African Crop Science Journal, Vol. 8. No. 4, pp. 429-440
MAIZE PRODUCTION UNDER TREE-BASED CROPPING SYSTEMS IN SOUTHERN MALAWI: A COBB-DOUGLAS APPROACH
B.C.G. KAMANGA, G.Y. KANYAMA-PHIRI and S. MINAE1
(Received 11 October, 1999; accepted 2 November, 2000)
Code Number: CS00045
Malawi is a land-locked, developing country, located at the southern end of the Great Rift Valley between latitudes 9°: and 18°: S and longitudes 33°: to 36°: E. It covers an area of 11.8 million hectares of which 9.4 million is land with the balance comprising Lake Malawi and other small lakes (Bunderson et al., 1995).
Having no valuable deposits of minerals, agriculture has dominated the economy (Bunderson et al., 1995). It contributes 40 % of the Gross Domestic Product (GDP), 85 to 90 % of foreign exchange earnings and 85 % of the labour force (World Bank, 1995). Malawis agriculture is composed of commercial estates and smallholder subsector. The smallholder subsector dominates the economy contributing 80 % of the total food production and about 20 % of the export (World Bank, 1990; Bunderson et al., 1995). Smallholder agriculture involves 1.8 million farms covering a total of 4.1 million ha with 70 % of the full time farmers being women (UNICEF, 1993; World Bank, 1995). Over 56 % of the households in Malawi cultivate less than one hectare of land, 32 % farm between 1 and 2 hectares and 12 % have more than 2 hectares (World Bank, 1990; Bunderson et al., 1995).
The steadily increasing human population, currently estimated at approximately 11 million people has forced people to continuously cultivate the same piece of land, thereby mining the natural resource base to meet their basic needs. This has contributed greatly to widespread fragmentation of farm holdings, declining soil fertility and crop yields, fodder deficiencies, shortage of fuelwood and building material, accelerated deforestation and loss of biological diversity (World Bank, 1995).
Soil fertility is a major determinant of crop yields (Banda et al., 1994). Continued decline of soil fertility against the background of increasing rural poverty is threatening the smallholder farmers long term food security and their source of livelihood. There is no doubt that the need to reverse the decline in soil fertility is becoming critical. The challenge today is to find sustainable ways to increase agricultural growth at a rate faster than that of population.
Smallholder farmers mitigate soil fertility decline by modifying their traditional cropping systems. This is done through their own experimentation and indigenous knowledge. Their most popular cropping system is intercropping (Georgis et al., 1989; Shaxson and Touer, 1992). In Zomba, Southern Malawi, more than 90% of the smallholder farmers practice maize-based intercropping systems (Kamanga, 1997; Phiri et al., 1999; Kanyama-Phiri et al., 2000). Kamangira (1997) observed that more than 96 % of the farmers in the study area incorporate crop residues to the soil in the belief that organic matter improves soil fertility.
Despite increased incorporation of crop residues, soil fertility continues to decline with falling crop yields. It is clear then that the outlooks for reversing this predicament by farmers alone are bleak. Improvement of the existing cropping systems through incorporation of tree legumes would assist in alleviating low soil fertility (Ónim et al., 1990; Szott and Kass, 1993; Mureithi et al., 1994; Banda et al., 1994; Snapp et al., 1998).
A Cobb-Douglas production function (Cobb and Douglas, 1928) has been commonly used either singly (Donovan and Darroch, 1991; Bravo-Ureta and Evenson, 1994; Gallechar et al., 1994; Ngongola and Mangisoni, 1994; Barro and Sala-I-martin, 1999) or in combination with other functions (Fulgitini and Perrin, 1998; Widawsky, et al., 1998) to analyse efficiency of smallholder agricultural production. It is linear in logarithmic transformation, empirically simple, gives elasticities, permits calculation of returns to scale and gives the best fit of the data used in the analysis. It is generally flexible and allows for analysis of interactions among variables (Byiringiro and Reardon, 1996).
Barro and Sala-i-Martin (1999) used a Cobb-Douglas production function to examine small-scale effects and showed that the expansion of the aggregate labour force raised per capita growth rate for a decentralised economy. The results thus showed the positive effect of labour on the private marginal product of capital.
In Central Malawi, Ngongola and Mangisoni (1994) used a Cobb-Douglas production function to explain variation in barley tobacco yield among tenants. Their results demonstrated that area under barley tobacco and quantity of fertiliser applied were the main factors determining tobacco yields. Donovan and Darroch (1991) reported estimates on research and development (R&D) using a Cobb-Douglas production function. In the estimation, rainfall per hectare, expenditure on technology, production costs per hectare and land under sugarcane had a significant impact on industrial yield of sucrose. An experimental model to study the relationship between output to land size, environmental and management indices (Odulaja and Kiros, 1996) showed that land size and environmental effects were significant in explaining variation among outputs of crops. The Cobb-Douglas function has also demonstrated that marginal value of products of land on small farms were above rental price of land, implying factors use efficiency and constraints to land access (Byiringiro and Reardon, 1996).
Bravo-Ureta and Evenson (1994) used a Cobb-Douglas function form to fit separate production frontiers for cotton and cassava using a maximum likelihood procedure. The dependent variable was annual total farm output of cotton or cassava and the explanatory variables were area devoted to cotton or cassava production, family and hired labour- days used on cotton or cassava production and value of materials such as seeds. The results showed an average economic efficiency of 40.1% for cotton and 52.3% for cassava, indicating that the sample households had plenty of room to increase productivity and output on their farms. In Argentine agriculture, A Cobb-Douglas type model was used to measure technical and cost efficiency (Gallechar et al., 1994). In the model, output was specified as a function of eight inputs and three dummy variables for location and climatic conditions. Results demonstrated that management, ownership and monitoring have a great effect on marketing efficiency than on either technical or cost efficiency
Fulginiti and Perrin (1998) examined changes in agricultural productivity in 18 developing countries using a combination of the Cobb-Douglas function and non-parametric output - based Malonquist index. They reported that half of the countries studied had experienced a decrease in agricultural productivity.
A two staged Cobb-Douglas production function and a translog production function were used to measure the productivity of pesticides, and the host -plant resistance and the substitutability between them (Widawsky et al., 1998). The results showed that under intensive rice production systems in Eastern China, pesticide productivity was lower than the productivity of host-plant resistance and that host-plant resistance was an effective substitute for pesticides. Returns to pesticide use were negative at the margin due to pesticide overuse. Thirtle et al. (1998) used a two-stage constant elasticity of substitution (CES) production function to test the induced innovation hypothesis, based on data from South African Commercial Agriculture and reported that farm size, research and extension expenditures and policy variables were important factors.
Shatiq et al. (1993) used regression methods to estimate a production function relating sunflower yield to number of plants per hectare, date of planting, quantity of nitrogen, soil type, usage of ridges and sunflower variety. The results showed that very little of the total variation in the yield was explained by agronomic variables. The only significant variables were those representing plant density, implying that priority in sunflower research should be placed on stand establishment. Economic analysis demonstrated that sunflower can be a good alternative to wheat. Cramer and Wailes (1996) analysed production efficiency of Chinese rural households in farming operations using a shadow price profit linear model. The shadow prices were estimated by a generalised profit function, which incorporates market distortions resulting from imperfect market conditions. The results showed that households living in mountain areas or whose family members were government employed are relatively inefficient.
The above literature has demonstrated quite vividly that the Cobb-Douglas production function can be effectively used either in isolation or in combination with other production functions to estimate smallholder production including that of maize.
It was against this background that this study was conducted in Songani, Zomba, to estimate maize production under tree-based cropping systems, using a Cobb-Douglas approach. The study aimed at investigating whether the existing cropping systems produce more returns to scale than would otherwise be the case with the legume-based.
MATERIALS AND METHODS
The study was conducted in Songani catchment of Malosa EPA, 150 18.5' South, 350 23.5' East and 785 metres above sea level (asl). The area has a high percentage of households with small landholding sizes (Malawi Government, 1994). Average maize production is about 500 kg ha-1 for local maize and 900 kg ha-1 for hybrid maize varieties (Kamanga, 1997). Soils are classified as Alfisols and Ultisols. Annual rainfall ranges from 800 mm to 1,100 mm and the annual mean temperature ranges from 20 °:C to 25 °:C.
The experiment was laid out as a 3 x 4 factorial in a Split Plot design. Landscape positions were the main plots with cropping systems serving as subplots. Four 15 m by 15 m maize plots were demarcated on the 48 participating farmers fields selected from three landscape positions (dambo valleys 0 - 12% slope, dambo margins 0 - 12% slope and steep slopes > 12%). In the first year, all the plots were planted with maize (MH18) and intercropped at first maize weeding with Sesbania sesban, Tephrosia vogelii and Cajanus cajan (pigeonpea) in three plots while the fourth plot had maize only to serve as a control. Bare rooted seedlings were used for sesbania at 75 cm x 180 cm while seeds were used for tephrosia and pigeonpeas at 90 cm x 180 cm. No inorganic fertilisers were applied to the plots. The legumes were left growing in the field after maize harvest. At land preparation for the second season, the legumes were cut, stripped and leafy biomass incorporated into the soil. In the second year, the four plots were split in two equal halves before maize planting resulting into a 3 x 4 x 2 factorial in a split-split plot design.
On the onset of rains, a Malawian hybrid maize variety (MH18) was planted in all the plots as a test crop. Three maize seeds were planted on hills spaced at 90 cm between ridges and 90 cm within the ridges. This planting pattern gave a population of 3600 plants per hectare. After two weeks of planting, 48 kg N ha-1 from Calcium Ammonium Nitrate was applied to each half of each plot.
Data collection and analysis. Data collected included labour used, fertiliser applied, and maize yield from each interplanting. Labour was measured in person-hours of the actual work done by members in the fields. Fertilisers were taken as a total of what the plant biomass contributed in the first year as a residual in the second year and the inorganic supplemented to the plots.
Maize grain yields were measured from a sample area of 5 m x 10 m and adjusted to12.5% moisture content. Data were entered in a computer spreadsheet with columns representing input factors and rows as individual farms. Analysis was done using the Statistical Package for the Social Scientists (SPSS) and analysed as required by the model. Means of the variables were used to perform gross margin analysis. Only net benefits are reported in the work.
Estimation of production function. Use of production function was intended to reveal the technological relationship between the output and the input used in the study. The revelations would establish the advancement of the production systems. Agricultural production is a function of input factors such as land, labour and capital. Use of these inputs varies and this directly affects the gross agricultural output (Abler and Shortle, 1995). Any general production function can be expressed as below;
Y = f(X1, X2 ,X3, ..., Xn)......(Equation 1)
where Y is the output and Xi(i = 1, 2, 3,..., n) are inputs used to bring about the yield (Bravo-Ureta and Rieger, 1990). In this study, a Cobb Douglas function was used to estimate the systems production functions. According to Chavas and Cox (1992) and Abler and Shortle (1995), elasticity of production and marginal productivity can help to establish the productivity of input factors.
Choice of a function involves a certain amount of subjective judgement, as does the choice of variable inputs to include in the production function. Production of crops involves a lot of inputs and it is difficult to list and use all of them in a production function. The production function must be simplified based on what one is examining.
The Cobb-Douglas production function was selected for analysis of smallholder production functions. It is linear in logarithmic transformation and thus being empirically simple, gives elasticities, permits the calculation of returns to scale and gives the best fit of the data used in the analysis. Charles W. Cobb and Paul H. Douglas proposed this function on the productivity of labour and capital in the United States (Cobb and Douglas, 1928). The general form of this production function model is:
Y = AX1a1 .X2a2 .X3a3 .Xnan......(Equation 2)
where Y is the quantity of output
In this study the Y is the level of maize from the systems and the Xi are the levels of inputs used to produce the level of corresponding yield. The ai then would measure the percentage change of Y as X changes (dy/dx.x/y). The additions of ai in this functions help to describe the marginal productivity (ai.Y/Xi) as either constant returns to scale , decreasing or increasing. Constant returns to scale occur when ai are within 0 and 1. If the ai are greater than unity then returns to scale are increasing. This means that marginal product dy/dx increases. When ai are non-positive then diminishing marginal returns to scale result (Abler and Shortle, 1995). Empirical data that gives diminishing marginal returns is meaningless since production is not expected to decrease when certain factors of production ceteris paribus increase. Estimation of constants (coefficients) for the establishment of the elasticities involves transformation of Equation 2 to a logarithmic linear function as below:
log Y = log A + a1logX1 + a2logX2 + a3logX3 + ... + anlogXn + e......(3)
Linear regression analysis was used to estimate these coefficients from this equation and then tested for their significance using t-test. In this study therefore the estimated production function used for the cropping systems was as follows:
Yj = A LABa1 j.LANa2 j.FERTa3j......(Equation 4)
where Yj is the physical output of maize in the jth cropping system in kg ha-1
A , a1 ,a2 and a3 are parameters estimated using logarithmic linear function expressed as below:
Log Yij = log A + a1logLABj + a2logLANj + a3logFERTj + e......(Equation 5)
where i denotes the ith observation in system j and e is the random error.
Returns to scale. Returns to scale describe the output response to proportionate increase of all inputs (Bjorndal and Salvanes, 1995). In a Cobb-Douglas production function, the regression coefficients of the log linear function indicate the returns to scale (Parikh et al., 1995). The Cobb-Douglas function allows for the sum of these coefficients to be between 0 and unity (Upton, 1979; Bjornson and Innes, 1992). Under this condition, returns to scale are decreasing if the sum is less than 1, constant if the sum is one and increasing if the sum is greater than one.
What is important to note is that the function has covered only those factors of production, which can be put under farmers control. These returns to scale were then tested for their difference from unity using the t-test. Returns to scale can be expressed as follows:
rj = a1j + a2j + a3j......(Equation 7)
where rj = returns to scale of the system
Gross margins. Gross margins (GM) analysis for each cropping system was performed by landscape positions. The gross margins are defined as the difference between the gross (total) income (GI) and the total variable costs (VC) involved in the production. Mathematically, it is expressed as:
GM = GI VC......(Equation 8)
where GM = gross margin (MK ha-1), GI = gross income (MK ha-1) and VC = total variable costs (MK ha-1)
Gross margins are a useful first step in deciding on the best combination of activities on a farm. The activity with the highest gross margin per unit of the most common limiting resource is chosen. Labour as a production unit common to all the farm activities is the most appropriate basis for comparison in the gross margins (Abbot and Makeham, 1990; Becker, 1990). Gross income was obtained from the total output multiplied by its price.
In this study, output from the systems included maize grain from all systems, pigeonpea grain from pigeonpea-based system, organic nitrogen from biomass and fuelwood yield in legume trees. Variable costs incurred in the use of labour (family or hired), seed for maize, pigeonpeas, tephrosia and seedlings for sesbania were used in gross margin analysis.
RESULTS AND DISCUSSION
Estimation of production function. Table 1 shows the coefficients (ai, i = 1, 2, 3) and constants (A) estimated by applying ordinary least squares regression technique on Equation 5. The coefficients of fertiliser (significant P = 0.001), land (significant P = 0.053) and labour (significant at P = 0.001) in the main estimate show that these are significant factors of production of maize with Sesbania sesban. Similar observations on the impact of fertiliser, land and labor have been reported for barley tobacco (Ngongola and Mangisoni, 1994), sugarcane (Donovan and Darroch, 1991) and other crops ( Barro and Sala-i-Martin, 1999; Odulaja and Kiros, 1996) where similar production functions were employed.
In this study, the coefficient for slope is negative. This is expected since when you increase cultivation in more sloppy fields most of the topsoil is washed away reducing the fertility of the land. Wang et al. (1996) observed that households living in mountainous areas had relatively inefficient farming operations. This is also shown in the estimate for the steep slopes where increased use of fertiliser gives negative returns. However, the dambo valleys have potential as shown by the coefficients in Table 1. The estimated coefficients for the input factors (ai) were non-negative indicating increased marginal productivity to the inputs in all landscape positions. This means that a one percent increase in fertiliser, land and labour lead to 0.14, 0.2 and 1.2 percent increase in output, respectively. Increased investment in labour in the systems in the dambo margins and the steep slopes gives more returns. In technical terms, maize-legume production in the study site was in stage I of the production implying that inputs were not optimally used in the system and need to expand to stage II of production. In stage I, Marginal Physical Productivity (MPP) is greater than Average Physical Production (APP). APP is increasing throughout this stage indicating that the average rate at which the labour input is transformed into product Y increases until APP reaches its maximum at the end of this stage (Ali and Chaudhry, 1990) with Total Production (TP) increasing at an increasing rate. In this case farmers should invest more of the inputs in the production to maximise production.
Basing on the size of the input elasticities, labour is the most important input in sesbania-maize relay cropping system followed by land. Fertiliser was marginal. The policy implication of these findings about fertiliser, land and labour is that the most critical issue in increasing maize production would be how to bring more fertiliser, land and labour under maize/ legume systems. The fertiliser issue is a critical one in Malawi since its prices are beyond the purchasing power of smallholder farmers (Carr, 2001), hence focus has to be made on alternative means of enhancing soil fertility such as agroforestry legume species. Increasing organic fertiliser usage would lead to increased maize production by resource poor farmers. The marginal increment on fertiliser indicated that more fertiliser is required to obtain maximum yields. The estimated production functions were;
All farmers: Y = 0.39 LAB1.16 LAN0.21 FERT0.14, R2=0.64, N=186......(7)
The return to scale (r) was calculated using the coefficients of the variables in Table 2. The statistical significance was tested by making an a priori assumption of constant returns to scale (r = 1, restricted model) and then testing for significance from unity by using t -test. The return to scale (1.32) was increasing indicating that there was need to expand use of fertiliser, land and labour in the system. The results entail the fact that agroforestry legume systems need farmers commitment if good results in maize yield are to be achieved. The findings of this study are similar to those of Kachule (1994) in South Mzimba and Parikh et al. (1995) in Pakistan where land and labour were found to be the most important factors of production. Returns to scale of the two studies indicated increasing benefits of the systems.
The increasing returns to scale suggest that, if all relevant factors are increased by a given percentage, production (Y) will increase by percentage greater than the percentage increase in the input factors. It is important therefore to note that increasing relevant input factors such as labour and land on maize-legume systems has the advantage of increasing productivity of the systems.
Gross margin analysis. Figure 1 shows results of the systems net benefits from the gross margins for the landscape positions. Labour was recorded the highest in sesbania based systems with and without fertilisers in all the slopes. These high values were attributed to high biomass production of the plant that demands a lot of time for cutting and incorporating. Returns to labour were highest in the potential dambo nich seconded by the dambo margin and the steep slope last. There were negative returns in the steep slopes and part of the dambo margins for the maize without organic and inorganic fertilisers. This is the system that farmers practise most in the area. The negative returns show how minimal the performance was for the technologies in this erosion prone niche. The technologies that were supplemented with 48 kg N ha-1 resulted in increased benefits at all landscape positions.
The variable costs for seedlings include the labour in the nurseries although the seedlings are sold at a subsidised price to encourage farmers to plant the legumes. The sesbania system was found to be an efficient enterprise from the economic point of view based on the net returns. Gross margin analysis was used to measure economic returns per unit of inputs to the legume systems. Gross margins are defined as the total output value less the total variable costs.
With the gross margins, relative efficiency of the systems is analysed and this may indicate the economic optimisation of the systems. This does not necessarily indicate the profit of the system because profit is obtained after excluding fixed costs. In smallholder farming situation, fixed costs are relatively difficult to calculate and the gross margin analysis in this case does not indicate the profitability of the systems.
The gross margin analysis was based on the premise that if a farmer had produced enough food he/she would not incur those costs on maize purchase as he/she would do if he/she had no maize. The produce would then be valued at a consumer price. Analysis of returns to labour (MK man-hour-1) indicated that the four systems were fairly similar. In the potential dambo, the sesbania-based system gave the highest value of returns MK(9.6) seconded by the pigeonpeas-based system MK(8.9) with the tephrosia-based system giving MK(8.5) and sole maize was the least MK(6.4). Tephrosia had slightly higher returns to labour because of lower total labour input that was used in the system. It is interesting to note that all the legume-based systems had returns to labour higher than the minimum daily wage rate of MK7.50 for the rural areas. They were about MK2.00 higher than the minimum wage rate. The implication of these results is that the agroforestry systems have higher opportunity costs than the labour for paid employment in estates, ceteris paribus.
By way of simple calculations, the total labour required by the Sesbania- based system (983 man-hours) would earn the farmer MK921.56 if engaged in ganyu (hired labour). The same labour devoted to producing sesbania biomass and incorporation earns from the subsequent yields a total of MK6249.30. Using consumer price of MK3.90 /kg of maize, MK921.56 can buy 236.3 kg of maize enough for one person throughout the year. This is only 17.3 % of the total food the family would require. However, the same labour if used in the sesbania-based system would provide the farmer with 114 % more maize than what the family requires per annum. This also showed that farmers might reduce the dependence on inorganic fertilisers while at the same time maintaining desirable crop yields from limited land. The results have indicated therefore that labour investment that could be made in these systems with half the costs of inorganic fertilisers could make more economic sense in smallholder farms.
These outputs imply that adopting the tree legume-based systems, especially the sesbania-based system, with or without half of the recommended nitrogen (96 kg N ha-1), the yield benefit achievable would be enough to bring many of the food insecure households to a certain level of food self sufficiency. The benefits were more so when the biomass was supplemented with inorganic nitrogen at 50% the national recommendation rate.
The results of maize production under tree legume-based cropping systems have shown that use of agroforestry legumes gave more yields over the traditional cropping systems. However, such improvements give higher returns when organic manures are fully incorporated and supplemented with inorganic fertilisers. This implies that farmers who do not have enough money to purchase the inorganic fertilisers would still be at a better position with agroforestry legumes. Labour investment in these technologies is beneficial in the long run. In the short run, farmers need to sacrifice their resources for the minimal benefits. Farmers with fields in the dambo valleys should be encouraged to use the tree legumes, since the net benefits from the technologies are encouraging.
However, in the steep slopes, more research has to be done on the growth of the legumes and biomass production. Under the conditions of this study, the Cobb-Douglas approach was effective in estimating maize production under tree-based cropping systems at the three landscape positions.
The authors gratefully acknowledge The Rockefeller Foundations Forum for Agricultural Resource Husbandry for funding the study, and Dr. Paul Woomer for reading through an earlier draft of this manuscript.
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