6.1 Trade-offs between milk and meat production
6.2 Profit maximization and the optimum production strategy
The two main outputs (milk and meat) of the system under study are technically interdependent. Production of milk alone is not possible without meat production, and vice-versa. Formally, the production process in the case of joint products can be represented by an implicit production function of the form (Henderson and Quandt, 1971)
H(q1, q2, x) = 0
where
q1 = quantity of milk produced,
q2 = quantity of meat produced, and
x = quantity of feed supplements provided.
Solving the above relationship explicitly for x yields the cost of production as a function of the quantities of the two outputs produced, i.e.
x = h(q1, q2)
A product transformation curve is defined as the locus of output combinations that can be produced from a given level of inputs. The family of product transformation curves for milk and meat production for the system under study is shown in Figure 13, obtained from the milk and liveweight offtake values given in Tables 11 and 12 24. Thus, for a given input level there exist infinite numbers of output combinations of milk and meat. The rate of product transformation (RPT) is defined as the quantity of one product that must be forgone in order to obtain more of the other without varying the input level. The measure of this rate is the negative of the slope at any point of the product transformation curves. Because the curves are concave to the origin, the higher the production level for one of the two products the higher the rate at which the production of the other is sacrificed. For example, moving from point A to point B on the ST 2.5 kg/head/d curve, i.e. increasing milk output by 10000 kg (from 20000 kg to 30000 kg), results in a reduction of meat output by about 100 kg, compared to a reduction of about 420 kg when moving from point C to point D, i.e. increasing milk output by the same amount (from 50000 kg to 60000 kg).
24 Assuming carcass weight is 50% of liveweight.
The higher performance of the ST over the T genotype is clearly shown in Figure 13. The production frontiers for ST are far above those of T for any level of supplementation. For example, at a supplementation level of 1.5 kg/head/d, an annual meat offtake of 7000 kg is associated with a milk offtake of 23900 kg for the T system, as compared with more than twice as much from the ST system, i.e. 56200 kg.
Due to the variable RPT along each product transformation curve, for a given level of feed supplementation the combination of milk and meat production that yields the maximum revenue will depend on milk and meat relative prices. It can easily be shown that revenue is maximized when the RPT equals the ratio of milk and meat prices, i.e. when
where
p1 = unit price of milk, and
p2 = unit price of meat.
There is only one point on each product transformation curve which satisfies the above condition, and the loci of such points constitute the output expansion path of the joint milk and meat production system.
The determination of the optimum production strategy must take into consideration, in addition to the relative prices of milk and meat, the cost of inputs to the system. In the short run only the cost of intermediate inputs and the revenue from intermediate outputs need to be taken into account. In the long run the initial and final capital value of the herd and all other capital holdings must additionally be taken into account. The optimum combination of milk and meat production will be that which maximizes annual net revenue (NR), i.e. gross revenue from the sale of milk and meat minus costs. NR can be expressed by the relationship
NR = p1q1 + p2q2 - rx - sz -w
where
r = the unit cost of feed supplements,
x = the quantity of supplements used,
s =the unit cost of labour,
z = the number of labourers employed, and
w =all other fixed costs.
With respect to supplementation, NR is maximized when the value of the marginal product of feed supplements for the production of each output equals the price of supplements. Net revenue from supplementation would increase if the return to its use for the production of either product exceeds its cost. Thus, the level of supplements employed would be that at which the returns from each product would be equal to the cost of supplements.
Table 16 presents current producer prices and associated costs. In addition to feed and labour costs, other-costs related to maintaining a "reasonably acceptable" level of management have been taken into consideration. These include the establishment of fences and boreholes, the provision of water, minerals and routine veterinary care and, in the case of a dairy system, extra costs for veterinary care, AI and dairy equipment.
Based on the presently prevailing price structure and the assumptions made in Table 16 about other related production costs, the annual net revenue from the different production alternatives is given in Table 17 and in Figure 14. It is clear that, under the present price structure, feed supplementation in a beef-only production system is not economical. A sensitivity analysis of annual NRs with variable costs of feed concentrates showed that their cost must be below P 0.10/kg for them to be used economically in a beef-only production system. Although not shown here, even in that case the optimum level of concentrates used is only 0.5 kg/head/d.
Table 16. Fixed and variable costs paid and prices received by producers in ranching enterprises in Borswana (1982)a.
|
Item |
Cost/price (P) |
|
|
Fixed costs: |
||
|
Maintenance of fencing and borehole (10% of establishment costs)b |
2640 |
|
|
Water, minerals and routine veterinary care (75 LU C d P 9.0/LU) |
675 |
|
|
Total fixed costs of a beef system |
3315 |
|
|
Additional costs of a dairy system |
|
|
|
|
- Extra veterinary costs (40 cows C d P 10.0/cow) |
400 |
|
|
- Al (40 cows C d P 5.0/cow)c |
200 |
|
|
- Dairy equipment (10% of purchase cost of P 500.0) |
50 |
|
Total fixed costs of a dairy system |
3965 |
|
|
Variable costs: |
||
|
Cost of feed concentrates per kg d |
0.22 |
|
|
Labour per worker/year c |
600 |
|
|
Labour requirements (worker-years) |
|
|
|
|
- beef system |
2 |
|
|
- dairy system |
|
|
· (a) annual milk output less than 25000 kg |
3 |
|
|
· (b) annual milk output between 25000 kg and 50000 kg |
4 |
|
|
· (c) annual milk output greater than 50000 kg |
5 |
|
|
Price received by producers: |
||
|
Milk per kg f |
0.30 |
|
|
Meat per kg g |
1.26 |
|
a Costs and prices represent mid-1982 levels and were provided by APRU scientists.
b For 75 LU at a recommended stocking rate of 10 ha/LU, 750 ha are required. This area is assumed to be fenced to form 7 paddocks requiring 19 km of bushwood and wire fencing. At a present cost of P 600/km the initial expenditure on fencing would be P 11 400. The cost of the borehole is estimated at P 15 000, resulting in a total initial establishment cost of P 26 400.
c Two inseminations per conception are assumed, C d P 2.50 per insemination.
d The cost of supplements to livestock producers depends on their quality and the location of individual producers. Dairy meal consisting of 15% protein, 3% fat, 9% fibre, 1.5% calcium and 0.6% phosphorus costs about P 200/t ex-Lobatse. An additional charge of 10% is assumed for transport and handling, bringing the total cost to the producer to P 220/t.
e A monthly wage rate of P 50 is assumed here. Although wages for unskilled labour can be substantially lower, it is assumed that for a dairy operation to be viable it must be located relatively near a consumption centre, where labour wages are much higher than in remote areas.
f Current dairy-gate milk prices paid to producers are P 0.35/kg. Transportation and handling costs of 15% are subtracted from this price, leaving a net price to the producer of P 0.30/kg.
g Botswana has a well established marketing system for beef cattle. The price paid by the abattoir in Lobatse is about P 1.30/kg of carcass weight for animals of average quality. Additionally, a marketing cost of P 10 per animal is assumed, bringing the net price received by producers to about P 1.26/kg of liveweight.
Table 17. Simulated annual net revenue (P) given current (1982) prices, for various supplementation levels and milk offtake rates a.
|
Milk offtake rate (%)
|
Genotype
|
Supplementation level (kg/head/d) |
|||||
|
0.0 |
0.5 |
1.5 |
2.5 |
5.0 |
7.5 |
||
|
0
|
T |
4206 |
3824 |
2508 |
1216 |
-756 |
-1656 |
|
ST |
4632 |
4279 |
3072 |
2111 |
-1705 |
-3591 |
|
|
20
|
T |
5905 |
5774 |
4658 |
3315 |
1284 |
294 |
|
ST |
9186 |
9265 |
9732 |
9377 |
6154 |
3297 |
|
|
40
|
T |
7725 |
7859 |
6 999 |
5727 |
3626 |
2614 |
|
ST |
12199 |
12713 |
13578 |
12541 |
9868 |
6830 |
|
|
60
|
T |
6545 |
7010 |
6195 |
5040 |
3054 |
2183 |
|
ST |
13795 |
14284 |
15749 |
16434 |
13995 |
11086 |
|
a Based on quantities of supplements used and the milk and meat output values in Tables 11 and 12 and the costs and prices in Table 16.
Before the economic merits of feed supplementation for the mixed beef - dairy production alternatives are discussed, a qualification is necessary on the basis of the findings of Section 5.2. In several production alternatives calf mortality was excessive and the viability of the herd could be threatened. Overall, calf mortality was relatively low up to a 40% milk offtake rate, but increased dramatically thereafter. High milk offtake alternatives, although associated with high average annual NR, also bear a high risk element which generally cautious livestock producers may not be willing to undertake. On the basis of these subjective risk considerations, the production alternative under which 60% of the milk yield would be extracted for human consumption is therefore not included in the set of economic alternatives.
The present annual NR level for a beef-only production system (i.e. no milking) without feed supplementation is taken as the basis for comparison. Simulated NR in this case equals P 4506 for the T system and P 4632 for the ST system. Under a 40% milk offtake rate, the highest income is obtained with a supplementation rate of 0.5 kg/head/d for T cows and 1.5 kg/head/d for ST cows. This optimum production strategy yields an annual NR of P 7859 for the T and P 13 578 for the ST system, or 75% and 193% higher, respectively, than present incomes.
The major determinants of profitability in the systems under consideration are the cost of concentrates and the prices received for meat and milk. With changing technological and marketing opportunities and constraints, current costs and prices must be viewed as temporary. Consequently, the extent to which the above results apply under different prices must be examined. These sensitivity analyses are depicted in Figures 15, 16 and 17 and are partial in the sense that in each case only one price is allowed to vary, whereas the other two prices are kept at their current (1982) levels. Thus, Figure 15 shows the simulated effect of the price of concentrates on annual NR, with the prices of milk and meat kept at their present levels. For the T system (lactating cows supplemented with 0.5 kg/head/d), annual NR is above present levels as long as the cost of concentrates is below P 0.49/kg, or more than twice their present cost. For the ST system (lactating cows supplemented with 1.5 kg/head/d), the threshold level is much higher, at P 1.09/kg or almost five times the present level.
Figures 16 and 17 depict the effects of the milk and meat prices received by livestock producers on their annual NR. Under present prices of concentrates and meat, annual NRs are higher than current levels as long as the price of milk is above P 0.19/kg for the T system and above P 0.12/kg for the ST system, or 63% and 40% respectively of the present net milk price received. Similarly, under present prices for concentrates and milk, annual NRs are above present levels as long as the price of meat is above P 0.86/kg for the T system and P 0.11/kg for the ST system, or 68% and 9% respectively of the present net price of meat.
Figure 14. Simulated effect of supplementation on annual net revenue for various milk offtake rates.
In summary, the alternative production system under which 40% of the milk yield is removed for human consumption and T and ST lactating cows are supplemented with 0.5 kg/head/d and 1.5 kg/head/d respectively yields substantially higher incomes than presently obtained. This conclusion holds true under a wide range of concentrate costs and milk and meat prices.
Figure 15. Simulated effect of concentrate cost on annual net revenue.
Figure 16. Simulated effect of milk price on annual net revenue.
Figure 17 Simulated effect of meat vice on annual net revenue.
