many parts of Sub-Saharan Africa. Traditional range management strategies tend to be associated with pastoral economies characterized by common or communal property in rangeland. That is, they tend to be associated with regimes in which all members of the community have rights of access to the range, regulated to some degree by community authorities. An important trend in this respect has been the steady erosion of the powers of traditional authorities to regulate access to the range. In conditions of open or unregulated access, it is well understood that individuals base their stocking decisions on a private cost benefit calculus that excludes costs carried by other users of the same resources (the 'tragedy of the commons' argument). The result is that mean levels of grazing pressure will be exceed the socially optimal level. In the Sub-Saharan African case it has been argued that while few rangelands can be described as open-access common property resources, the erosion of community powers of regulation over access has led to overgrazing not only in an economic sense, but also in an ecological sense [see for example Jamal, 1983]. It is interesting that this has not, in general, led to the evolut!on of private property rights in rangeland. A number of authors have argued that a necessary condition for the ecologically -6 - sustainable use of rangeland is for communal property rights to be replaced by a system of private rights in which individual resource users are encouraged to take full account of the social opportunity costs of their activities [Ault and Rutman, 1979; Dorner, 1972; Harrison, 1987]. In fact, although traditional rights of access to grazing land in Sub-Saharan Africa are continually changing [Feder and Noronha, 1987; Bruce, 1988; Dyson-Hudson, 1984], there has been no systematic tendency for private property in grazing land to develop [Behnke, 1990; Dixon et al, 1990]. In part this may be because of the lack of evidence favouring private over communal property regimes. Empirically, the introduction of private property in land to traditional producers in Sub-Saharan Africa appears to have offered no advantages over communal tenure systems in respect of either productivity or access to credit [Migot-Adholla et al, 1991; Cousins, 1987]. Nevertheless, in the absence of either privatization or the regulation of access to communal rangeland, there has been a strong tendency to increasing stocking densities on existing ran?-land, and (where population pressure has been extreme) to the extension of pastoral activity into ever more marginal rangelands (Mosely and Smith, 1989; Barbier, 1988; Pearce, Barbier and Markandya, 1988]. One needs to be cautious about ascribing too much to population pressure. It is, for example, well understood that while there is a strong positive general correlation between population pressure and resource degradation, overgrazing bears no systematic relation to population increase [Kates, Johnson, and Haring 1977; Repetto and Holmes, 1983; Pearce, 1987].' But population growth can only exacerbate the effects of weaker institutional controls over access to communal rangeland. The net effect of these institutional trends is for individual pastoralists to discount the impact of their decisions on others, both in the present generation and in future generations. The incentive effects of I Where, for example, the out-migration of labour results in environmental maintenance tasks being neglected, land degradation and and a declining population may go together. Evidence from elsewhere supports the general proposition that population changes can work both ways. In the dryland environments of Mexico, for example, Garcia-Barrios and Garcia-Barrios [1990] argue that emigration is one of the main factors in the weakening of institutions charged with regulating access to resources held in communal property. . 7 communal or common property are overlain by the incentive effects of growing insecurity of tenure. Both those moving on to previously unoccupied land (as squatters), and those holding usufructual rights in systems of communal tenure are increasingly insecure in their tenure of the range encouraging an increase in herd sizes [see, for example, Bruce, 1988]. 2.3 The market environment One other set of trends that has been critical to the evolution of traditional range management strategies has been those associated with the development of national and International markets for livestock products. These are not uncorrelated with the climatic and insdtutional trends already discussed, since they are partly driven by climatic changes, nor are they vncorrelated with each other. Three trends stand out. The first involves a secular decline in real agricultural commodity prices (illustrated in figure 1) on the international market. While this has had the effect of depressing rural incomes it has been exacerbated by a second trend involving the use of government monopsony to depress producer prices below border prices. The third important trend involves an increase in the variance of prices related to local climatically induced fluctuations in supply. Pearce et al (1988] have argued that these trends are in fact the major cause of both the agricultural crisis in Sub-Saharan Africa and the environmental crisis. While government intervention in domestic agricultural product markets may have been motivated by a desire to protect farmers against the volatility of international prices, the affect has been to depress rural incomes and to discourage investment in conservation measures [cf Warford, 1987; Ghai and Smith, 1987; Markandya, 1991. Nor has it been effective in its primary goal. It has, for example, been argued that all famines in the Sudano-Sahelian region in the last three decades have been caused not by food availability decline, but by the collapse of real incomes due to fluctuations in food prices [Sen, 1981; Speece, 1989]. While price distortions have meant that markets have been unable to guide the allocation of resources in a socially efficient way, the effect on both the mean and variance of real rural incomes has introduced a significant additional *8 - risk into pastoral production. Like the increase in climatic risks, the increase in market risks has been a major factor in the evolution of traditional range management strategies. Figure 1: Real agricultural commodity prices, 1950-1986. Index (1979-1980 = 100) 300 -- 250 200 . *Non-food product 150SO " o Food piodvict 100 F - p*,. 0. . 1950 1955 1960 1965 1970 1975 1980 195 Sources: World Bank [1987], World Resources Institute [1990] -9 - 3. Opportunistic Range Managements Strategies A number of recent studies of range management in semi-arid areas of South Central Africa have argued that what differentiates traditional range management strategies in that area from strategies predicted by the equilibrium range succession models is that they are opportunistic[Flirt, 1986; Westoby et al, 1989; Walker et al, 1986; Scoones, 1990; Abel, 1990; Biot, 1990, Benhke and Scoones, 1992]. To approach the analysis of the ecological effects of traditional strategies, therefore, it is useful to consider just what opportunism in range management implies. 3.1 Equilibrium range succession and state-and-transition models The central assumption of the range succession models is that there exists a unique equilibrium state in the absence of grazing: the climax state. Moreover, this state is globally stable. Succession in rangelands away from the equilibrium state is assumed to converge monotonically on that state. Grazing pressure has the effect of perturbing the system, and the depletion of rangeland due to grazing is assumed to take the form of a monotonic change in the opposite direction to the successional tendency. Range regeneration and range depletion functions in this model are assumed to be not only monotonic, but continuous. It is accordingly possible to achieve a long run physical equilibrium in the management of rangelands by ensuring that the marginal rate of range depletion due to grazing is equal to the marginal rate of range regeneration due to succession. Range succession models do admit the stochastic infl; -nce of rainfall, drought being assumed to have the effect of reducing the rate of regeneration and increasing the rate of depletion. But they make no allowance for the potential for the global instability of the system - implying the possibility of either total collapse or irreversible change. * 10 - The arguments against the range succession models concern the assumptions of the global stability of the climax state, and the monotonicity and continuity of regeneration and depletion functions. Empirical research has shown that vegetation change as a result of grazing is frequently discontinuous, non-monotonic, and irreversible. For example, perennial grasslands have frequently been converted to annual grasslands as a consequence of grazing, but have not reverted on the cessation of grazing. Similarly, unpalatable grasses which have become the dominant species on rangelands due to grazing have frequently remained the dominant species on the cessation of grazing. In some cases, the removal of livestock from semi-arid range has resulted in vegetational change opposite to that predicted by the models [Walker et al, 1986; Westoby et al, 1989]. It is argued that the abundance of particular plants may vary with stocking rates in a highly non-linear, non-monotonic way [Walker and Noy Meir, 1982]. In addition, changes in soil conditions as a consequence of changes in vegetation, such as the erosion of surface soil due to devegetation, may not be reversible on the sort of time scale that is relevant to the range management problem [Westoby et al, 1989]. As a result, it has been argued that it is more useful to describe rangeland dynamics in terms of a set of persistent 'states' and the 'transitions' between those states, the transitions being triggered by some exogenous shock or 'event'. Such events may be either natural shocks, such as extreme climatic events or fire, or they may be the consequence of management actions, such as a change in the stocking rate, the destruction of existing species or introduction a new species, a change in the availability of water through dam construction or the drilling of wells, or a change in the composition of the soil or air through the addition of fertilizers, herbicides or pesticides. In addition, it is argued that there exist a set of 'transient states', which are states that have the capacity to evolve in ihe direction of different persistent states, depending on the events that occur during such transient states [Westoby, et al]. The significance of these 'events' is that they are, in principle, independent of herd density or grazing pressure. In the range succession model, equilibrium is maintained by herd 'density-dependent' factors. That is, birth and death rates are a function of herd size relative - 11 - to the carrying capacity of the range. In systems that are away from equilibrium, it is argued that 'density-independent' factors, such as rainfall, dominate herd dynamics [Scoones, 1990, Behnke and Scoones, 1992]. This last argument is based on the findings of a study of herd dynamics in Zimbabwe, which showed that during years of average rainfall, density-dependent factors adequately explained livestock mortality. However, during years of drought, termed 'stress years', livestock mortality was highly correlated with rainfall, and bore no apparent relationship to herd density. There are two substantive innovations in the method of thinking about rangeland dynamics offered by the 'state and transition' models (and other work along the same lines). The first of these lies in the implicit recognition that persistent or equilibrium rangeland states are locally, not globally stable. That is, if a system at some equilibrium 'state' is sufficiently perturbed, it will not reconverge on that equilibrium, but will instead converge on some other equilibrium. It will be irreversibly transformed from one persistent state to another. Moreover, the limits of the local stability of any given equilibrium will define threshold values for livestock, vegetation, water flows and so on. If any one of these variables is driven beyond such threshold values, the system itself will undergo irreversible change. A second real innovation lies in the recognition that what drives change of this sort are exogenous shocks or 'events', and that such exogenous shocks include not only climatic variation or naturally occurring events such as fire, but also human activities. The sensitivity of an equilibrium state to an 'event' of a certain sort and a certain severity (say a drought year with a given total rainfall), will depend on what other 'events' are occurring [Westoby et al, 1989]. So, for example, the sensitivity of an equilibrium state to climatic perturbation will be a function of the stress to which it is subject as a result of human intervention. Symmetrically, the sensitivity of an equilibrium state to human perturbation is a function of the stress to which it is subject due to the variance in rainfall. Thus semi-arid and arid grasslands which are subject to considerable climatic variation will be sensitive to changes in grazing pressure. An opportunistic approach implies that the key range management decisions, those governing the * 12 - size of the herd and so grazing pressure, should depend on the current state - whether this is 'persistent' or 'transient' by the definition of Westoby et al [1989]. Pastoralists should take advantage of current conditions and trends. 3.2 Elements of an opportunistic grazing model There are a large number of range management models specifically developed for semi-arid rangelands, and based on Clemenstian principles of range succession. All link some meat production model with one or more soil, vegetation, water and climatic models. The model used in this paper is canonical, at least in this respect. It is a highly simplified variant of May's [1974] predator-prey model, linking a meat production model of the same general form as that adopted by Barrett [1989, 1991] with a vegetation model. The vegetation model has, however, been adapted to include the positive feedbacks of grazing pressure that so disturb Clementsian succession in actual rangelands. The adaptation permits changes in current stocking density to feed back directly into the future carrying capacity of the range. Hence the model ensures that current carrying capacity of rangeland is not independent of the history of rangeland use. While this may be a more minor modification than is suggested by the range ecology literature just cited, it does accommodate the positive feedback between economic pressure and the resilience of the range. The underlying growth functions for the herd and the vegetative cover of the range are assumed to be logistic, which is consistent with the standard range succession models. But the future growth in the carrying capacity of the range is also assumed to depend on the current herd density. Hence the recuperative powers of the range are jointly determined with current offtake decisions. In terms of the distinction between range succession and state-and-transition models made by Westoby et al [1989], a canonical treatment of this sort may look closer to a range succession model than to a state-and-transition model. That is, it is implied that without grazing the vegetative cover of the range will converge monotonically to some stochastic maximum value (the climax vegation). But notice that what is in fact being assumed is that there exists a 'state', - 13 - defined in terms of some maximum carrying capacity, which is locally stable with respect to perturbation due to climatic variation, but which can be destabilized through grazing pressure. In other words, what is being modelled is one locally stable state. If there are assumed to exist other such locally stable states, and if the rules of transition from one such state to another are defined (at least probabilistically), we would have a complete state-and-transition model. The model solves for the optimal level of grazing pressure given the following: the objectives pursued by pastoralists, the range management strategy employed, the set of economic parameter values (prices, discount rate etc), the herd and range dynamics, and the variability in the environinent within which pastoralists operate. The range management strategy has the effect of filtering the uncertainty created by variation in the environment within which the pastoralists operate, and is described in more detail later. The net benefits of pastoral activity may be expressed in terms of a general benefit or welfare function, but in the exercises carried out to to test the sensitivity of grazing pressure to parameter variations, it is assumed to be given by the difference between the revenue generated through offtake in that period and the net costs of livestock maintenance. The relative benefits of different strategies are then assessed in terms of the net present value of the stream of benefits over the period appraised. Summarizing these elements, and assuming discrete time, we have: T max E ptW(x,,k,,u) (1) ful tin0 subject to x,+, - x, a,x(l - x,/k) - (2) k,+, - 1, = Pk(1 - k/k) - y(, - u) (3) x. > 0 = x(O) (4) 1>0 = k(O) (5) -ktau,wa7,or 0 ; a: , (6) * 14 - x k ;- 0 '(7) where: x, = herd size at time t (0 a x, a k); k, = carrying capacity at time t (0 a1e k,); K. = maximum carrying capacity of the range; u, = offtake at time t (in the most general case -k a u, a x); a, = the net growth rate of the herd on the range (-1 a Q-) A = the rate of regeneration of the range (-1 a 0); r, = the rate of depletion of the range due to the herd (, a 1); T =the time horizon over which offtake is to be optimized; and P = [1/(1+ d)] a discount factor, with d being the rate of discount. The state variables, x, and k, are restricted to non-negative values. Offtake, i,, may in principle be positive or negative. If offtake is positive (implying that livestock is being drawn off the range) it is limited to values less than or equal to the size of the herd. If offtake is negative (implying that the range is being restocked) it is limited to values less than or equal to the maximum carrying capacity of the range. In the absence of supply restrictions or other constraints, restocking will generally be a part of an optimal strategy in a stochastic environment, whether the strategy pursued is an equilibrium or opportunistic one. If restocking is not carried out in most communal grazing lands, u, is restricted to values 0 a u, a x,. The net growth of the herd in any given period (2) is equal to the difference between offtake and the natural growth of the herd, given the degree of grazing pressure, x,/k. The net growth in the carrying capacity of the range (3) is the difference between the net depletion of the vegetative cover of the range as a consequence of the stocking decision, and the natural rate of regeneration of the range. Offtake accordingly has both direct and indirect effects on the size of the herd. If livestock are drawn off in the current period, the current size of the herd is reduced but the * 15 - future growth potential of the herd is improved due to the effect on the carrying capacity of the range via the damage function -Y(x, - u). This last is the extra term in the vegetation model, and is intended to capture at least some of the positive feedbacks observed by range ecologists. While it is not immediately obvious how one would estimate the parameter K, or that this damage function is the best way of accommodating these feedbacks, it is clear that some such modification of the standard range succession model is required to meet their concerns. Derivation of the conditions for offtake to be optimal in this model is given in appendix 1. Given the optimal level of grazing pressure, it is then possible to determine whether the range will be overgrazed. The indices of overgrazing used include both an economic measure, and an ecological meLure. Overgrazing in an economic sense is said to exist wherever the actual level of grazing pressure exceeds the optimal level of grazing pressure. Overgrazing in an ecological sense is said to exist wherever the actual level of grazing pressure exceeds the level of grazing pressure at the maximum sustainable yield. Whether optimal grazing pressure is greater or less than the level of grazing pressure at the maximum sustainable yield depends on the parameters of the system - both economic and ecological. If relative prices are such that it is optimal to 'mine' the range, then the optimal grazing pressure will exceed the maximum sustainable grazing pressure. On the other hand if relative prices are consistent with the sustainable use of the resource, the optimal grazing pressure will be less than or equal to the grazing pressure at the maximum sustainable yield. Economic overgrazing will accordingly be said to exist wherever (I/,*) - 1 > 0, V, being the current level of grazing pressure and t,* being the optimal level of grazing pressure. Ecological overgrazing will be said to exist wherever (q/q.) - 1 > 0, v.the being the level of grazing pressure at the maximum sustainable yield of the range. Since W,. may be greater than, less than, or equal to v,,, it follows that whether a system is overgrazed in an ecological sense does not necessarily imply anything about whether it is overgrazed in an economic sense. But if the optimal level of grazing pressure is equal to or greater than the level of grazing * 16 * pressure at the maximum sustainable yield, economic overgrazing will imply ecological overgrazing. 3.3 Equilibrium versus opportunistic strategies Finally, notice that the general form of the optimization problem and its solution are common to both an equilibrium and an opportunistic strategies being considered here. In both strategies, the solution to the economic problem requires that offtake be increased up to the point where the marginal benefits of offtake equal the marginal costs. Optimal offtake u, * = x, - WAM(s is the same irrespective of the strategy being considered. The difference between the two lies in the treatment of variation in the ecological parameters of the system. More particularly, under an equilibrium strategy, optimal grazing pressure is defined in terms of the expected values of the ecological parameters of the system, U, & and X. Under an opportunistic strategy, the optimal grazing pressure is determined for the current values of the ecological parameters, a,, 0, and y,. To put this another way, if pastoralists adopt an equilibrium range management strategy then, for any given state of nature, they will base their current stocking decisions on the long term average value of rainfall, soil moisture, vegetation growth and so on associated with that state. If pastoralists adopt an opportunistic strategy, on the other hand, they will base current stocking decisions on current values of those ecological parameters. The point has already been made that a canonical treatment of the problem cannot deal with the transition between states. But even if the system included several possible states of nature, an opportunistic strategy would still be driven by current ecological conditions in the prevailing state. Whether herd densities differ under opportunistic and equilibrium strategies will, other things being equal, depend solely on the variance of the ecological parameters. If there is no variation in ecological conditions (or * 17 - if variation is very small), the outcome of the two strategies will be identical (or very close). If variation is very large, then differences in current stocking densities will be large. It follows that one implication of the increase in climatic variation referred to in section 2 will be greater differences in current stocking densities between pastoralists following equilibrium and opportunistic strategies. 4. The Ecological Effects of Traditional Opportunistic Range Management Strategies 4.1 The general characteristics of traditional pastoralism The first point to make is that it should be clear from what has been said to this point that traditional strategies are characterized by a good deal more than their opportunism. It should not be surprising, therefore, that the difference in herd densities observed in communal and private grazing lands of Sub-Saharan Africa is only partly a function of the choice between opportunistic and equilibilum strategies. Optimal grazing pressure depends on the relative benefits of livestock holdings and offtake in traditional and commercial pastoralism, and these in turn depend on a wide range of institutional, cultural and political factors. These factors turn out to be much more important in explaining observed differences in herd density than the choice of range management strategy. Livestock provide various non-market benefits to traditional farmers in the form of draft power, animal products, social status and insurance, none of which are factors in commercial ranching. Hence the marginal private net benefit of offtake relative to inventory tends to be lower in traditional than in commercial livestock farming. Consider just one of these non-market benefits: insurance. Both drought and the volatility of food prices have had a major impact on rural welfare in recent decades, increasing production and marketing risks for pastoral and arable producers alike. Greater climatic variation would be expected to lead to greater variation in stocking densities under an opportunistic strategy, but what one does observe is a risk management strategy that has used input mix to minimize output fluctuations. That is, risks are managed through choice of technique. In marked contrast to the - 18 * countries of South and South-East Asia, in which green revolution technologies were enthusiastically embraced, African producers have persisted with a very conservative choice of inputs. While this is in part due to the lack of successful research and extension for dryland cropping, it also reflects a conscious attempt to minimize both market and climatic risks through input choice. Producers whose current income level is such that they cannot take a current loss without risking starvation adopt "survival algorithms*, to borrow Lipton's [1968] term, involving well tried farming practices, and a product mix that includes drought resistant livestock or crops which are suitable for both market production and direct consumption. That is, products are selected which are robust in the face of climatic variation, and which preserve the option of direct consumption should the terms of trade turn against agricultural producers. This has lead to the selection of livestock capable of surviving in drought years, and to a pattern of herd growth in which herd sizes are built up in good years to provide stocks that will carry herders through drought years. The excess of livestock over the number required to satisfy consumption needs represents savings. That is, under traditional risk management strategies, savings take the form of the accumulation of real assets - cattle - which may be directly consumed or redistributed in times of need. The economic explanation of this is straightforward. Both the risk of declining availability of food as a result of drought, and the risk of adverse movements in the rural-urban terms of trade (often for the same reason) favour a strategy of saving in real over financial assets. If food prices are expected to increase sharply in periods of drought, the conversion of surplus livestock or crops into financial assets itself carries risks. This, together with the fact that financial institutions are still scarce in many parts of rural Sub-Saharan Africa, has encouraged pastoralists to hold their savings in the form of livestock, thereby insuring against the risks of both food availability decline and price volatility during periods of drought [see for example Speece, 1989]. Opportunism is important only as one of the means exploited to maintain herd sizes - 19 - under unfavourable climatic conditions, but the optimal size of the herd is a function of the non-market benefits of livestock holdings relative to offtake. 4.2 Ecological effects in model simulations To see the environmental implications of the choice of strategy under differing economic parameter values in the context of the model described above, the model calibrated in appendix 2 was run over a thirty year horizon at different parameter values. The degree of ecological overgazing associated with each of four different options and at each parameter value is summarized in the following figures. The four options include two variants each of the opportunistic and equilibrium strategies already discussed. One of the variants allows restocking as part of the management strategy. The other does not. The inclusion of these variants is partly motivated by the questions about the welfare effects of restocking after drought raised by Mace [1990], but it is also motivated by an interest in the ecological implications of (a) commercial livestock imports and (b) the movement of livestock within the region through entrustment mechanisms. It turns out that whether a strategy admits restocking or not is a more important source of difference in grazing pressure than whether it is opportunistic or not. And whether restocking is or is not part of a particular range management strategy is more a function of institutional constraints, income levels and market imperfections than it is of opportunism. Figure 1 shows that ecological overgrazing is a monotonically decreasing function of the discount rate. This is an expected outcome if one thinks that pastoralists exploit a renewable resource (the herd). The higher the rate of discount, the higher will be their rate of exploitation of that resource, and 'mining' the herd implies a reduction in levels of grazing pressure. By contrast, figure 2 shows ecological overgrazing to be an increasing function of the net benefits of livestock holdings (a decreasing function of the net costs of livestock holdings). Once again this is quite intuitive. The point has already been made that traditional pastoralists derive significant benefits from liveitock holdings aside from the benefits realized through sales. In .20 - fact, it is quite possible for the net cost of livestock holdings to be negative: that is, for the net benefit to be positive. Livestock may be a good investment irrespective of whether they are sold for meat. Figure 3 shows that ecological overgrazing is a decreasing function of the costs of range access. This is less Intuitive, and requires some explanation. The particular model calibrated here includes a cost of range access to communal lands that is different from, say, a grazing fee, in that it is not directly dependent or herd densities. That is, it is closer to a land price. Since this makes it a quasi fixed cost, the incentive created by higher costs of access is to increase and not decrease stocking densities. The higher is the cost of access to the range, the greater the optimal herd size, and so the greater the pressure on the range. Finally, figure 4 shows that ecological overgrazing is a decreasing function of the sale price of livestock, and is also quite intuitive. The four strategies are denoted as follows in the figure legends: EqWR = Equilibrium strategy with restocking EqNR = Equilibrium strategy without restocking OpWR = Opportunistic strategy with restocking OpNR = Opportunistic strategy without restocking -21 • Figure 1:Ecological overgrazing as a function of the discount rate 0.00 -0.10 -0.20 -0.30 -0- Eo10GEIVR -0.50 -0.60 OE GOI0pVR -0.70 ---W--EcoPOG0NR -0.00 -0.90 -1.00 .22 - Figure 2:Ecological overgrazing as a function of the net benefit of livestock holdings 0.20 0.10 0.00 1 . "l 40.10 'a EooGEtWit -0.20 O 20010011R 0.30 -0.40 -* Eco1GOptVR ZQQIO(;OjNR *0.60 40.70 40.80 a0 * * * * a * a u n u n un u a V *23 - Figure 3:Ecological overgrazing as a function of the net cost of range access 0.20 IIIII -0.25 R110EIVR .-.-O-- colOG3EgIt 4.35 -*- EcolGOWR --**- EcoloGOplat 4.40 9 9 9 U U U U a -24 - Figure 4:Ecological overgrazing as a function of net producer prices 0.40 0.20 0.00 EooGEjYR --***3* EcolOGEINR .0.20 *- EolOGOpVR -0.40 ---Eo N *0.60 4.80 0 '4 to4 g-I U I IU U If U of 04 1% A Ai of ft 4% Since these measures of ecological overgrazing are averages taken over the whole period they do not say anything about the incidence of overgrazing on a year-by-year basis. The low levels of average ecological overgrazing observed in the case of strategies without restocking mask the fact that those strategies are associated with considerable environmental stress at particular moments. To see this, figure 5 describes the time path of ecological overgrazing associated with each of the four strategies when c = 1 (when the net benefits of livestock holdings are, on average, equal to the net price of livestock sales). The period has, it will be recalled, distinct wet and dry phases, and these show up sharply. While figure 2 indicates that the average ecological overgrazing under an opportunistic strategy without restocking is negative - actual grazing pressure is less than maximum sustainable grazing pressure, figure 5 shows that on a year-by-year basis ecological overgrazing is positive and very high over the whole of the dry phase of the cycle. .25 - Figure 5:Ecological overgrazing, four strategies, c = 1. 0.8 0.6 -- *8. a- V-- Ecol o'g:E%VR 0.4 --***--- Ecol olg:EINR 0.2 - 0sn . - E0o1 o'g:OPVR -0.4 -0.6 *0.8 It is the variations in this year-by-year fluctuation in grazing pressure which are significant from a policy perspective. The figure shows, as one would expect, that equilibrium strategies are associated with lower variation in the level of ecological overgrazing than opportunistic strategies. It also shows that strategies without restocking place less pressure on the environment during the wet phase of the cycle than strategies with restocking, but more pressure during the dry phase of the cycle, although strategies with restocking place more sustained pressure on the environment over the whole of the cycle. The environmental problem posed by choice of strategy lies in the response of pastoralists at the onset of drought. If herd sizes are not reduced at the onset of drought in proportion to the drop in carrying capacity this raises the risk of overgrazing. While all four strategies overshoot to some degree at the start of a drought, the problem is worse for strategies involving restocking -26 - since herd sizes under such strategies will have built up at a faster rate during wet years. What is noticeable about this example, though, is that contrary to expectation opportunistic strategies do not adjust more rapidly to a fall in the carrying capacity of the range during drought. While this would seem to be rather counterintuitive, it is reflected in the adjustment processes in actual rangelands. In Botswana, to take one example, the onset of the drought in 1981 had a substantial and immediate impact on offtake rates in the commercial sector but little immediate impact on offtake rates in the traditional sector.' Since the current carrying capacity of the range was falling sharply in this period, the result was very substantial degradation of the range [Arntzen and Veenendaal, 1986]. The point to underline here is that the stocking decisions of pastoralists on the communal rangelands of Sub-Saharan Africa are determined by factors other than the 'opportunism'. Livestock densities under traditional strategies tend to be higher than under other strategies for reasons that have nothing to do with opportunism, but herd sizes tend to fluctuate more for reasons that do have to do with opportunism. Herds are 'encouraged' to grow as fast as possible (through natural increase) during 'good' years, but offtake tends not to increase during drought years proportionate to the fall in carrying capacity. Hence herds suffer exceptionally high levels of mortality. The average rate of offtake is low, and offtake is highly variable [Abel, 1990]. 5. Policy Implications While economic conditions (the set of economic parameter values) do have a central role in determining the optimal level of grazing pressure, that rote is a complex one - and varies with " Percentage rates of offtake from commercial and traditional livestock farms in the first four years of the drought were as follows: Commercial Traditional 1981 23.7 7.8 1982 33.7 8.2 1983 39.9 8.5 1984 38.8 7.3 Source: Arutzen and Veenendael [1986], Table A.2.6. -27 - both the ecological parameters of the system and the initial values of the state variables. The system turns out to be, at most, locally stable with respect to perturbation of the economic parameters - prices and discount rates - and whether a given change in price or discount rate is sustainable depends on the values of the remaining parameters. That is, a change in producer prices of a certain magnitude will have greater or lesser effects depending both on the strategy being pursued, and on the current net cost of livestock holdings, range access, and the rate of discount. A price change that causes a strategy to 'crash' under one discount rate, for example, may not do so under another. Nevertheless, the general implications of a change in any one economic parameter on the optimal grazing pressure under different strategies, and the relative dominance of strategies at different economic parameter values are reasonably well defined. It is therefore possible to discuss, if only in a contingent way, the environmental effects of policy choice. Three related sets of policy questions are important. All concern the relationship between policies, the choice of range management strategy, and the ecological sustainability of the strategy selected under the given economic conditions. The first deals with prices, the second with incomes, and the third with restocking. 5.1 Prices The first set of questions has been canvassed in considerable detail in the literature and what is of interest is the different insights into the impact of familiar economic parameters offered by the model discussed in this paper. It is useful to begin by isolating the main arguments in the literature. The conventional wisdom among environmental economists is that the degradation of the agricultural resource base is a major factor in the near-collapse of the rural economies of many countries in Sub-Saharan Africa, and that degradation of the resource base is a function of the set of relative prices - particularly output prices - confronting resource users. A stylized description of agricultural input and output markets in Sub-Saharan Africa would be that there are two types of market: the near-monopsonistic markets established by centralized marketing boards or meat commissions which set prices largely independently of domestic supply conditions; and the competitive 'parallel' markets in which prices are largely driven by local -28 - supply conditions [cf Harvey, 1988]. It has been very forcefully argued that it is the (producer) price signals generated by the former which have led to the environmental 'crisis' in agriculture [Pearce et al, 1988]. More particularly, it is claimed that the existing system of administered prices in African agricultural markets has driven a wedge between the private and social opportunity cost of the use of resources, so encouraging a misallocation of those resources. There are, by now, numerous examples of this. In respect of agricultural inputs, there are a range of 'subsidies' on developmental work - 'destumping', fencing, borehole and ploughing subsidies - which have encouraged the incorporation of increasingly marginal range and arable land. In respect of outputs, administered producer prices have typically been set below the border prices of agricultural products [Repetto, 1986, 1989; Warford, 1987; Perrings et al, 1988]. As a result, environmental and resource economists have supported price liberalization for tradeable agricultural outputs. Indeed, many have gone so far as to argue that price liberalization is a necessary condition for the conservation of the resource base [Bond, 1983; Cleaver, 1985, 1988; Warford, 1989; Barbier, 1988, 1989b; Markandya, 1991]. Evidence on the impact of price liberalization has so far been mixed. It is not at all clear that price liberalization has improved the stability of agricultural producer prices, but where it has been applied it has resulted in an increase in the producer price level - albeit within the context of a downward trend in world agricultural commodity prices. The introduction of the principle of export parity pricing agricultural products has, however, been uneven, and most countries continue impose costs on agricultural producers through the protection offered the industrial sector [Moseley and Smith, 1989]. Moreover, the results of work on supply elasticities where price regimes have been liberalized has been contradictory. One recent survey of arable agriculture found positive long run supply elasticities for all crops tested [Gammage, 1990], I While the short and long run supply elasticities for cocoa, coffee and sisal were reported to be sgnificantly different, the short and long run elasticities for cotton, groundnuts, palm kernels, and palm oil were reported to be identical. .29 - but others have found supply elasticities to be either very low or even negative [Green, 1989; Rao, 1989]. One set of explanations offered for this is that that price responsiveness is more tightly constrained by institutional factors in Sub-Saharan Africa than elsewhere [Delgado and Mellor, 1984; Lipton, 1987; Junankar, 1989].' A second is that input constraints (especially natural resource constraints) limit the ability of pastoralists to respond to price incentives. It has, for example, been argued that in many parts of Sub-Saharan Africa, both arable and livestock farmers cannot increase output at the extensive margin because they do not have access to land [Feder and Norohna, 1987]. A third is that since a considerable proportion of goods and services are not traded, farmers are less sensitive to price changes than elsewhere (Ghai and Smith, 1987; Beynon, 1989]. The last explanation is worth further consideration. The important point is that farmers sensitivity to observed changes in relative market prices reflects unobserved movements in non-market transactions. Typically, agricultural resources are allocated on the basis of a set of relative costs and benefits that have both market and non-market components, and it cannot be assumed that non-market costs and benefits are either unaffected by price movements, or that they do not also vary independently over time. There are few data on the movement of non-market costs and benefits to parallel the data on price movements, and no analysis of producer responsiveness to change in non-market costs or benefits. However, if we consider only the tendency for growth to have occurred at the extensive margin, it is apparent that this in part reflects a distortion in the private cost of non-marketed inputs caused by the structure of property rights. It is a matter of fact that despite the increasing scarcity of non-tradeable agricultural resources - land, vegetation and water in particular - those resources continue to be implicitly or explicitly subsidized. A dominant feature of the relative cost structure of agriculture in much * It is instructive that most of the evidence on own- and cross-price elasticities of supply and demand that is used to support the use of economic incentives in agriculture is drawn from non African data [Markandya, 1991]. - 30 . of Sub-Saharan Africa, for example, has been the implicit subsidy on land and other natural resources offered by communal land tenure systems. The private cost of land has been almost universally below its marginal social cost, and in most cases it has been 'free' to the user. The same is true of vegetation and, to a lesser extent, water. It is not at all surprising, therefore, that producers should have responded to an increase in aggregate demand through extensive rather than intensive growth. The important point here is that producers respond to changes in both market prices and the non-market costs and benefits of livestock holdings. The key decision as to whether to market output or not is a function of the net costs and benefits of the two options. It cannot, therefore, be assumed that supply responses are 'normal' in the sense that the price elasticity of supply of marketed agricultural products will always be positive. For one thing, market prices do not necessarily reflect the private opportunity cost of livestock. Aside from the fact that livestock may be directly consumed, they are also a source of a range of non-marketed animal products and services of value to the household, most important of which is draft power. They are also a source of prestige and social standing. For example, livestock are a privileged currency in a range of social transactions, including the crucially important 'bride price'. It is highly misleading to cast livestock in traditional agriculture as inputs in a process of commercial meat production. A second, and equally important reason why it cannot be assumed that supply responses will be normal (in the sense described above) is that at low levels of income, the income effects of price changes tend to be very pronounced. Indeed, income effects frequently dominate the substitution effects of price changes of livestock at low levels of income [Perrings, 1989b; 1991]. To summarize, the main propositions coming out of the literature on incentives are (i) that the depression of prices for marketed agricultural output and the subsidization of (marketed) agricultural inputs have both increased the degradation of environmental resources in agriculture; and (ii) that changes in the costs and benefits of non-marketed inputs and outputs has had a -31 * largely indeterminate effect, except for assets such as land where it has had a negative effect. Consider these propositions in turn. The model predictions on prices are unambiguous. If producer prices are increased relative to the net cost/benefit of livestock holdings and access to grazing land, the degree of ecological overgrazing will fall. This is partly because the model does not pick up any positive longer term feedback between producer prices and herd sizes. It has, for example, been argued in the literature that the 'high' producer prices negotiated by certain beef suppliers under the Lome Convention - Botswana, being a case in point - have had a dual effect. On the one hand they have encouraged higher rates of offtake which has reduced pressure on the range. On the other, it has been claimed that they have been responsible for higher stocking densities and that this has counteracted the environmentally beneficial effects of higher offtake [cf Nzinge, 1984]. The second effect is not observed in this model. The general policy implications of this are that raising producer prices may indeed be an effective means of mitigating the degradation of environmental resources in the pastoral economy. The model admits two categories of 'input': one associated with the costs/benefits of livestock holdings, the other associated with the costs/benefits of access to the resource. It follows that wherever a cost is negative, implying that there are benefits of either livestock holdings or range access of greater value than the costs, what is being defined as an input involves a flow of goods or services that are, more properly, outputs. That is, the production function implicit in the maximand (1) involves a vector of outputs associated with each of the control and state variables u, x, and k,. The economic parameters p., cj and r, are not simply prices, but measures of either net cost or benefit. This makes the model very flexible, but it means that care should be taken in interpreting the results of simulations. From a policy perspective, what is important is that the higher the net benefits of livestock holdings relative to offtake, the higher will be the level of optimal grazing pressure; and, similarly, the higher the cost of range access, the higher will be the level of optimal grazing pressure. -32 - As has already been remarked, the relationship between grazing pressure and the not cost/benefit of livestock holdings is both intuitive and consistent with the literature. Anything which raises the ratio c,/p, will increase the level of grazing pressure, and anything which lowers it will have the opposite effect. That is, the risk of ecological overgrazing will increase with subsidies on water provision, fodder, veterinary services, fencing etc that lower the cost of livestock holdings; non-marketed benefits of livestock holdings in the form of animal products or services, such as draft power, or service as collateral in credit markets; negative externalities of livestock holdings that are not compensated by taxes/user fees or other market based instruments. Which is most significant in any given economy is an empirical matter, but all tend to be present in some degree. The easiest to deal with are those directly or indirectly linked to current policy, the most important of which are the range of subsidies on farm inputs. The most difficult to deal with are those with either a cultural, institutional or structural basis. The role of livestock in securing social status, or as a medium in social transactions is not something with which government readily tamper. Similarly, the role of livestock as collateral or insurance against either famine or inflation reflects structural weaknesses in markets due, in part, to the nature of property rights. With respect to negative externalities, although it is well understc xl that these may be internalized through levying taxes equal to the marginal external cost, there are enormous difficulties in estimating such external costs. The relationship between grazing pressure and the cost of range access is less intuitive, and requires some understanding of the basis on which the costs of access are assumed to vary. Recall that r, is held to be an increasing function of the productivity of the range, measured in terms of its current carrying capacity. That is, the net cost of access is assumed to fall as the carrying capacity of the range falls: drought stressed pasture is less costly to the user than productive pasture. The point was made earlier that this is not the only way of modelling the cost of access to grazing land in communal areas, nor is it necessarily the best way. However, given the form in which costs of access are incurred in the sort of economies we are talking about - varied direct and indirect contributions to the village economy which establish - 33 - membership of the community, and so rights of access to community resources - it seems appropriate. Such contributions tend to be an increasing function of income (ability to pay), and so tend to be higher in good years than drought years. If there exist markets for land, either leasehold or freehold, then the form of the access cost function is less controversial, since land prices will be an increasing function of land productivity (representing the discounted value of the income stream associated with the use of the land). There are certainly examples of both: the leasehold ranches created under Botswana's Tribal Lands Grazing Policy, for instance, and the commercial ranching sector based on freehold land. But in general, grazing land is held on a communal basis, and the costs of access are of the former, less well-defined, sort. The arguments in the literature center on the assumption that costs of access to communal land are zero at worst, and strictly less than the marginal social opportunity cost of grazing at best. It is therefore assumed that this too is subsidized, with the result that land is overgrazed. But given the access cost function assumed here, the simulations suggest a conclusion that is diametrically opposite: the lower the cost of access, the lower the optimal level of grazing pressure. It is important to distinguish between those conditions which imply a subsidy on the cost of maintenance per livestock unit, and those which imply a subsidy on the quasi fixed cost of access to rangeland. The former give rise to increased grazing pressure, the latter do not. Two implications which are independent of the rangeland management strategy being pursued follow: First, a policy which results in an increase in the quasi fixed costs of access to rangeland will cause optimal grazing pressure to rise. An increase the 'price' of leasehold land, for example, will increase and not decrease the level of grazing pressure. This means that increasing the costs of rangeland access in the interest of reducing ecological overgrazing is counterproductive. Second, a policy which results in a decrease in the net benefits or an increase in the net costs of livestock holdings will cause optimal grazing pressure to fall. That is, if the aim of policy is to reduce ecological overgrazing through price incentives targeted at 'inputs', a reduction in .34 - (i) subsidies on the cost of livestock holdings and (ii) the benefits of livestock holdings will both cause the optimal level of grazing pressure to fall. 5.2 Income and asset distribution The measures of income and wealth used in this paper are, in part at least, very indirect. The initial values of the state variables measure the relative size of the economic and natural asset holdings (livestock and land), but can give no indication of whether these indicate 'high' or 'low' wealth. The only measure of this, the discount rate, depends on the functional relationship assumed to exist between the rate of time preference and the degree of subjective poverty. It was earlier argued that the level and distribution of rural income and assets is a significant part of the explanation for both the risk aversion of agricultural producers, the adoption of risk management strategies involving the use of drought resistant species of livestock suitable for direct consumption, and the tendency for savings to take the form of real assets (livestock). It has also been suggested that part of the explanation for the mixed evidence on the price responsiveness of agricultural producers in the region is to be found in the dominance of income over substitution effects - also a function of the distribution of rural income. In short, the poverty of resource users is argued to have a powerful influence both on attitudes to risk and innovation, and on savings and investment decisions. The result is a 'vicious circle' of responses to external incentives, in which the options available to successive generations are steadily eroded [Perrings, 1991]. There is certainly considerable evidence that rural poverty in Sub-Saharan Africa is both deepening and widening. Not only is the proportion of the rural population receiving or in need of emergency relief growing, so too is the shortfall of actual incomes or assets on either the poverty datum line or the set of assets defined to constitute 'basic needs'. Coincidentally, the distribution of both income and assets has been widening over time. The importance of increasing impoverishment is argued to lie in its impact on the resource user's rate of time preference or rate of discount. The deeper the impoverishment of resource users, the higher will their rate of time preference tend to be [Perrings, 1989a]. Increasing poverty - 35 * accordingly means that the future or user costs of current decisions will be discounted at an increasing rate. One implication of this is that costs of environmental degradation that bear only on future generations will be ignored in the cost-benefit calculus carried out by present users. What is relevant here, though, is that since the optimal rate of extraction of both exhaustible and renewable natural resources is an increasing function of the rate of discount, it follows that increasing impoverishment of the rural population implies increasing optimal rates of depletion of the asset being exploited - in this case the herd. The exercises reported in appendix 2 show the rate of discount to be significant both in the choice of range management strategy, and in the level of grazing pressure associated with each strategy. To be more specific, income levels work on the level of grazing pressure through the rate of discount in two rather different ways. First, the higher the rate of discount relative to the natural rate of growth of the herd, the lower will be the average optimal level of grazing pressure relative to the maximum ecologically sustainable level of grazing pressure. For all strategies, the higher the rate of discount the more rapidly is the herd run down. So, as figure 1 shows, the impoverishment of pastoralists (measured through the rate of discount) is reflected in lower mean herd sizes and so lower mean levels of grazing pressure - not in overgrazing. Second, for the example examined in appendix 2, as the rate of discount is increased the relative dominance of strategies changes. Whereas equilibrium strategies dominate at low rates of discount, opportunistic strategies dominate at high rates of discount. This too has implications for grazing pressure. Care should be taken both in interpreting and in drawing too definite a set of policy conclusions from this example. The extreme myopia of poverty is 'good' for the environment in the sense that the rapid consumption of the herd ensures that the range will not be overgrazed. But what may be ecologically sustainable is not necessarily economically sustainable. Opportunistic strategies dominate equilibrium strategies above certain rates of discount in this example precisely because the longer term private costs of those strategies (negative income) are fully -36 - discounted. To make this transparent, figure 6 shows the time path for the herd size under each of the four strategies at a discount rate, 35 per cent, at which opportunistic strategies dominate. In the pattern very similar to that observed in a number of pastoral economies in Sub-Saharan Africa, during the wet phase of the rainfall cycle herd sizes are built up at a higher rate under opportunistic than equilibrium strategies, but during the dry phase they also undergo a much more severe decline. Since the flow of income generated under each strategy corresponds to the movement in herd size, it is evident that the opportunistic strategy dominates only where the future costs of a collapse in herd size are sufficiently discounted. Figure 6 Herd sizes, four strategies, d 0.35. 80 70 60- 50 40 * so 20 10 0 Period *37 - While the mean level of ecological overgrazing associated with the dominant opportunistic strategies in this case is very low, it should be remembered that the example is based on a set of economic parameter values that favor offtake (the net benefits of livestock holdings are low relative to the net producer price). A typical characterization of the endowments and circumstances of impoverished pastoralists would include both low levels of livestock holdings, and a level of net benefits of livestock holdings that is 'high' relative to the net benefits of offtake. Poor livestock farmers tend to be those with very few livestock, on which they rely heavily for draft power and other services. If the ratio of net benefits of livestock holdings to net producer prices is high enough, then irrespective of the rate of discount, the level of ecological overgrazing will be high. The direct 'cause' of overgrazing in such circumstances is not poverty but the ratio of net benefits of livestock holdings to net producer prices - even though the two may be closely related. From a policy perspective, it is this ratio which is important. Under all strategies, and for any positive rate of discount, if the ratio of private net benefits of livestock holdings to net producer prices is high enough, and if there are no restrictions on herd growth, it will be optimal to degrade or 'mine' the range. The central policy problem is to identify and address the factors which lie behind these ratios. 5.3 Restocking The third set of questions concern the desirability of restocking as a policy option [Mace, 1990], and so include the relationship between policy and the various market imperfections that preclude restocking as an option. There are three rather different questions here. The first is whether strategies involving restocking involve higher levels of ecological stress than strategies with no restocking. The second is whether restocking is part of an optimal strategy. The third is what precludes restocking from occurring even when it is part of an optimal strategy. The answers to the first two questions are, as one would expect, conditional. First, whether strategies with restocking place greater stress on the environment than strategies with no restocking depends on the economic parameter values, the 'economic environment'. If relative -38 - prices are such that optimal herd densities are higher than initial herd densities, then strategies with restocking will both dominate strategies without restocking, and place greater pressure on the range. Second, if the relative costs and benefits of livestock holdings are such that optimal herd densities are low, the difference between strategies in terms of both the net present value of income and the optimal level of grazing pressure will be small. But in the simulations reported in appendix 2, strategies it. olving restocking generally to dominate strategies without restocking. Indeed, strategies without restocking are dominant only at very high rates of discount or very high levels of producer prices. In general, therefore, restocking is economically desirable. This makes the third question particularly interesting: what prevents restocking from taking place? It has earlier been suggested that this is related to imperfections in a number of markets, of which the most important is the market for rural credit. There is something of a chicken and egg problem involved - at least in respect of traditional range management strategies. The high ratio of net benefits of livestock holdings relative to net producer prices which makes restocking part of an optimal strategy is itself a function of imperfections in the market for credit. More particularly, an important part of the flow of benefits from livestock holdings is the potential value of livestock as (formal or informal) collateral in raising rural credit, given that under the communal land tenure system other assets are unacceptable. But the difficulty of securing loans for investment in livestock is what most often stands in the way in of livestock acquisition. The problem for policy is a complex one involving reform not just of the existing financial institutions, but also of a system of inalienable property rights which makes it impossible for investors to use the assets over which they have some control as collateral. Various alternatives short of freehold tenure have been canvassed in the literature, including the possibility of making the usufructual rights of members of the community owning communal lands fully tradeable [Perrings, 1991]. It is beyond the scope of this paper to deal with such specific recommendations, but it is important to underline the fact that the admissibility or otherwise of * 39 - restocking as part of an optimal strategy involves the resolution of a particularly intractable set of institutional problems. 6. Conclusions It is transparent that whatever the range management strategy employed, the net present value of the income stream is an irtzreasing function of the net producer price (of offtake) and the net benefits of livestock holdings; and is a decreasing function of the not costs of rangeland access and the discount rate. What is not transparent is the precise relationship between change in any of these magnitudes, choice of range management strategy, and environmental degradation. The link between optimal grazing pressure and each of the economic parameters is reasonably well defined. That is: * The net producer price and optimal herd densities are inversely related: increasing the net producer price of offtake causes the mean optimal grazing pressure and the mean level of ecological overgrazing to fall. * The net benefits of livestock holdings and optimal herd densities are directly related: increasing the net benefits or reducing the net costs of livestock holdings relative to the net producer price causes the mean optimal grazing pressure and the mean level of ecological overgrazing to rise. * The net costs of access to grazing land and optimal herd densities are directly related: increasing the net cost of access to grazing land causes the mean optimal level of grazing pressure and the mean level of ecological overgrazing to rise. * The dominance of strategies involving restocking over strategies that do not involve restocking is an increasing function of the net benefits of livestock holdings relative to -40 - the net benefits of offtake (producer prices); and a decreasing function of the initial herd size relative to the carrying capacity of the range. The relation between the economic parameters and the choice of management strategy is much less well-defined. Opportunistic strategies are generally associated with greater variability in herd size and so greater variability in grazing pressure relative to the current ecologically sustainable level of grazing pressure. Hence, for a given set of economic parameters, opportunistic strategies will have a greater propensity to cause the system to 'crash' than equilibrium strategies as the variance in rainfall increases. Opportunistic strategies will accordingly dominate equilibrium strategies in such circumstances only if the future net benefits of avoiding a crash are discounted at a high enough rate. That is, opportunism is an increasing function of the discount rate. But note that at very high rates of discount all strategies converge, since at very high rates of discount it is optimal to 'cash in' the herd irrespective of the strategy pursued. This suggests that it is income rather than prices which may determine the choice of strategy in variable climates. It is worth re-emphasizing, therefore, that the fundamental problem in rangeland degradation does not appear to lie in the choice of management strategy per se, but in the set of institutional and economic parameters within which that choice is made. The private decisions of pastoralists tend to be based on a calculus of costs and benefits that ignores many of the user and external costs of grazing, while constraints on livestock acquisition mean that those with low initial livestock holdings are progressively disadvantaged over successive rainfall cycles. Not only does a smaller herd size carried into the dry phase of the rainfall cycle provide less protection against the price and output effects of drought, it is more easily lost altogether during drought. And even if it is not lost altogether, it provides a much lower platform for rebuilding during the wet phase. Moreover, the progressive impoverishment of livestock owners in an institutional environment which inhibits the reallocation of resources from one use to another implies a progressive reduction in the opportunities available to future users of those resources. -41 - The general trend in policy in recent years has been for producer prices in livestock sectors to be moved in the direction of border prices (net of transport costs). At the same time, while there has been some tendency for subsidies on farm inputs to be reduced, the effect on rural incomes of subsidy cuts during a period of secular decline in world agricultural prices has inhibited governments from either reducing subsidies or invoking powers to restrict grazing pressure by limiting access to the range. The net result is that on a private cost benefit calculus pastoralists have tended to increase herd densities. While concern for the impact of policy change on rural incomes is very well founded, the results of this paper suggest that there may be better ways of addressing the problem. The model results indicate that the producer price is an effective lever on stocking densities, but that the positive environmental impact of an increase in producer prices may be readily offset by increases in the net benefits of livestock holdings. If offtake prices are increased by less than the net benefit of livestock holdings, the result will be higher, not lower, stocking densities. It is a characteristic feature of livestock and mixed farm development programmes that they have been built around systems of subsidies that have exactly this effect. Given the current structure of private costs and benefits in the livestock sector, it is clear that the pricing of livestock 'inputs' at marginal social cost and the introduction of a livestock tax or grazing fee equal to the marginal external cost of grazing would reduce the net benefit of livestock holdings, while the pricing of offtake at marginal social opportunity cost would increase the net benefit of offtake. Note that the second element does not imply an increase in the quasi fixed cost of access (which would imply an incentive to increase the level of grazing pressure). It implies an increase in the cost of maintenance per livestock unit. The important point here is that ecological overgrazing is primarily a function of relative net benefits of livestock holdings, grazing access and offtake. These are partly determined by relative prices, partly by a variety of non-market costs and benefits, and partly by the structure of asset holdings - since these influence the average net benefits of livestock holdings or inventory relative to offtake. If it is socially optimal to maintain the viability of the rural economy then, from an environmental perspective, it is better to deliver that support via the net benefits of offtake than via the net benefits of inventory. This may well imply producer prices *42 - above current border prices, and the argument here is that while this may be motivated by equity considerations is not necesssarily socially inefficient (where the substitution of meat imports for domestic production itself generates externalities). Indeed, if producer prices in excess of border prices were 'funded' from the proceeds of grazing fees or livestock taxes, the additional financial cost to society would be zero. Finally, on the issue of opportunistic versus equilibrium policies, it seems clear that while the variability of ecological parameters is a necessary condition for opportunistic strategies to dominate equilibrium strategies, it is not a sufficient condition. Which strategy dominates depends on both the ecological and the economic conditions (parameter values) within which pastoralists operate. The results of the exercises reported here do not show the environmental implications of opportunistic strategies to be significantly different from equilibrium strategies, and it has been argued that the very high stocking densities observed in areas where pastoralists pursue an opportunistic strategy is likely to have more to do with the high level of net benefits of livestock holdings than with opportunism. Similarly, the high levels of ecological overgrazing and associated herd mortality observed in dry periods is likely to have more to do with the absence of restocking, than with opportunism. It is these relative costs and benefits, rather than the opportunism of the strategy, that should be targeted by policy. -43 Appendix 1: Optimal grazing pressure The time paths of the herd and the carrying capacity of the range are described by the sequences sequences {x} and (k,), both measured in terms of livestock units, and generated by the forward recursions: x1+1 - x, = a,x(l - x/k) - u, (Al) k+.. - k = AkW( - kk) - yA(, - U) (A2) the variables and parameters defined as in the text. Maximization of the vegetation growth function (A2) with respect to current carrying capacity shows that the maximum rate of regeneration of the range is k, = k, = 1/2k,. The maximum sustainable yield of the range is the point at which the net rate of depletion of the range due to grazing is equal to the maximum rate of its regeneration. From (Al) and (A2), the size of the herd corresponding to the maximum sustainable yield is given by: x. = (k/4v){-(1 - a) ± [(1 - v) + 2oA/yTI2) (A3) and the maximum sustainable level of offtake is given by u. = ox,(1 - x,/k,) = x - 1/2(/la)k, (A4) The time path for all variables depends on the ecological parameters, a, A and y,. These are stochastic, and are assumed to independently distributed random numbers with means g, a and X, and variances o.2, oq' and .2*. The system is thus subject to 'process noise'. As a result of the variance of , and A, the time behaviour of the recursions (Al) and (A2) may be extremely complex - even in the absence of offtake. The herd growth function may have normal compensatory, overcompensatory, depensatory and critical depensatory properties for similar herd sizes at different periods. There is no reason to believe that normal compensatory growth -44 - (which leads asymptotically to convergence to equilibrium values for both herd size and range carrying capacity) will be encountered in reality. Indeed, it is more likely that growth will be overcompensatory (leading either to convergence via damped oscillations, or to non-convergent oscillation). But it also perfectly possible for the growth function to be critically depensatory (leading to the collapse of the herd) where carrying capacity falls sharply over consecutive periods. In general, change in the size of the herd will vary directly with change in the level of grazing pressure given by the ratio x/k,. In general, that is, overgrazing will lead to a decline in the size of the herd. However, it is important to add that since the natural rate of growth of both herd and carrying capacity is assumed to fluctuate, and since negative values for a,and b, are admissible, this will not necessarily be the case. The decision problem is summarized in equation (1). The current value Hamiltonians for this problem under the equilibrium and opportunistic strategies respectively are: H(x,,Aj W(x,,ks,u) + pA,.,{ax,(l - x/k,) - u,}+ pC.j{k(1 - k/k.) - X(x, - u)} (AS) and H(x,,U,,A) = W(x,,k,,) + pAY,,{o,x,(1 - x/k) - u}+ pt.,(Ak,(1 - k/k) - y,(x, - u,)) (A6) The first order conditions for an optimum under an equilibrium strategy require that 0 = H. =- A., + pC.,y (A7) pAW, - A = -H, = -W - pA,,g(1 - 2x/k) + pC,lx (AS) P.,- = -H. = -W. - pA,.,g/k2 - pC.&( - 2l/k,) (A9) X,4, - Xt = H,. = ax,(1 - x,/k) - % (AlO) k.+ I - k, = H.,. fik(1 - k/k.) - X(x, - u) (All) x0 = x(O) (A 12) 1c = k(O) (A13) ut 6 U .45 - To obtain the first order conditions for an optimum under an opportunistic strategy, the mean values of a. and Y in these equations are replaced by their current values. As in all such problems, the maximum condition (A7) requires that at the optimal level of offtake, the marginal benefit of offtake, W,, should equal the marginal (user) cost. The adjoint equations, (A8) and (A9), describe the evolution of the shadow prices of the state variables as a function of offtake policy and the dynamics of the physical system. If a steady state solution exists, such that A, As, , and C + ,, (A7), (A8) and (A9) may be used to define a steady state 'rule' for determining the optimal level of grazing pressure. Defining the ratios: K, a KtIK (A14) , a X1 (A15) S is on/got, (A16) Wk i (/O, (A17) solving (A8) and (A9) for the steady state values of A and r from, and inserting these into (A7) yields the quadratic: 0 = &It(+W.) - W*2alM(1-2, - Wur- 41 + Wel( - a + 6) + fX(1 -2q - 41wa + 9 - 41 (A18) or, in the opportunistic case 0 = ,* y,(1+W) - *2 g(1-2K) - ay46 + wiyt(1 - , + 6) + IA(1-24 - 61m.+ a.- 41 (Al9) W,*, a positive root of the quadratic defines the optimal level of grazing pressure. It will differ between (A18) and (A19) whenever the current value of the ecological parameters is not equal to the mean value of those parameters. In each case, given r,* the optimal herd size *46 - corresponding to ., is obtained directly. The optimal offtake is that which adjusts the herd size to its optimal value. It is defined by: tk * = xt- VIA (A20) and is subject to the restrictions imposed the admissible values of u,, which vary depending on whether restocldng is admitted or not. This rule for determining the optimal offtake in identical under each strategy. In both cases if restocking is admitted, the optimal offtake 'restores' grazing pressure to the optimal level, given the current carrying capacity of the range. If restocking is not admitted, the optimal offtake gets as close to the optimal grazing pressure as possible. -47 - Appendix 2: Simulation results This appendix simulates time paths for the main economic and environmental variables in each of the strategies being evaluated. The economic variables of Interest are measures of the level and dispersion of 'income' or market and non-market benefits from pastoral activity to be defined momentarily. The environmental variables of interest are the ratio of current carrying capacity relative to the maximum carrying capacity (defined by equation A14); the index of grazing pressure, defined by (A15); and the two measures of overgrazing defined in the text. The measure of economic welfare used the following simulations is the present value of the stream of income generated over a thirty 'year' time horizon. The welfare function is assumed to have the simple form: W(ut,xi,k) = put- ex&- rk (A21) where p = the 'price' of offtake c = the net cost of livestock maintenance r = the 'cost of carrying capacity' t = {1,...,30) p denotes the producer price, or the price per livestock unit net of the cost of transport to the point of sale. c denotes the net cost of livestock on the range. c may be positive or negative. If it is negative, which may well be the case in traditional livestock farming, the benefits from the maintenance of livestock exceed the costs. Since what is being modelled is the behaviour of a particular locally stable state, and since it is -48 * assumed that for such a state the range succession is given, the ecological parameters of the model are based on a set of fixed values. a = 0.2(rate of herd growth) 0 = 0.25(rate of range regeneration) y = 0. 1(rate of range depletion due to grazing) These values are assumed to be subject to the influence of variation in climatic and other environmental conditions. In 'good' years, the rate of herd growth and range regeneration, , and A, will be greater, and the rate of range depletion, ,, less than these values. In drought years, the opposite will be true. In the particular example for which time paths of the key economic and ecological variables are shown, 0.15 & a, 5 0.27, 0.19 5 A s 0.34 and 0.07 5 y, 5 0.13. While many of the properties of the model can be illustrated by assuming that rainfall is stochastic, we are interested in the application of different strategies under the reasonably well-defined cycles observed in the semi-arid areas of Sub-Saharan Africa. The variation in the ecological parameters of the model are accordingly assumed to follow a cyclic pattern, although no attempt has been made to approximate actual cycles. In Southern Africa, for example, the cycle frequency is approximately 18 years, but in what follows it has been assumed that the time horizon over which the performance of different strategies is evaluated covers one cycle only - implying a cycle frequency of thirty 'years'. This avoids the complications brought by shorter cycles, whilst illustrating the general significance of the cycle for both the economic optimality and ecological impact of different strategies. The time paths for the ecological parameters, given this cyclic variation in rainfall, consists of two sets of random numbers - one corresponding to the 'good' years in the cycle, the other corresponding to the drought years. If the maximum 'sustainable' yield is estimated on the basis of current rather than expected values, it follows that it will vary with rainfall. Table Al records the ecological parameters and -49 - the corresponding maximum sustainable yield size of the herd (MSYH) used in the following simulations. While the outcome is sensitive to the particular parameter values chosen, the results reported below are more sensitive to assumption made about the pattern of rainfall variation than they are to the mean values of ecological parameters. It turns out that rainfall cycles have an important role to play in the selection of strategy, and in the environmental effects of different strategies. The economic parameters include (a) the set of relative prices, or more properly, marginal utilities, and (b) the rate of discount. The latter is included in this category less because of its relation to the rate of interest, than because it is the only available proxy for the level of income of farmers relative to their subjective perception of their own subsistence needs. The rationale for treating the discount rate as a proxy in this way is the observed relationship between dissaving and subjective poverty [cf Drewnowsd, 1977; Perrings, 1989a]. People in subjective poverty - whose income falls below their subjective assessment of their subsistence needs - tend to dissave to maintain consumption. Dissaving indicates a 'high' rate of time preference. The link between 'high' discount rates and (subjective) poverty does not have the status of an empirical 'law', but it is sufficiently widespread to use the discount rate as a proxy for income in the present context. If the relationship between the rate of discount and income were sufficiently well defined it would be possible to endogenize the discount rate within the model, but for now it is assumed to be given exogenously. 50 - Table Al: Ecological parameter values (cyclic rainfall case) Period a, A Vt MSYH Period e, A MSYH 1 0.269 0.336 0.074 247 16 0.160 0.200 0.125 66 2 0.268 0.335 0.075 245 17 0.161 0.201 0.124 67 3 0.205 0.256 0.098 127 18 0.155 0.193 0.129 60 4 0.247 0.308 0.081 201 19 0.151 0.189 0.132 56 5 0.237 0.296 0.084 183 20 0.157 0.196 0.127 62 6 0.204 0.256 0.098 127 21 0.179 0.223 0.112 89 7 0.233 0.292 0.086 176 22 0.164 0.205 0.122 70 8 0.249 0.311 0.080 205 23 0.170 0.213 0.117 78 9 0.212 0.265 0.094 139 24 0.164 0.205 0.122 70 10 0.261 0.327 0.077 231 25 0.172 0.215 0.117 80 11 0.219 0.274 0.091 151 26 0.184 0.230 0.109 96 12 0.228 0.285 0.088 167 27 0.162 0.202 0.124 68 13 0.222 0.278 0.090 157 28 0.171 0.214 0.117 79 14 0.248 0.310 0.081 204 29 0.168 0.210 0.119 75 15 0.231 0.289 0.087 172 30 0.149 0.186 0.135 $3 The values assumed for each of p, c, r and 6 are indicated at the point where the results of the simulation are reported. Since these are all potential policy instruments, the simulations are designed to show the economic and environmental impact of change in any one, holding the others constant. Two output price regimes are considered: one in which output prices are exogenous, and one in which output prices vary inversely with rainfall. The first reflects a small open economy assumption. The second reflects the drought-related price risks that feature so prominently in the literature on famine [cf Sen, 1981] and non-market consumption [cf Lipton, 1968]. While p is restricted to positive values, both c and r are allowed to take positive or negative values - for reasons which have already been explored. r may be thought of as a productivity-related charge for the use of grazing land of a defined area, or an access fee. r 0 corresponds to the open access common property model. r > 0 implies that the cost of putting livestock on to the range is positive. r < 0 implies that the cost of puitting livestock on to the range is negative - or that there is a direct benefit in rights of access. This last case is more common than might be supposed. If there are no community charges or levies on grazing land, and if there are positive external effects associated with access (say hunting, gathering or water rights), r may well be negative. This is not the only or even the best way of modelling the costs of grazing land. It is intended to reflect the fact that the private -SI - costs of access in Sub-Saharan Africa are not, in general, directly related to the number of animals on the land. Nor are they related to the scarcity of land. They are more in the nature of fixed costs. However, to the extent that they do vary, they appear to be an increasing function of the productivity of land. The exercises that follow address a number of questions raised by the range management and ecological literature on opportunistic grazing, including those mentioned in the introduction to this report. These questions fall into three categories depending on whether they relate to the choice of strategy, to environmental effects, or to policy. The first of these concerns the economic implications of different strategies. The question here is what are the conditions in which one strategy dominates another [Scoones, 1990]. The second concerns the ecological implications of different strategies. The questions here are what determines the 'high' level of stocdng densities in traditional opportunistic range management and what is the relationship between optimal ecological and economic grazing pressure (Scoones, 1990]; what are the ecological implications of the mean level [Biot, 1990] and variance [Abel, 1990] of stocking densities. In terms of the state-and-transition models which underlie the theory of opportunistic management, the question is how different strategies may affect the evolution of the ecological systems supporting pastoral activity. The third category concerns the policy implications of the choice of strategy, and includes questions about the value of positive intervention to exploit current changes in the state of the range, whether through restocking [Mace, 1990] or more comprehensive environmental engineering [Westoby et al, 1990]. The policy implications of an equilibrium strategy have been thoroughly explored in the literature, though rather less throughly tested in real situations. The first set of questions addressed concern (a) the conditions in which one strategy dominate any others, and (b) the environmental implications of different strategies. It is intuitive that a sufficient condition for the pastoralist to be indifferent between strategies is that there is no variation in rainfall, and so no uncertainty about the value of ecological parameters. More particularly, for a given set of economic parameters, the present value of income generated -52 - under equilibrium and opportunistic strategies, and the environmental impact of those strategies, will be the same if the ecological parameters are constant over time. It follows that if there is no variation in rainfall, and so no uncertainty about the value of ecological parameters over time, the effect of changes in the economic parameters on both producer income and the environment will be independent of the strategy pursued. Specifically, under both equilibrium and opportunistic strategies, grazing pressure will be a decreasing function of the benefits of offtake (producer prices), and the costs of herd maintenance and access to grazing land, and an increasing function of the costs of offtake (transport to the point of sale), and the benefits of both livestock on the range and access to grazing land. If there is variation in rainfall, and so uncertainty about the value of ecological parameters, the two strategies will generally differ in respect of both the present value of the income stream generated and in their environmental impact. To see this in the case of a cyclic pattern of rainfall and for a given set of economic parameters, consider the following simulations of optimal size of the herd, carrying capacity, offtake and the present value of the income stream associated with each strategy. The initial values of the economic parameters have been selected to reflect the main characteristics of the pastoral economy based on communal grazing lands in Sub-Saharan Africa. The price of offtake net of transport costs, p, is assumed to vary inversely with the ecological parameters. That is, producer prices are assumed to rise during the dry phase and fall during the wet phase of the cycle. The net cost of herd maintenance is assumed to be negative. More particularly, it is assumed that livestock are, on average, 20 per cent as valuable to the pastoralist on the range as when sold. The net cost of access to the range is assumed to be positive, but low relative to the producer price. This approximates a situation in which (a) there is something very close to open access common property, and (b) livestock confer a range of non-market benefits to the owner. It is assumed that the rate of discount is 10 per cent. It is assumed that the herd size is initially below the carrying capacity of the range. In particular, it is assumed that x. = 50, and that k. = 100. This is the position that may be expected at the .53 * end of a dry phase of the cycle when livestock fatalities and offlake have cut herd sizes. The time paths for optimal herd size, carrying capacity and offtake for each of the four strategies is reported in figures Al to A4. Table A2: Economic parameter values Period 6 c r p Period 6 c r p 1 0.1 0.27 -0.07 0.75 16 0.1 0.16 -0.04 1.25 2 0.1 0.27 -0.07 0.75 17 0.1 0.16 -0.04 1.25 3 0.1 0.20 -0.05 0.98 18 0.1 0.15 -0.04 1.30 4 0.1 0.25 -0.06 0.81 19 0.1 0.15 -0.04 1.33 5 0.1 0.24 -0.06 0.85 20 0.1 0.16 -0.04 1.28 6 0.1 0.20 -0.05 0.98 21 0.1 0.18 -0.04 1.12 7 0.1 0.23 -0.06 0.86 22 0.1 0.16 -0.04 1.23 8 0.1 0.25 -0.06 0.81 23 0.1 0.17 -0.04 1.18 9 0.1 0.21 -0.05 0.95 24 0.1 0.16 -0.04 1.22 10 0.1 0.26 -0.07 0.77 25 0.1 0.17 -0.04 1.17 11 0.1 0.22 -0.05 0.92 26 0.1 0.18 -0.05 1.09 12 0.1 0.23 -0.06 0.88 27 0.1 0.16 -0.04 1.24 13 0.1 0.22 -0.06 0.90 28 0.1 0.17 *0.04 1.17 14 0.1 0.25 -0.06 0.81 29 0.1 0.17 -0.04 1.19 15 0.1 0.23 -0.06 0.87 30 0.1 0.15 -0.04 1.35 -54 - Figure Al: Herd size, range carrying capacity and offtake: Equilibrium strategy with restocking x,, u, 180 40 160 140 20 120 - 60 -------.a 10010 40 20 0 -80~ Period -55 - Figure A2: Herd size, range carrying capacity and offtake: Equilibrium strategy with no restocking 200 $ 190 20 10 140 120- 100 - - - - 40 60 20Pi 0 14+.uuu4 ___________ q4 .e.4 q. - I. t < ø~ If t~ ø 0> U>Paw -56 - Figure A3: -Herd size, range carrying capacity and offtake: Opportunistic strategy with restocking x,,k u, 180 25 160 120 140 1215 120 10 kt 60 5 --- - 60 40- 20 - - 0i i i i i i i i i i i i i i i i i i 5 Period - 57 - Figure A4: Herd size, range carrying capacity and offtake: Opportunistic strategy with no restocking 200 80 ISO . 180 - --2 to . 25 140 -0 120 - ---.- kt to00 15 -* d, sos 100 - 1 40 20 Period All strategies share the general characteristic that herd sizes are built up in good years, and are reduced during periods of drought. However, maximum herd densities tend to be greater under strategies with restocking than under strategies without restocking. If initial grazing pressure is less than the optimal grazing pressure, herds are built up during the wet phase of the cycle to higher levels under strategies with restocking than they are under strategies without since. In strategies that do not admit restocking, herd sizes are built up, at most, at the maximum natural rate of increase. In the present example this results in a gap between actual and optimal herd size during the wet phase of the cycle. The result is that the carrying capacity of the range increases more rapidly under strategies without restocking than with restocking during the wet phase of the cycle. *58- It is immediately obvious that the differences in herd sizes and offtake recorded in figures Al to A4 will have implications for income flows between strategies with and without restocdng. It is rather less obvious how income flows will differ between equilibrium and opportunistic strategies. The income flows associated with each strategy are recorded in figure AS. Recall that the four strategies are identified as follows: Equilibrium strategy with restocking EqWR Equilibrium strategy without restocking EqNR Opportunistic strategy with restocking OpWR Opportunistic strategy without restocking OpNR Given that livestock are assumed to offer benefits other than at the point of sale (the net cost of herd maintenance is assumed to be negative), strategies involving restocking dominate strategies without restocking. Specifically, strategies with restocking generate an income stream with a higher discounted value than strategies involving no restocking. This is because the restocking option enables pastoralists to exploit the increased carrying capacity of the range during the wet phase of the cycle. In respect of the distinction between equilibrium and opportunistic strategies, if the pairs of strategies with and without restocking are considered separately, the equilibrium strategy with restocking dominates the opportunistic strategy with restocking, but if restocking is not admitted, an opportunistic strategy is marginally more productive than an equilibrium strategy. Overall, the dominant strategy in terms of present value of the stream of income is, in this example, an equilibrium strategy with restocking. The distinction between strategies with and without restocking is intended to capture the effect of imperfections in a number of markets - especially rural credit markets. The 'no restocking' option can therefore be thought of as reflecting the existence of an exogenous constraint on the acquisition of livestock. In environmental terms the constraint means that, in this example, the level of grazing pressure will be lower during the wet phase of the cycle, but higher through the -59* dry phase. The 'with restocking' option, by contrast, places greater stress on the range during the wet phase of the rainfall cycle, but involves lower levels of stress during drought periods. Figure AS: Income: four strategies Income 70 50 40 --*- Incom ena 30 ---aXa4ft R 2o -*--WMoXesjM 0 -10 Period To see how economic conditions bias the choice of strategy, the following exercises test the implications of variation in each of the parameters,6, p, c and r, for the net present value of the income stream and the degree of ecological overgrazing associated with each of the four strategies. In every case, the values of those parameters not being varied are as in table A2. The rate of discount is assumed to bear a well defined relationshp to the level of income of the decision-maker. More particularly, it is assumed that the rate of discount varies inversely with asset holdings, so that the poverty of pastoralists is proxied by high rates of discount. In the following simulation, the discount rate is varied between 5 and 50 per cent. The net present *60 - value and variance of incom6 corresponding to the discount rates tested are reported in table A3. A zero entry implies that the strategy concerned is not viable at the given rate. So, for example, at a 5 per cent rate of discount, an opportunistic strategy with restocking 'crashes'. The net present value of income is a decreasing function of the discount rate. This partly reflects a direct effect, and partly reflects that fact that the higher the rate of discount, the faster the rate at which herds are run down. Table A3 Net present value and variance of income for 0.05 5 6 5 0.5 PV(Y)Eq PV(Y)Bq PV(Y)Op PV(Y)Op Var(Y)E Var(Y)E Var(Y)O Var(Y)O WR NR WR NR qWR qNR pWR pNR 8 0.050 275.11 259.02 0.00 256.99 137.88 126.08 0.00 106.41 * = 0.100 147.40 136.84 141.53 136.33 147.49 125.67 92.25 112.65 a = 0.150 88.81 82.44 86.31 82.14 156.82 126.97 102.66 134.15 8 - 0.200 59.12 55.58 57.96 55.18 167.71 134.41 149.19 177.05 6 - 0.250 42.94 41.51 42.53 41.01 183.36 143.81 243.12 249.12 8 = 0.300 33.69 33.22 33.82 33.43 208.67 161.89 410.61 373.56 = 0.350 28.27 27.82 28.84 28.94 252.46 185.67 433.99 425.16 & = 0.400 25.08 24.49 26.07 25.98 181.19 106.38 317.06 238.01 6 = 0.450 22.55 22.48 24.03 24.28 84.17 78.43 193.67 106.83 & = 0.50 21.68 21.68 22.53 23.05 90.03 90.03 84.72 83.22 The relative dominance of strategies is indicated in figure A6, which shows the net present value of the income stream associated with each strategy over the range of discount rates tested, as a proportion of the average net present value of income under all strategies. Given the ecological and economic parameter values assumed here, it can be seen that the choice of strategy depends on the rate of discount. If economic conditions admit restocking, then at low rates of discount (< 0.3) the equilibrium strategy dominates the opportunistic strategy, but at high rates of discount (> 0.3) the position is reversed. The same is true if economic conditions do not admit restocking. At low rates of discount the equilibrium strategy dominates, at high rates of discount the opportunistic strategy dominates. More interestingly, at rates of discount greater than 0.35, an opportunistic strategy without restocking dominates an opportunistic strategy with restocking. Note that for rates of discount approaching 100 per cent, all strategies yield the same net present value of income. The general implications of the link between discount rates and the dominance of different strategies is considered the text. -61 - Figure A6: The dominance of strategies as a function of discount rates Relative dominance of strategies 1.04 1.02 -- PV(Y)EiVR 1.00 - --PvmzN~1R 0.98 9VYOY 0.95 - PVMYOINR 0.94 0.92 I Il1l 00 C 0 0 0a 0 0 0 a U U Q Q a The next relationship investigated is that between income and the net maintenance cost of livestock holdings. Given the parameter values assumed in this example, there is no strategy which yields an income stream with positive net present value if the net maintenance costs of the livestock are positive (net benefits negative). That is, all strategies are viable only if livestock yield positive benefits in excess of their maintenance costs - whether as draft animals, sources of milk, collateral, currency in social transactions. Hence the range of c tested is from zero to 1. c = 0 implies that livestock yield benefits exactly equal to their maintenance cost, c = 1 indicates that livestock yield net benefits equal, on average, to their net sale price. The nt present value and variance of income corresponding to the values of c tested within this range are reported in table A4. *62 - Income is naturally an increasing function of the net benefits of livestock on the range. Moreover, in terms of the relative dominance of strategies, it is quite intuitive that strategies with restocking will increasingly dominate strategies without restocking as these net benefits rise. In this example, there is no level of net benefits of livestock holdings for which opportunistic strategies dominate, although it should be born in mind that the same would not be true if discount rates were much above the 10 per cent assumed here. Table A4:Net present value and variance of income for 0 S c s 1 PV(Y)Bq PV(Y)Eq PV(Y)Op PV(Y)Op Var(Y)E Var(Y)E Var(Y)O Var(Y)O WR NR WR NR qWR qNR pWR , pNR c = 0 *9.78 -9.78 -6.71 -6.83 8.30 8.30 39.68 81.16 c - 0.1 58.28 56.09, 56.70 55.18 60.54 57.02 50.68 85.70 c 0.2 147.40 136.84 141.53 136.33 147.49 125.67 92.25 112.65 c - 0.3 251.67 225.48 241.34 224.72 248.39 185.54 175.30 160.38 c - 0.4 366.30 315.27 351.23 314.71 367.21 250.85 314.58 228.65 C - 0.5 487.91 406.50 467.83 406.07 514.42 337.41 525.23 327.05 C - 0.6 614.21 498.43 588.88 498.08 699.75 466.98 820.49 459.96 c - 0.7 743.73 590.76 712.91 590.63 930.29 600.16 1210.99 593.95 c = 0.8 875.49 683.33 838.93 683.42 1210.81 793.65 1704.92 781.07 c = 0.9 1008.85 776.09 966.32 776.49 1544.40 971.74 2308.54 970.75 C = 1 1143.37 868.96 1094.63 869.63 1933.05 1186.58 3026.65 1196.95 Figure A7: The dominance of strategies as a function of the net benefits of livestock holdings. Relative dominance of strategies 1.20 ***oo*** PV(T)EVR 1.1 ~PVYOEtVR 1.0 0 PV(Y)ENR 1.00 0.90 t 0.85- 0 1 1 1 1 1 The same clear dominance attaching to strategies involving restocking may be observed in relation to the cost of access to grazing land. It is assumed here that the cost of access is positive, and this assumption has been preserved in the following exercise. r is varied over the range -0.15 S r S -0.000001, and the net present value and variance of income associated with each strategy for the values tested within this range are reported in table AS. The relative dominance of the difference strategies as r varies is shown in figure A8. *64 - Table A5:Net present value and variance of income for -0.15 M r ! -0.000001 PV(Y)Bq PV(Y)Eq PV(Y)Op PV(Y)Op Var(Y)Eq Var(Y)Eq Var(Y)Op Var(Y)0p WR NR WR NR WR NR WR NR r = -0.150 16.84 -1.15 12.41 -1.94 174.94 131.45 90.63 110.84 r = -0.125 49.16 33.24 44.47 32.73 165.11 127.30 84.79 120.88 r = -0.100 81.70 67.70 76.70 67.46 157.24 125.84 82.81 136.57 r = -0.075 114.45 102.23 109.07 101.69 151.36 125.02 85.09 120.79 r = -0.050 147.40 136.84 141.5 136.33 147.49 125.67 92.25 112.65 r - -0.025 180.55 171.59 174.05 171.02 145.68 127.63 105.15 106.68 r = 0.000 213.87 206.46 206.56 198.73 145.96 131.39 125.10 113.80 Figure A8: The dominance of strategies as a function of the net cost of access to grazing land. Relative dominance of strategies 1.25 1.20 + 1.15 1.05 -.-..____ - --PI)jI 1.00- - VYO R 0.95 0.0 PVrnOPNR 0.85 0.80 This indicates that where the cost of access to grazing land is 'high', strategies involving restocking dominate those with no restocking, and amongst those strategies involving restocking, the equilibrium strategy dominates the opportunistic strategy. The degree of dominance of strategies involving restocking reduces as the costs of access to grazing land -65 * fall, but even where pastoral land is 'free' the equilibrium strategy with restocking yields a higher net present value of income than the opportunistic strategy with restocking. Recall that the cost of access to grazing land is not a livestock unit-based grazing fee, but is closer to a fixed cost. The importance of restocking is simply that it enables the costs of access to grazing land to be spread over a larger (income generating) herd. Finally, consider the effects of a change in producer prices (or the cost of livestock transport to the point of sale). As in the case of the discount rate, changes in producer prices turn out to reverse the relative dominance of the four strategies. A wide range of producer prices is considered, with 0 s p s 7. The net present value and variance of income associated with each strategy is reported in table A6, while the relative dominance of each strategy is indicated in figure. Table A6:Net present value and variance of income for 0 ! p s 7. PV(Y)Eq PV(Y)Eq PV(Y)Op PV(Y)Op Var(Y)B Var(Y)E Var(Y)O Var(Y)O WR NR WR NR qWR qNR pWR pNR p M 0 232.60 121.25 0.00 121.25 139.59 39.59 #NUMI 39.59 p = 1 147.40 136.84 141.53 136.33 147.49 125.67 92.25 112.65 p = 2 186.87 184.44 183.28 183.85 236.40 233.40 238.69 291.37 p = 3 242.37 241.20 241.78 246.33 330.32 327.00 504.59 572.45 p = 4 302.39 301.51 305.12 311.68 446.44 444.45 889.40 951.10 p = 5 364.28 363.67 370.49 377.48 590.04 588.83 1393.46 1424.01 p = 6 427.12 426.78 436.91 443.89 763.17 762.61 2017.00 2003.71 p m 7 490.52 490.45 503.94 510.73 966.82 966.73 2760.17 2695.27 The position is similar to that with the discount rate. At 'low' producer prices, restocking strategies dominate no-restocking strategies, and equilibrium strategies dominate opportunistic strategies. However, at 'high' producer prices, not only do opportunistic strategies dominate equilibrium strategies, but opportunistic strategies without restocking dominate opportunistic strategies with restocking. 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