Modelling economic outcomes of livestock production systems

"A good model is one that abstracts from all the details that are unnecessary for the purpose of solving the problem at hand."

"Farming systems research rests on two central propositions: (i) that effective research in agricultural technology starts and finishes with the farmer: (ii) that integration of the perceptions of biological and social scientists is an essential element in such research."

The purpose of model building

Objectives and values

The purpose of model building is to improve our understanding of systems in order (i) to operate them, (ii) to repair them, (iii) to improve them and (iv) to construct new ones (Spedding, 1975). Applied to livestock production these aims amount to either better management of an existing system or the design of improvements. In either case same criteria are needed for evaluating performance. We can only judge whether a system is operating effectively if the objectives have been defined. Similarly, we can only judge whether an improvement has been achieved in relation to specified objectives.

It is now widely recognised that the producer's objectives are critical in this respect. There is no point in developing systems which maximise meat offtake per hectare if this is not the pastoralist's main objective; the new system simply will not be adopted. Hence, effort is needed to elicit the livestock producer's aims, often no easy task, before evaluation can be attempted. Sometimes the producer's aims conflict with declared national objectives or the public interest, for instance where overstocking occurs. The solution then is to develop new institutions, which eliminate the conflict: New techniques of production on their own will not eliminate the conflict. It is assumed for the remainder of this paper that systems are operated and designed to meet the producer's objectives, insofar as they can be ascertained.

Closely linked with the formulation of objectives is the measurement of value. If we can evaluate inputs and outputs in the producer's terms, then system performance might be measured in terms of net increase in value (value added) or productivity (value of output divided by value of input). It may be noted that the two measures do not necessarily result in the same ranking. Thus, the productivity of small ruminants per kg liveweight of the dam is probably higher than for cattle, but the net liveweight production per dam per year is probably lower.

Within a system, inputs may be evaluated in terms of their contribution to output or value added, the measures being known as the 'shadow prices'. For instance, the shadow price of pasture might be measured in terms of livestock production from that land. Problems of valuing inputs only really arise where inputs cross the boundaries of the system. This consideration may influence where we draw the boundaries.

Boundaries of the system

The treatment of a very small part of the universe as a separate system is arbitrary in order to limit the scale and complexity of the modelling task. Generally, farming systems research is limited to those items which are under the producer's managerial control; his crops, his livestock and his family (Figure 1). However, there are various external relationships with the natural environment and the economic and social environment. Inputs and outputs must be evaluated at these boundaries.

Figure 1. Various circumstances affecting farmers' choice of a livestock technology (Based on: CIMMYT, Planning Technologies Appropriate to Farmers: Concepts and Procedures (Mexico: 1980))

The farming system may be subdivided into three main subsystems: crops, livestock and the household. Some livestock enterprises, such as pigs and poultry or small ruminants in West Africa, do not compete directly with crop production for the use of land. If there is division of labour within the household, the enterprises may not compete for labour. In these circumstances the livestock form a supplementary enterprise and may be considered independently of the rest of the farm. 

For pastoral systems the three subsystems of rangeland, animals and household are clearly linked in both directions (Figure 2). Nonetheless, for purposes of analysis it may be necessary to model the subsystems gently and then to link the models together.

Figure 2. The Borana System

Time-dependence

Much farming systems analysis and model building is essentially static in nature. It is concerned only with inputs and outputs over a single production period, often taken to be one year. This may be appropriate in the case of annual crops, but represents an arbitrary curtailment of a time-dependent process when dealing with permanent crops or livestock. A breeding flock or herd of livestock, at any point in time, is the outcome of reproduction and growth in the past, and may be expected to survive into the future. In economic terms it is capital.

All populations of livestock, or anything else, develop over time according to what Boulding (1978) calls 'the bathtub principle,' namely that change in population over a given time interval is equal to inflows minus outflows. For a herd of livestock we have the simple difference equation:

Pt – Pt– 1 = B (t)–  D (t)                                  (1)

            where Pt = herd population at date t

B (t) = inflows in t– th time period

(births and immigration)

D(t) = outflows in t– th time period

(mortality and offtake)

In practice, net immigration, through receipt of gifts or phases from outside the herd, is often unimportant and may be ignored. Also, it may be convenient to separate offtake, a control variable directly under the producer's influence, from mortality, a parameter largely influenced by environmental factors (Figure 3). However, for simplicity, in the following remarks, the two are combined.

Figure 3. The dynamics of herd development

Generally, inflows and outflows are, measured as proportions of the existing stock and are assumed to remain constant, on average, over time so that equation (1) becomes:

Pt = (b + 1 –  d) . Pt– 1                                (2)

   where   b = rate of inflow (birthrate)

   and        d = rate of outflow (mortality and offtake)

  1– d = survival rate

If the herd is changing in size and perhaps ageing, there are problems in estimating the change in value; that is, the herd appreciation or depreciation. Most accounting methods are rather arbitrary. There are two ways of avoiding the problem. One is to consider the whole lifetime of a herd over many years and to use discounting methods for evaluation. The other, simpler, approach is to assume that herd size and structure remain constant, this being achieved by adjusting offtake so that inflows equal outflows. Thus the herd structure remains in a steady state or, more strictly, a stationary state.

In order to analyse the implications for herd structure, the herd should be subdivided into sex and age cohorts and reproductive rates and survival rates made age specific¹ Equation (2) is then replaced by a set of simultaneous equations relating herd structure at date t to structure at date t– 1. Thus, for instance,

Number of calves 0– 6 months at date t

= net calving rate x number of cows at date t– 1

          Number of calves 6– 12 months at date t

= survival rate 0– 6 months x number of calves 0– 6 months at date t– 1

¹Note that the adult breeding female is the central unit in flock structure. Numbers of males are simply linked through the required ratio of breeding males to females.

Choice of the number of age cohorts and the time interval between one date and the next involves a trade-off between complexity and precision, but also depends upon data availability. The whole simultaneous equation system may be represented in matrix vector form as

P_t= [ T ] . P_t1                                                       (3)

where P_t is a vector of populations at date t for each sex-age cohort and [T] is a transition matrix, based on reproductive and survival rates (see Hallam, 1983, or Nhirdie, 1976) .

Cohort analysis shows that achievement of a stationary state or steady state growth (without fluctuations) requires the establishment of a particular herd structure in terms of the relative numbers in each cohort. This herd-growth model may be used in various ways. For instance, we could calculate for a given matrix [ T ] (i.e. given reproductive, mortality and offtake rates) and the existing herd structure, what will be the pattern of herd development over time, whether it is likely to achieve a steady state and if so, when. Alternatively, and this is the approach used in the remainder of this paper, we can calculate, for given reproductive and mortality rates, (i) what offtake rate and (ii) what herd structure is appropriate to maintain a stationary state. In short, the only empirical data used in the evaluation are productivity and mortality data. The existing herd structure is irrelevant.

Before leaving the question of time, it should be noted that the interaction of the pastoralist with his environment may be a very long-term process. This may pose serious problems for economic evaluation, and is not attempted here. The problems are exacerbated by shorter term environmental variations, which are a major cause of risk.

Sensitivity analysis

The incorporation of risk greatly complicates model building. There are problems both of measuring risk and of evaluating the producer's attitude to it. Thus risk has an important effect on choice of objectives; the pastoralist may be more concerned with maintaining an adequate output for survival in all conditions than with maximising average value added. Much work remains to be done on attitudes of livestock producers to risk, but no attempt is made here. The sensitivity analysis carried out is aimed simply at measuring risk or variability of outcomes.

Sensitivity analysis is a fairly crude means of measuring risk. It consists of selecting certain key parameters that affect performance, such as reproductive rates, growth rates and mortalities, and repeating the analysis for different values of these key parametres by substituting these alternative values in the model. The parameters may be varied individually or in combination, and may be changed in a direction likely to improve performance or in an adverse direction. In order to limit the number of repeat analyses, and for simplicity, a case can be made for only varying the parameters individually and in an adverse direction. Thus, separate analyses may be made to estimate performance with low reproductive rates, or with low growth rates or with high mortalities.

The question then arises as to how low or high these parameters should be set. Ideally the choice should be based on objective measures of the range or variability of the key variables where standard errors have been estimated from empirical data, these may be used to determine a lower (or upper) limit for the appropriate confidence interval. However, this approach may mislead if the data series on which the estimated standard errors are based is too short to cover all possible environmental variations.

Sensitivity analysis may also be used to test the effect of purposive variation of control variables, such as varying the offtake rate or nutritional levels of the animals.

Small ruminants in southwest Nigeria

The model

Dwarf sheep and goats are kept as a supplementary enterprise on many arable and tree–crop farms of southwest Nigeria. The system has been studied extensively by the ILCA Humid Zone Programme based in Ibadan and described by ILCA (1979), Matthewman (1980) and Upton (1985). Since the enterprise, consisting of only three or, four animals, represents a small part of the whole household economy and, according to the farmers themselves, is operated mainly for financial gain, the use of market prices to evaluate output seemed appropriate. For goats the market price of a yearling in 1983 was N 20 while that of a breeding doe was N 36. (Note N 1 was worth approximately $1 US in 1983).

Goats, in particular, are left to scavenge on scraps found in the centre of the village, so they do not compete with crops for land. Labour and other inputs are minimal. For these reasons it seemed appropriate to treat the breeding flock as an independent system, with virtually no input costs other than those of the animals themselves. Goats were analysed separately from sheep.

The goat flock was divided into five age cohorts:

1. Female kids less than 1 year old;

2. Replacement does;

3. Breeding does;

4. Male kids less than 1 year old; and

5. Adult males.

Productivity data, derived from more than 400 individual records by the ILCA/Ibadan team (Mack, 1983) were used to predict the steady-state flock structure and annual offtake. The results all related to a single breeding doe are as follows:

Flock structure		Offtake
Female kids less than 1 year old	1.2	Female yearlings	0.37
Replacement does	0. 25	Male yearlings	0.61
Breeding does	1
Male kids less than 1 year old	1.2	Total	0.98
Adult males	0.08

Evaluating the offtake figures at market prices gives a net value added per doe per year of N 17.27, and a rate of return on the value of the stock of 34%.

Sensitivity analysis

For purposes of sensitivity analysis, standard error estimates for productivity parameters from the ILCA survey were used to determine the corresponding standard error for a flock of four goats. Each key variable was adjusted in an adverse direction by one standard error to test the impact. The results (Table 1) show that variation in mortality has the greatest impact on economic performance, followed next by reproductive performance. Variation in prices had the least effect. Similar results were obtained for dwarf sheep though generally at a higher level. These results, therefore, suggest directions for research policy, in that the first aim should be to reduce or stabilise mortalities if this can be achieved relatively cheaply. Secondly, emphasis should be given to stabilising reproductive performance. Improved marketing to reduce price variation may produce few benefits and, since it would require seasonal production to meet peak demand, is difficult to achieve.

Table 1. Sensitivity analysis of returns to Dwarf goat production (average rate of return 30) .

Parameters changed	Change	Net output per doe	Rate of return %
1. Reproductive—
(a) Mean litter size	Reduced
(b) Parturition interval	Increased	8.27	18
2. Mortality—
(a) Survival to 3 months	Reduced
(b) Survival to 12 months	Reduced
(c) Breeding stock mortality	Increased	–0.31	–0.6
3. Growth—
Liveweight at 12 months	Reduced	12.05	24
4. Price per kg.	Reduced	14.00	29

Southern Ethiopian rangelands

Objectives and the household economy

The Borana pastoralist system of the southern Ethiopian rangelands is much more complicated than the small ruminant system discussed above. Here the cattle and supplementary sheep and goats form the basis of the household economy. The Borana are almost entirely dependent on livestock for their survival. However, this is a semi-subsistence system. A substantial portion of the diet is made up of home-produced milk and dairy products and some, particularly fallen, meat. However, animals are also sold, together with some milk. Indeed, it is estimated (Cossins and Upton, 1984) that at the present ratio of livestock to human populations the Borana could not survive without trading some livestock produce for grain, which is a much cheaper source of metabolisable energy.

Thus, there is a problem of how best to evaluate inputs and outputs. For traded items, money values are appropriate, but for subsistence produce, nutritional values such as the metabolisable energy content are more relevant. In cases such as this, scarce form of multi-objective programs may be appropriate, incorporating both nutritional and cash-income goals. However, since it is not clear how these goals should be specified or weighted, and to avoid undue complexity, both methods of evaluation were used.

Of course, the nutritional value of a foodstuff does not depend solely upon the metabolisable energy content. Indeed, livestock products are particularly important as a source of protein. However, given that energy deficiency is the most prevalent form of malnutrition, and that protein malnutrition is unlikely to occur among pastoralists, it seemed reasonable to concentrate only on energy values as a measure of nutritional contribution.

As mentioned earlier, the study of pastoralist systems should involve the rangeland, the herd and the household (Figure 2), but rather than attempting to build a comprehensive model of the entire system, the three subsystems may be modelled separately, for greater simplicity and flexibility in analysis. This separation requires some means of evaluating the output of each subsystem as it contributes inputs to another. We have already considered how the output of the livestock herd can be evaluated in terms of its contribution to the household economy. Given the ratio of livestock to human population and the allocation of offtake between subsistence consumption and sales, energy and financial budgets can be used to model the household economy. Estimates of the total energy value of subsistence consumption, when compared with total household food energy requirements, show what deficits must be made up from purchased food. Estimates of the cash value of sales provide measures of the disposable income available to meet additional food and other needs. These measures are the ultimate test of the viability of the system.

The rangeland system

Various models are available for estimating primary productivity of rangeland, generally based on vegetation type and length of growing season. In order to relate the livestock subsystems to the rangeland system, it is necessary to arrive at the carrying capacity in terms of hectares per grazing livestock unit (ha : LSU, or its reciprocal). This may be based on estimates of primary productivity and the assumption of a minimum 'offer requirement' per livestock unit of between 7 and 8 tonnes, as was done in the southern rangelands study (Cossins and Upton, op. cit.) or directly from environmental and climatic data as suggested by Gartner (1981). Although the definition of livestock units and the conversion factors for different classes and age groups of livestock are arbitrary and inaccurate, they are necessary to allow sufficient flexibility for comparing alternative livestock and pasture management policies. Thus value added per LSU is a useful measure of the livestock production in relation to a limited carrying capacity of the rangeland.

It is important that the variability in carrying capacity over time should be determined both between wet and dry seasons within the year and between years of good rain and of drought. According to the general principle that the most limiting constraint actually determines what is feasible, the primary productivity in dry or drought seasons is effective in determining carrying capacity. Availability of surplus dry matter in good seasons is irrelevant unless policies can be devised to make use of these surpluses. However, in many cases, and probably in the southern rangelands of Ethiopia, water is the most limiting factor. Again, a distinction must be drawn between wet- and dry-season water; normally the latter is the effective constraint. That being so, improvement in dry-season water supply is the key to increased rangeland productivity. Naturally if too much water is provided then primary productivity becomes the limiting constraint and overgrazing will occur. Generally speaking, accurate estimation of rangeland dry-matter production and attempts to improve primary productivity or to increase wet-season water supply are of little value if these are not effective constraints.

Modelling dry-season water supply is a challenging problem in location theory since wells and ponds represent spatially distributed key centres. With a relatively sparse distribution of water points, overgrazing (i.e. dry matter being the effective constraint) in the vicinity of these points and under-utilisation of the pasture (i.e. water being the effective constraint) elsewhere is inevitable. A denser scatter of low-yielding¹ water points would result in more even and better utilisation of the rangeland, but would be more costly. The transhumance or settlement patter of the pastoralists also affects the utilisation of water and rangeland (Figure 4). Some exploratory analysis of the effects of location of water points has been done (Andreae, 1966; Helland, 1977; Cossins, 1983), but no comprehensive model exists to take account of such complexities as separate management of dry and milking herds and variations in the frequency of watering.

Figure 4. The size of the grazing area, showing its dependence on the distance from the watering place to the homestead 
(1) Watering place at the boma : large pasture area. 
(2) Watering place removed: smaller pasture area.
 (3) Watering place far removed: small pasture area

¹Low-yielding water points have the advantage that fewer animals can be watered so that less overgrazing occurs in their vicinity.

For the southern rangelands study, a crude analysis based on mapping of grazing areas accessible from dry-season water points suggests that dry-season water supply limits rangeland utilisation, particularly in the northern and western parts of the area. An increase in the number of strategically-sited wells could raise the average livestock support capacity by 100 000 LSUs or 25% of the existing average.

The cattle subsystem

Production parameters for Boran cattle have been collected in the southern rangelands by the ILCA team (Nicholson, 1984) and these were used to construct a herd-growth model, as outlined above. The main parameters and their effects are illustrated in Figure 5. Under the existing traditional system, Boran cattle do not reach maturity until 4 years old, although faster growth rates are achieved on ranches. This slow growth is due, at least in part, to the human consumption of milk which competes with supplies to the calf. On average 312 litres, or more than a third of the total yield, is taken per lactation for household consumption. Therefore, in the first analysis it was assumed that animals are slaughtered, sold, or drafted into the breeding/milking herd at 4 years of age.

                  Use:For any given number of Cows N
                          To calculate 1. Number of animals in other age/ sex classes hence total herd size
                                               2.Total milk production/year
                                               3. Total offtake/year

Figure 5. Cattle sub-model (annual model)

The resultant stationary-state herd structure differed significantly from that recorded in a large number of observations at watering points (Table 2). In particular, the observed herds included fewer immature animals, which suggests that offtake occurs at an earlier age in practice, even at less than 1 year of age. Further evidence of this was obtained from market surveys, where sales of calves were recorded.

Table 2. Borana herd structure.

A comparison was, therefore, made between the system with offtake at 4 years of age and that with offtake mainly at 1 year, when animals have much lower cash and energy values. In both cases an average milk offtake of 312 litres per lactation was assumed. Cash and energy values of the offtake per livestock unit, with the energy value of home-consumed fallen meat added in the latter case, and the rate of return on the value of stock were all used as criteria for comparison (see first two lines of Table 3). These results suggest that early offtake of calves is sound policy for maximising both cash and energy production per livestock unit. The reason for this somewhat surprising result is the high value of milk offtake in both cash and energy terms. Milk is the most valuable product for the Borana pastoralist. Hence, a system which reduces the proportion of immature followers and increases the proportion of milking cows in the herd raises total returns per livestock unit.

Table 3. Sensitivity analysis of Borana cattle performance.

Sensitivity analysis in this case was aimed at exploring the potential for improved performance under alternative management practices rather than evaluating risk. Two main alternatives were considered; first, increased growth rates and earlier maturity which might be achieved through improved calf nutrition and second, increased milk offtake. The former policy might require reduced milk offtake and/or supplementary feeding of concentrates. Improved nutrition should reduce mortality besides increasing growth rates and this prospect was also considered. In either case there is a clear improvement over the system of offtake at 4 years maturity, as might be expected. However, the advantage over the early offtake of calves is less clear when evaluated in cash terms.

Increasing milk offtake by 50% brings about substantial increases in the energy output per livestock unit, even though it may increase calf mortality. This is perhaps to be expected since milk represents nearly two-thirds of the total energy offtake even at the average level of consumption. However, in practice there is a limit on the quantity required for domestic consumption, whilst clearly the required offtake per cow decreases with increasing cow ownership per person. Milk is a highly priced commodity at Birr 0.11 per MJ of metabolisable energy, compared with Birr 0.03 per MJ for maize. However, the market is strictly limited, except for the few pastoralist households within easy access of a town. Hence, improved dairy processing and market facilities would be needed to allow the Borana pastoralists to benefit from the milk-production potential of their cattle.

Conclusions

This paper illustrates the use of simple herd growth models in the evaluation of livestock production system. Such models take account of the time dependency of livestock production and are suitable for use in sensitivity analyses to test the effects of random biological variation or of alternative management policies. Useful insights are obtained. However, it is necessary to separate the production relationships within the breeding herd from the rangeland or fodder subsystem. It would be exceedingly difficult to incorporate complex physiological relationships, and this would undoubtedly reduce the flexibility of the model.

The model also has other uses which have not been explored here. For instance, it could be used to test alternative culling policies in the face of drought and to map the changes in flock structure during the period of recovery. In assessing the producer's objectives, it is not really adequate to assume that he maximises value in some sense. This does not explain, for instance, why small ruminant producers in southwest Nigeria generally restrict the number of animals kept per household to four or five, or how pastoralists decide on their flock sizes. Much work remains to be done in modelling the application of alternative objectives, alternative policies to minimise risk and alternative flock and herd growth patterns.

References

Andreae. 1966. Weude wirtschaft in Sudlichen Afrika. Geog. Z. 15.

Boulding K. 1978. Ecodynamics. Sage Publications.

CIMMYT (International Meat and Maize Improvement Center). 1980. Planning technologies appropriate to farmers: concepts and procedures. CIMMYT, Mexico.

Cossins N J. 1983. The crucial centres: water production and well efficiency in Borana. Joint Ethiopian Pastoral Systems Study Research Report No. 12.

Cossins N J and Upton M. 1984. The productivity and potential of the southern rangelands of Ethiopia. Unpublished manuscript, ILCA.

Gartner J A. 1981. Evaluation of feed supply from grassland and other sources. Paper presented at the informal meeting on modelling livestock production in developing countries, 8–12 September 1981, Winrock International, Arkansas.

Hallam D. 1983. Livestock development planning: a quantitative framework. Centre for Agricultural Strategy, University of Reading, UK. Paper No. 12.

Helland J. 1977. Social organisation and water control among the Borana of southern Ethiopia. In: S B Westley, ed. East African Pastoralism: Anthropological perspectives and development needs. ILCA, Addis Ababa.

ILCA (International Livestock Centre for Africa) . 1979. Small ruminant production in the humid tropics. Systems Study No. 3. ILCA, Addis Ababa.

Mack S D. 1983. Evaluation of the productivities of west African dwarf sheep and goats in south-west Africa. ILCA programme document No. 7.

Matthewman R W. 1980. Small ruminant production in the humid tropical zone of southern Nigeria. Trop. Anim. Health Prod. 12:234.

Murdie G. 1976. Population models. In: J G Andrews and R R Mclone, eds. Mathematical modelling. Butterworths, London, UK.

Nicholson M J. 1984. Calf growth, milk offtake and estimated lactation yields of Borana cattle in the southern rangelands of Ethiopia. Joint Ethiopian Pastoral Systems Study Research Report No. 6.

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Discussion

Question – Do the results presented in Table 2 mean that the modelled herd size is much bigger than observed?

Answer  – Well, it is all expressed per milk cow.

Question  – So, my statement is not necessarily true but, if you have the same number of cows in the model as observed, then presumably the model gives a much bigger herd size?

Answer  – The observed data refer to a series of observations at wells, reduced to proportions of the total number of animals observed, and then related to one cow. So they do rot refer to individual herds. However, these model figures assume the steady state, unchanging herd structure, and the herd structure in reality could be changing.

Question  – Are young female animals also sold?

Answer  – In the market data, sales of young animals were observed and the low proportion of heifers worries us. They would allow only a very low replacement rate of about 8 or 9%. Possibly these figures represent a decreasing herd size due to the high mortality.

Question  – Could the observations have been biased, because young animals are in the dry herds and not watered at the wells?

Answer  – They are watered at the homestead, but these figures were. adjusted accordingly.

Question  – Is cash value of offtake calculated at a fixed price per kilo for meat, so that it equals biomass?

Answer  – Market prices for animals in specific age groups were used.

Question  – Could you explain what you mean by livestock unit?

Answer  – It is the weight of the cow, plus the necessary replacement. Expressing the results per livestock unit implies that, with early off take, cows represent a higher proportion of the stock and since cows produce milk and calves, that higher proportion gives a larger return from early offtake. So, on the basis of these calculations, it looks as if it is sound policy to get rid of calves before maturity.

Question  – Is not the difference in rate of return entirely determined by the price ratio between mature and immature animals?

Answer  – The situation would be different if prices were different, but these are based on the prices that have been collected in local markets.

Question  – Do the data in Table 3 show that the mortality rate for these cattle is not important, while for goats (Table 1) it seems to have a big effect?

Answer  – Mortality was adjusted for age, so the increased mortality means higher mortality of young stock. Early offtake reduces the proportion of the young stock, which increased the productivity of the system per livestock unit.

Question  – Could it be that early offtake is increasing the productivity because it decreases the number of non-productive animals?

Answer  – That could be the biological reason.

Statement  – Herd productivity is increased by earlier offtake but in fact the herd will die out.

Reply  – No, the basic assumption is a steady-state herd that is replacing itself.

Question  – can you explain why increased milk offtake gave a better result?

Answer  – Because it is high-priced. It was assumed that all the extra milk offtake is sold.

Question  –If an animal dies under the extra milk offtake, that would increase mortality. Is the value of that included in the rate of return?

Answer  – The value of fallen meat is not included in the cash offtake but only in energy offtake, so the similarity in return in the last two lines of Table 3 is somewhat surprising.

Statement  – If it is considered that the second line in Table 3 in fact represents current practice in the region, it seems there is very little scope for improvement, which again shows that the farmers are exploiting the resources optimally.

Reply  – That would indeed appear to be the case.