John McIntire^{1}, Jess D. Reed^{1}, Abate Tedla^{1}, Samuel Jutzi^{1}, and Yilma Kebede^{2}.
1. International Livestock Center for Africa, P.O. Box 5689, Addis Ababa, Ethiopia.
2. Institute of Agricultural Research, Nazareth, Ethiopia.
Introduction
Joint products and production efficiency
Evaluating grain and straw
The conflict between grain and straw yield
Choosing efficient cultivars
Conclusions
References
Discussion
Cereal lines in breeding trials are usually evaluated on mean grain yield, although attention is sometimes given to yield stability or grain quality. Mean yield is most relevant where there is only one product of interest, such as grain, but may be misleading where there are joint products, especially if uses of the products differ. One such example is sorghum.
This paper proposes a method to estimate the tradeoff between sorghum grain and straw yield in agronomic trials. First, a theory of the conflict between the two products is described. Second, data from sorghum cultivar trials in Ethiopia are presented. Third, a method of valuing sorghum grain and straw is given. Lastly, conclusions about breeding strategies are drawn.
The conflict between grain and straw yield can be modeled with the theory of joint products (Henderson and Quandt, 1971). Consider a sorghum cultivar producing both grain and straw from a single input, land, as illustrated in Figure 1. The curve in Figure 1 is commonly known as a transformation curve of two outputs as function of one input.
The relation describing the outputs of the two products is expressed as an implicit function of land input:
1 = f(g,s)
where s is straw, g is grain, and l is land.
By taking the total differential of this function and setting it equal to zero, one can solve for the ratio of the derivatives with respect to land input[(ds/dl)/(dg/dl)]the rate at which one product is sacrificed to produce the other at a given level of land input. The negative of the ratio of the derivatives is defined as the rate of product transformation.
The choice of the point at which to operate along a transformation curve is determined by the prices of the outputs, p(g) and p(s), where 'p' represents market price. Assuming that market prices are fixed, the optimal production point on a transformation curve is that where
[p(g)/p(s)] = [(ds/dl)/(dg/dl)]
that is, where the ratio of grain price to straw price is equal to the rate of product transformation of straw into grain. The ratio of grain price to straw price is the tangent in Figure 1.
Two types of efficiency can be analysed with Figure 1. Technical efficiency means producing the maximum amount of either product for a given amount of the other product; that is, a producer who is technically efficient operates at some point on the transformation curve. Allocative efficiency means producing the two products in the right proportions, where those proportions are dictated by the price ratios of the products. A producer who is allocatively and technically efficient operates at the optimal point on the transformation curve. Graphically, the optimal point is that at which the price ratio is tangent to the transformation curve, shown by point E in Figure 1. It is possible to be allocatively efficient and technically inefficient, and vice versa.
Figure 1. Transformation curve, grain and digestible straw.
Data from sorghum trials conducted by the Ethiopian Institute of Agricultural Research and ILCA were used to test the theory outlined above. Table 1 shows descriptive statistics for grain yield, straw yield and digestibility for sorghums tested at Debre Zeit in 1984 and at Debre Zeit and Nazareth in 1985 (JAR, 1986). Debre Zeit is at 1850 metres above sea level, in the transition zone between the highlands and lowlands of Ethiopia. Nazareth is at 1500 m and has a hotter, drier climate.
The sorghum cultivars were evaluated in the field in the usual way. Straw samples of each cultivar were analysed in the laboratory for digestibility (Reed et al, 1987). In 1984, digestibility was estimated for leaves and stems and in 1985 for leaf blades, leaf sheaths and stems. The digestibilities in Table 1 are weighted averages of whole plant digestibility, where the weights are the fractions of each plant part in the ovendried straw dry matter (DM) of the plant samples^{1}.
1. A more complicated case occurs when straw is fed for an extended period. If straw quality degrades, then its quantity over the feeding period must be adjusted. However, only if there were different rates of decay for different cultivars, would decay affect the comparisons among cultivars.
Table 1. Descriptive statistics for three sorghum trials.

Grain yield (t ha^{1}) 
Straw yield (t ha^{1}) 
Apparent digestibility (%) 

Debre Zeit, 1984 


Brown sorghums 
2.61 
5.38 
53.6 

Red sorghums 
2.50 
5.97 
51.4 

White sorghums 
2.54 
5.18 
51.5 

Overall 
2.55 
5.51 
52.2 
Debre Zeit, 1985 


Brown sorghums 
4.46 
8.37 
52.3 

Red sorghums 
5.72 
7.11 
55.5 

White sorghums 
2.94 
6.49 
54.0 

Overall 
4.58 
8.13 
52.8 
Nazareth, 1985 


Brown sorghums 
4.18 
5.13 
57.3 

Red sorghums 
3.68 
4.93 
60.1 

White sorghums 
0.92 
2.80 
57.0 

Overall 
4.00 
5.02 
57.7 
The value of grain for sale is the market price. Market prices for sorghum grain are given in Table 2 for the area around Debre Zeit. There are three possible values of sorghum straw. The first is its market price. The second is its value in maintaining a herd if it is the only feed. In this case, the value of sorghum straw is the value of annual production from the herd, at market prices, divided by the quantity of straw necessary to maintain the herd. This is called the average maintenance value in Table 2. The third is its value as a supplemental feed. In this ease, assume that maintenance feeding requirements are satisfied from pastures and crop residues and that sorghum straw is used as a supplement for milk production. An energy balance model of milk production can then be used to calculate the value of the straw (Sandford, 1978). This is called the average supplementation value in Table 2. (Details of the calculations of the maintenance and supplementation values of sorghum straw are given in Appendix 1).
Table 2. Unit values of sorghum grain and straw.

Average 



(Oct 1984 Sept 1985) 
Oct Jan 
March April 
July 

Grain price (EB kg^{1})^{1} 
0.53 
0.50 
0.50 
0.60 
Straw price (EB kg^{1}) 
0.23 
0.20 
0.20 
0.30 
Average straw digestibility (%)^{2} 
54.3 



Sorghum digestibility as % of teff digestibility 
80.0 



Digestible straw price (EB kg^{1}) 
0.34 
0.29 
0.29 
0.44 
Grain/straw price ratios 




Average market value 
1.50 
1.70 
1.70 
1.36 
Average maintenance value 
3.50 
3.43 
3.13 
3.94 
Average supplementation value 
1.23 
1.30 
0.98 
1.42 
Meat price (EB kg^{1} LW) 
1.97 
1.90 
2.00 
2.00 
Milk price (EB kg^{1}) 
0.57 
0.50 
0.66 
0.55 
Manure price (EB kg^{1}) 
0.05 
0.05 
0.05 
0.05 
1. EB = Ethiopian Birr. 1 US $ = 2.07 Ethiopian Birr.
2. The average sorghum straw digestibility is the mean of the three trials.
3. Digestible sorghum straw price is estimated by multiplying the teff straw price by the sorghum digestibility as a percentage of teff digestibility.
Table 2 gives illustrative values of sorghum grain/straw price ratios using the three methods. The highest grain/straw value ratiothat which places the lowest value on strawis the maintenance value. The lowest ratiothat which places the highest value on strawis the supplementation value.
The value of a cultivar is expressed in equations (1) and (2).
(1) V(g) = p(g)*q(g)
(2) V(s) = p(s)*q(s)
where V=value per hectare, p=price per kg, g=grain, q=quantity in kg per hectare, and s=straw. The quantity of animal production for a given straw consumption is given in equation (3).
(3) q(a) =f(q(s))
where q(a) is a quantity of animal product. Equation 3 can be understood as a very general representation of any of the three methods of calculating the productivity of straw.
The total value of a cultivar is
(4) V(t) = V(s) + V(g)
where V(s) and V(g) are estimated from equations (1) and (2), and t=total Table 3 gives typical values for the total values of cultivars in the three trials.^{2}
2. Assumptions are that seed rates do not differ significantly between cultivars, so that net grain output per hectare is a linear transformation of gross output. All grain is sold and evaluated at market prices. Grain value would be affected if some is retained for home consumption. However, the results would be affected only if the fraction retained differed significantly between cultivars. Third, it is assumed that there are no market price differences between sorghum grain qualities, as shown by grain colour. Such differences would have an effect on the intercultivar comparisons. Fourth, no mixed straw sale/straw feeding strategies are allowed. All straw is assumed to be sold, or to be fed for one purpose. Mixed strategies would only affect the comparison between cultivars if the proportions sold and fed differed between cultivars.
The transformation curve in Figure 1 illustrates the conflict between grain and straw yield. To estimate the curve, the mean of each cultivar's grain and digestible straw DM yield was calculated across replicates at each site. Then, assuming that straw yield was zero if grain yield was zero, the Pythagorean theorem was used to calculate the maximum distance from the origin at each site by finding the maximum of the sum of the squares of grain and straw DDM yield for each cultivar, denoted by:
max(grain_{i}^{2} + straw DDM_{i}^{2})
where 'i' is the cultivar index. This maximum distance was the most efficient combination of grain and straw production for cultivars at a site.
Table 3. Total values of cultivars (grain and digestible straw).
Using that maximum distance, the efficient straw yield (S_{i}) corresponding to every grain yield was calculated by
(S_{i}) = [max(grain^{2 }+ straw DDM^{2}) grain_{i}^{2}]^{1/2}
Plotting the efficient straw yield against actual grain yield gave the transformation curve in Figure 2 for pooled data from the three trials.
The slopes of the transformation curves, which are interpreted as the losses in digestible straw yield with an increment in grain yield, are shown below. They were estimated for each trial by regressing the efficient straw yields on actual grain yield and on actual grain yield squared.

Grain yields 

Mean 
Maximum 

Debre Zeit, 1984 
0.69 
1.10 
Debre Zeit, 1985 
0.72 
1.33 
Nazareth, 1985 
0.55 
0.88 
Figure 2. Transformation curve, grain and digestible straw, pooled trials.
For example, at Debre Zeit in 1984, at the mean grain yield of 2.55 t ha^{1}, a 1 kg increase in grain yield would have reduced sorghum straw DM yield by 069 kg; at the maximum grain yield of 3.58 t ha^{1}, a 1 kg increase in grain yield would have reduced sorghum straw DM yield by 1.10 kg.
Transformation curves can be used to choose cultivars that are technically and allocatively efficient. Technical inefficiency is measured by the value of the straw yield lost by not producing on the transformation curve for a given grain yield; it is equal to efficient straw yield minus actual straw yield times straw price, i.e.
(S_{i}  s_{i})*p(s).
In terms of Figure 1, an increase in allocative efficiency, represented by the movement from point A to point E on the curve, raises grain yield and reduces straw yield. A movement from point B to point E reduces grain yield and raises straw yield. Both movements are increases in allocative efficiency.
The slopes of the estimated transformation curves at the mean grain yields were between 0.55 and 0.72. The absolute values of those ratios are smaller than the grain/straw price ratios, implying that an allocatively efficient cultivar would have a higher grain yield and a lower straw yield than any tested in these trials. Therefore, allocative inefficiency is measured against the standard of the cultivar having the highest grain/straw ratio, not against the allocatively efficient price ratio. Allocative inefficiency is equal to the value of the grain yield lost (gained) in moving along the transformation curve minus the value of the straw yield gained (lost).
Table 4 shows the costs of technical and allocative inefficiency in sorghum cultivars in the three trials. Technical inefficiencyproducing too little straw at a given grain yieldis the major cost of inefficiency in these trials.
In practice, only cultivars with high grain yields are usually included in extension programmes. Such programmes concentrate on one part of the grain yield distribution and neglect the overall value of the plant. What are the consequences for farm income if only cultivars with higher grain yields are selected for extension?
Cultivars were ranked by grain yield, by the total revenue at market prices from grain and digestible straw production, by technical efficiency, and by allocative efficiency (Table 4). These criteria were chosen because grain yield is probably the extension criterion; the value of production is the overall return to the cultivar; technical inefficiency is a measure of the return to raising straw yield while holding grain yield constant; allocative inefficiency is a measure of the return to reallocating drymatter production in line with the prices of grain and straw.
Spearman rank correlations were as follows:

Grain yield 
Technical efficiency 
Revenue 
0.878** 

Technical efficiency 
0.164 

Allocative efficiency 
0.313** 
0.654** 
** Significant at P<0.01
Table 4. Costs of inefficiency in sorghum cultivars.
Selecting cultivars for grain yield would, in effect, select for revenue and for allocative efficiency. However, it would tend to select cultivars that are technically inefficient, in that they produce too little straw for their grain yields.
In Ethiopia, grain/straw price ratios are so high that continued emphasis on grain yield at the expense of straw is justified. The estimated tradeoff between grain and straw yield is small enough that much higher grain yields would have to be achieved before that tradeoff began to reduce total revenue from sorghum production. However, one study from central India (Walker, 1987) shows lower grain/straw price ratios, which would favour cultivars with higher straw/grain product ratios.
There was a significant (P<0.01) positive correlation between cultivar rank on grain yield and rank on revenue. With few exceptions, those cultivars having the highest grain yields would not suffer a straw yield penalty large enough to make them inferior to low grain yielders, which gave more straw. This suggests that extension programmes could, like breeding programmes, safely insist on grain yield, if the market prices of grain and straw reflect their values to the farmer.
If the choice is among sorghum cultivars to include in a screening programme, these data imply that straw yield would probably not be relevant. Of the 10 cultivars yielding more than 5.5 t of grain DM ha^{1}, eight ranked among the top 10 on revenue and four ranked among the top 10 on straw yield. The tradeoff between grain and straw yield would not dramatically affect decisions about including cultivars in a screening programme. Furthermore, the low revenue ranks of some cultivars might simply reflect selection for high grain/straw ratio, and not a necessary physical tradeoff between grain and straw yield.
The situation might be different in an extension programme. Where the choice is among cultivars to extend to farmers in different environments and with different preferences, the decisions to extend a cultivar with high grain yield (e.g. #21 in 1984, highest grain yield and second lowest straw yield) would have to be chosen carefully because of the obvious possibility that its low straw yield would impair its adoption where the grain/straw price ratio is lower than that used in this paper. To take the converse case, it is unlikely that a high straw/low grain cultivar would be adopted simply because of its superior straw yield.
Many cultivars are technically inefficient, in that they produce much less straw, at given grain yields, than do the more efficient cultivars tested. Major gains could be made by raising straw yields to efficient levels while preserving grain yields.
The general advantage of grain over straw would be changed if sorghum straw is a supplement to a maintenance regime of pastures. In that case, the grain/straw price ratio falls and it becomes more profitable to select sorghum cultivars with lower grain/straw ratios. However, it is unlikely that peasant farmers have sufficient pastures for maintenance: they are thus obliged to use crop residues for low productivity maintenance as well as for higher productivity supplementation.
The apparent differences in straw yield, straw digestibility, leaf and stem digestibility and leaf/stem ratios across cultivars (and, in the case of stem dry matter, across grain colour groups) need to be investigated systematically. It is possible that overall digestible straw yield is not the most relevant criterion to use in considering straw yield in such trials. It may be that some cultivars with high leaf/stem ratios could be exploited to provide highly digestible feed at key times in the cropping season when other sources of feed are scarce.
Acknowledgments
The authors acknowledge the helpful comments of Stephen Sandford, Gil Rodriguez, Jr., Ray Brokken, and P. N. de Leeuw on earlier drafts.
Gryseels, Guido and Anderson, Frank M. 1983. Research on farm and livestock productivity in the central Ethiopian highlands: Initial results, 19771980. ILCA Research Report 4.
Henderson J M and Quandt R E. 1971. Microeconomic theory: A mathematical approach. McGrawHill, New York.
IAR (Institute of Agricultural Research). 1986. Ethiopian Sorghum Improvement Program Progress Report 13. Addis Ababa.
Reed, Jess, Abate Tedla, and Yilma Kebede. 1987. Phenolics, fibre and fibre digestibility in the crop residue from birdresistant and non bird resistant sorghum varieties. Journal of the Science of Food and Agriculture. 39:113121.
Sandford, Stephen. 1978. Some aspects of livestock development in India. Pastoral Network paper 5c. ODI, London.
Walker T S. 1987. Economic prospects for agroforestry interventions in India's SAT: Implications for research resource allocation at ICRISAT. ICRISAT Resource Management Program, Economics Group, Progress Report79. Patancheru, India.
APPENDIX 1. STRAW VALUE CALCULATIONS.
Herd structure 
No. 
End of year LW (kg) 
LW per class (kg) 
Off take^{1} (kg LW) 
Breeding cows 
1.0 
250 
250 
20 
Calves 
1.0 
100 
100 
8 
Heifers 
1.0 
167 
167 
13 
Males 
2.0 
312 
625 
50 
Total 
5.0 

1142 
91 
1. Assumed offtake rate of 8.0% for all classes.
Animal productivity parameters
Annual LW in herd (kg) 
1142 
Calving rate (%) 
50.0 
Milk production per lactating cow per year (kg) 
400 
Base intake of digestible dry matter (DDM) (% LW per day) 
2.5 
Annual DDM intake per herd (kg) 
10 418 
Percentage of intake converted into manure 
20.0 
Maintenance model, assuming all intake is from crop residues
Annual LW offtake (kg) 
91 
Annual milk production (kg) 
200 
Annual manure production (kg) 
2084 
Value of draught oxen for grain production (Birr) 
384 
Annual value of production from herd (Birr) 
782 
Average straw value (Birr kg^{1} DDM) 
0.08 
Supplementation model, assuming maintenance is from pastures
Potential 1 milk yield (kg cow^{1} yr^{1}) 
1200 
Intake of DDM per cow per year for maintenance (kg) 
2281 
Intake of DDM per cow per year for growth 

Assumed extra daily intake (% of base intake) 
33.0 
Intake of DDM growth (kg cow^{1} yr^{1}) 
3034 
Average straw value (Birr kg DDM) (from energy budget) 
0.46 
Energy budget for cows in milk
Feed intake (kg DDM day^{ 1}) 
8.31 
Energy content of sorghum straw (kcal) 
4000 
Energy intake (keel) 
33 250 
DM (% fresh feed weight) 
50.0 
Sorghum straw digestibility (%) 
54.3 
Metabolisable energy (ME) as percent of net energy (NE) 
87.5 
ME converted to NE in milk (%) 
70.0 
NE of milk (kcal litre) 
830 
Average annual milk price (Birr litre^{1}) 
0.57 
Energy value of straw (kcal kg^{1} DDM) 
666 
Milk production (litre kg feed) 
0.80 
Average straw value (Birr kg^{1} DDM) 
0.46 
Witcombe:  Can you explain exactly how the parameters grain and digestible straw yield relate to your terms technical and allocative efficiency?
McIntire: The terms are products of the first two parameters
Nordblom: Your analysis appears to ignore the differentiation of plant parts in terms of nutritive value.
McIntire: The digestible straw yield is, in effect, the weighted average of the fractions. There is, however, much more to be gained from exploiting differences in straw yield than differences in digestibility.
Witcombe: How do you make the final decision to select amongst the varieties that are similar in grain yield?
McIntire: The final choice depends upon prices.
Jenkins: The prices may vary considerably between seasons. How do you take this into account in your analysis?
McIntire: One can use longterm price expectancy figures.
McDowell: You have not included the benefit of preserving capital as live animals in your estimate of the value of straw for maintenance.
McIntire: Market prices are generally higher than the maintenance value, so this aspect is not important.
McDowell: Maintenance implies a minimum value for straw digestibility so that your parameter of digestible straw yield is not meaningful.
Berhan: There are other uses for sorghum stalks, such as house construction, which should be considered in the model.
McIntire: These are included in the market price.
Nordblom: This is only true if there is no market failure.
Reed: In parts of India the supplementation value is considerable and prices may be higher than you suggest.