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Revista de Economia e Sociologia Rural

Print version ISSN 0103-2003On-line version ISSN 1806-9479

Rev. Econ. Sociol. Rural vol.41 no.1 Brasília Jan./Mar. 2003 

The soybean production frontier and economic efficiency in Mato Grosso do Sul, Brazil



Alceu Richetti; Ricardo Pereira Reis

Master in Farm Management, Researcher at EMBRAPA - CPAO. Dourados - MS. Brazil. CEP 79804-970. B.O. Box 661. Email:
Doctor in Agricultural Economics; Department of Administration and Economics - UFLA. Lavras - MG. Brazil. 37200-000. B.O. Box 37. Email:




This work evaluates the economic efficiency of productive resource utilization in the cultivation of soybeans in the state of Mato Grosso do Sul, Brazil. The study area comprises the state’s main soybean producing counties. Economic efficiency was estimated for a sample of 151 soybean producers through the production frontier function. The producers in the state’s northern region are operating near the established production frontier, signaling a favorable tendency in resource reallocation and achieving efficiency.

Key words: Production frontier, economic efficiency, soybean



1. Introduction

The task of a professional agriculture business manager implies adapting and/or changing existing management theory and practice to improve an agribusiness’s economic results by successfully modifying its agricultural practices. The agricultural professional must broaden his knowledge and control of the production unit’s structure and functioning. Hence, analysis of the technical and economic efficiencies of rural enterprise activity is becoming increasingly important to these professionals.

Estimation of an enterprise’s level of economic efficiency may help decision making directed to improve current performance and determine the direction of new technological development intended to increase production rationally. Furthermore, efficiency estimates draw attention to recognition disparities between the production potential of a new technology and the actual level of production.

The development of a new Brazilian institutional environment in the 1990s increased economic competitiveness by facilitating the linkage of the nation’s product and service markets and brought more efficient production units. This efficiency came from lowered costs, rationalized production scale, technological availability, and improved logistics (storage, production transportation, and flow). In this setting, Brazilian agriculture found a new challenge: to improve agricultural competitiveness through greater production efficiency (which has become a professional business activity).

The soybean complex, according to Coelho (1996), has assumed an important role in the Brazilian economy due to increased export sales. This growth has had direct and indirect effects on the rest of the economy and generated substantial income in states where soybeans are intensely cultivated.

The state of Mato Grosso do Sul is Brazil’s fifth greatest soybean producer, contributing approximately 8.9% of Brazil’s total production. The state producers produce 2.8 millions of tons of soybeans annually and have achieved an average yield of 2.6 thousand kg per hectare, which compares favorably with the national average of 2.4 thousand kg per ha. However, because of high production costs and the great distance to market, the state’s soybean producers’ profit margins are low. Because of the large amount of soybeans produced for sale into the export market, international prices determine the prices received by Mato Grosso do Sul’s soybean producers, and foreign producers provide important competition.

Due to the restricted range of return that this agricultural activity has yielded in recent years, market competition, and an increase in production costs, production and investment decisions based on accurate, complete information and business vision are fundamental to the maintenance of soybean producers. The present work was designed to provide updated information for use by soybean producers and other interested parties.

This study has as its general goal the evaluation of the economic efficiency in the use of soybean productive resources in Mato Grosso do Sul, Brazil. Specifically, we intend to estimate the soybean production frontier and to identify the economic efficiency of the use of productive factors by the state’s producers.


2. Methodology

2.1. Efficiency measurements

To analyze productive resource management, the indicators of interest are the technical, allocation, and economic efficiencies.

An economically efficient production process is understood as one in which factor costs are minimized (allocation efficiency) and production occurs on the technological frontier (technical efficiency). The measure of economic efficiency is a combination of technical and allocation efficiencies.

From this vies, the technical efficiency measure quantifies how near an enterprise is to maximum production when using the optimal resource combination. Technical efficiency considers the relation between inputs and final products, that is, deals with the physical production process.

The allocation efficiency measure quantifies how near an enterprise is to using the optimal combination of production inputs when the goal is maximum profit. Allocation efficiency exists when resources are best allocated by an enterprise according to market prices and production necessities.

Studies about efficiency and frontier measurements began with the work of Farrell (1957). He gave definitions for both technical and allocation efficiencies, starting from the deterministic frontiers concept. To define his concept of efficiency, the author considered an enterprise that uses two inputs x1 and x2 in the production of one product y. The technology was summarized by a linearly homogenous production function, y = f(x1, x2). This function can be written as 1 = f(x1/y, x2/y), that is, the technological frontier can be represented by a unitary SS’ isoquantum, as shown in Figure 1. By definition, enterprises that operate on the isoquantum are efficient as none is below SS’.



Admitting input combinations represented by points A, B and C, the ratio between the distance from origin O to point B and the distance from O to A, that is, the OB/OA ratio, measures technical efficiency (ET), which is the ratio of the inputs necessary to produce y in relation to the actual inputs used.

Considering that line WW’ in Figure 1 is the isocost curve, representing the ratio of the x1 and x2 input prices, the OC/OB ratio measures allocation efficiency (EA) or price. The cost at point C is the same as that at allocationally efficient point D and lower than at point B.

Finally, OC/AO measures the total efficiency or economic efficiency (EE), which is given by the product of the technical and allocation efficiencies. Hence, we have:


Efficiency analysis provides technical and economic indicators of the degree of efficiency with which an enterprise uses its inputs in the production process. Hence, an efficient production unit is one that achieves maximum production with the resources it uses.

The maximum possible productivity of a production unit using a specific input combination and production technology is defined as its production frontier. However, not all enterprises present the same efficiency in the transformation of inputs into products, which permits the possibility of less efficient enterprises. Some authors consider that a production unit’s distance below the production frontier as an inefficiency measure.

2.2 Empiric model of the frontier function

Efficiency studies that begin with an estimate of the production function, especially the production frontier function, are becoming more accepted and more sophisticated. Bravo-Ureta and Rieger (1990) measured the economic efficiency of dairy production of many farms in the United States. Ali and Chaudhry (1990) analyzed production efficiency in different Pakistani agricultural regions. Neff, Garcia and Nelson (1993) estimated the technical efficiency of a group of grain producers in the state of Illinois, United States. Bravo-Ureta and Pinheiro (1997) estimated the technical, allocational, and economic efficiency of small agricultural producers in the Dominican Republic’s, Dajabon region.

In Brazil, Tupy (1996) estimated the economic efficiency of a sample of poultry producers. Ferreira (1998), by means of a homotetic-ray function, analyzed the efficiency and the scale economies of poultry production in Minas Gerais. Conceição (1998) estimated the technical efficiency of a sample of producers representative of Brazilian commercial agriculture. Ferreira, Becker, and Waquil (1999) analyzed the technical efficiency of rural establishments that have dairy production as their main activity. Gomes and Alves (2000) measured the technical efficiency of a sample of dairy producers from the states of Minas Gerais and São Paulo.

The production frontier function used in this study is obtained from a homotetic-ray frontier function, which allows variable returns to the producer’s scale. The function coefficients were estimated using the Ordinary Least Square method (OLS) and are based on the usual suppositions regarding error term and model specifications. Factors that effectively participate in the soybean production process were used as explanatory variables.

The empiric model of the production frontier function adjusted in this study can be specified as:




being that Y is the value of soybean production; T’lnT is the cost of land weighed by its participation in total cost; M’lnM is the cost of machinery and equipment including depreciation, maintenance, and other use costs weighed by its participation in total cost; S’lnS is the expense for seed weighed by its participation in the total cost; I’lnI is the expense for fertilizers and pesticides weighed by its participation in the total cost; O’lnO the stable and eventual labor expense weighted by its participation in total cost; b0 = lnA and e* = ln e= E(lne), so that the property of the error term maintains an average equal to zero.

The model’s variables were estimated as follows:

  1. production value (Y) – defined by the sum of the quantity of soybeans produced on the property multiplied by the respective unitary price in Brazilian reais paid in the studied region;

  2. land (T) – area of the properties effectively cultivated with soybeans multiplied by the region’s mean value for land rights in reais per hectare ;

  3. machinery and equipment (M) – defined by the monetary value in reais for the use, maintenance, and depreciation of agricultural machinery and equipment to cultivate and harvest soybeans;

  4. seeds (S) – expressed by the value of expenses in reais for seeds used in areas cultivated with soybeans;

  5. inputs (I) – expressed by the value of expenses in reais for chemical fertilizers, fungicides, herbicides and insecticides used in the areas cultivated with soybeans;

  6. operational services (O) – expressed by the value of expenses in reais for permanent and casual labor used to cultivate and harvest the soybean crop.

In equation (2), for firm i, if ei* is equal to zero then the enterprise is on its production frontier, producing the maximum product from the inputs it uses: the economically efficient enterprise. The economic efficiency of production of enterprise i is therefore estimated through:


Thus, the economic efficiency index (EE) for enterprise i is calculated using the ratio between the enterprise’s current production value (Y) and the value of its production if it were economically efficient (Yi), that is:


For determination of the production frontier and analysis of economic efficiency, the state’s soybean producers were considered as a group and were considered by producing region: north or south Mato Grosso do Sul. Large properties predominate in the state’s north, and small and medium size properties predominate in its south.

The following statistical criteria were among those used when calculating the equations through OLS: the adjustment degrees measured by the coefficient of determination (R2) and the coefficient of determination corrected for degrees of freedom (2); the significance of each equation’s regression parameter estimations (Student’s "t" test ), and the significance of the regression equation (test "F").

The statistical selection criteria, the regression coefficient signals’ coherence with economic principles, and the importance of each variable in the productive process were observed for inconsistencies. Knowing that highly correlated explicative variables may cause multi-colinearity problems, we examined these variables using correlation coefficient calculus.

Following the same procedure adopted by Ferreira (1998) and Gomes (1999), we considered that the soybean producer was economically efficient if the economic efficiency (EE) measurement was between 0.9 and 1. The .1 interval was intended to allow for data collecting errors.

From the standard residue matrix, the production frontier of each region and of the state was measured. To construct the probabilistic frontier, the highest residual standard value was added to the functions estimated by the OLS for each adopted criterion. After the estimation of each production frontier, economic efficiency (EE) levels were calculated. Economic efficiency was related with each observation, as shown in expression (5).

In this study, the stratification of efficiency levels with 0.09 intervals was used in the result presentations. This stratification was based on similar studies conducted by Ferreira (1998) and Gomes (1999).

2.3 Study area and source of data

This study includes the main soybean producing counties in Mato Grosso do Sul, Brazil: Dourados, Itaporã, Laguna Carapã, Ponta Porã, Amambai, Aral Moreira, Rio Brilhante, Maracaju, Sidrolândia, São Gabriel do Oeste, Costa Rica and Chapadão do Sul.

The data were collected directly from the state’s soybean producers by means of structured and semi-structured questionnaires. This survey was realized by a group of researchers from Embrapa Pecuária Oeste, Dourados–MS, from October 1996 to September 1997. The sample was made up of 151 soybean producers that conducted their activities as entrepreneurs and used "crédito rural" to finance their agricultural activities. The 151 producers were selected at random with each county contributing approximately 10% of the total number. The producers were considered by producing region (north or south) and the state as a whole.


3. Results and Discussion

3.1. Characterization of the interviewed soybean producers

Most of the interviewed soybean producers, 72.85%, were from the state’s south region. They controlled 50.13% of the total soybean production area included in our study and each cultivated 262.98 ha on average. The state’s north contains 27.15% of the interviewed soybean producers. These producers control 49.87% of the soybean production area addressed by our study soybean producing area and each cultivates 701.78 ha on average. As these data indicate, Mato Grosso do Sul’s small and medium sized soybean properties are located in the state’s south while large properties with large areas under soybean cultivation predominate in the state’s north (Table 1).



3.2 Production frontier function for the soybean producing areas

When the production frontier function for the regions of Mato Grosso do Sul was estimated, the coefficients of determination (R2) were 0.9786 for the south region, 0.9905 for the north region, and 0.9834 for the state. This means that 97.86%, 99.05% and 98.34% of the observed soybean production value variations are explained by the production factors considered for the north and south producing regions and for the entire state respectively The corrected coefficients of determination (2) were 0.9776, 0.9891, and 0.9828 respectively (Table 2).



In the analysis of the set of explicative variables, the F value was significant at 1% in all the three estimates. This demonstrates that land cost (T’lnT), machinery and equipment cost (M’lnM), seed cost (S’lnS), chemical inputs cost (I’lnI), and operational service costs (O’lnO) significantly influence the values observed for soybean production in the state and the two regions

The land cost (T’lnT) variable in the south region and state estimations had a negative coefficient, indicating that as more land is opened for soybean cultivation, total production value decreases. This may be related to the extensive utilization of this factor by these sample producers. Although land use was found to be a statistically significant variable in the determination of economic efficiency, this result implies that less land can be cultivated with soybeans without compromising economic return in the state as a whole or in its south region.

Verifying the soybean production frontier function of the south region and of the state, the significance level of the production explicative variables was inferior to 1%. This highlights these variables’ degree of importance to the value of soybean production in the south region and the entire state (Table 2).

In the north region, the test t indicates that the costs of land (T’lnT) and seed (S’lnS) were not significant while machinery and equipment costs (M’lnM), chemical input cost (I’lnI), and operational service costs were statistically significant. This result suggests that these last three variables are more important to the economic efficiency of soybean cultivation than land and seed costs in the state’s north.

The t-test values and estimated coefficients for the cost of machinery and equipment (M’lnM) and the cost of seed (S’lnS) in the state’s north region were negative. This result indicates that these factors are intensely used by the soybean producers. We point out that this region is composed of large properties on which soybean cultivation is a totally mechanized process.

3.3 Economic efficiency per soybean producing region

The results from this study’s economic efficiency estimates are summarized in Table 3. The mean economic efficiency level of Mato Grosso do Sul’s soybean producers was 0.8028. The state’s north region achieved the best efficiency level, 0.8705, while the south region’s level was 8% lower, at 0.8059.



For Charnes and Cooper (1990), enterprise inefficiency consists of its failing to reach an "efficiency frontier," that is, the enterprise’s production (output) is not optimized given the productive inputs. Thus, due to the .1 interval for data collecting errors, the average economic inefficiency level of the soybean producers in Mato Grosso do Sul was between 0.0972 and 0.1972, that is, between 9.27% and 19.27% (0.90 – 0.8028; 1 – 0.8028). In the north region, inefficiency was between 2.95% and 12.95%; in the south region it was between 9.41% and 19.41%. These results indicate that to be considered economically efficient the state’s soybean producers need to increase production volume between 9.27% and 19.27% using the same level of inputs. To be considered efficient, the south region’s producers should increase output from 9.41% to 19.41% using the same inputs. The north region’s producers, being nearer to this study’s adopted production frontier, need only to increase production between 2.95% and 12.95%.

It was expected that Mato Grosso do Sul’s soybean producers would obtain better levels of economic efficiency and operate very near or at their efficiency frontier. However, our results (Table 3) indicate that the producers are operating below optimal economic efficiency, combining their production resources in a less than optimal manner.

We verified that none of our sample soybean producers achieved the maximum efficiency level. A mean efficiency level of 0.8152 (0.80 –| 0.89 range) was achieved by 56.29% of the state’s soybean producers, while the others (43.71%) achieved a mean level of 0.7868. The north region’s soybean producers achieved a mean efficiency level of 0.8705, in the 0.80 –| 0.89 range. In the south region, 67.27% of the studied producers are in the 0.80 –| 0.89 range with an average of 0.8155, while the others (32.73%) achieved a mean efficiency of 0.7860.

The differences observed between the two regions may be due to farm size, land ownership regime, labor, mechanization, management, and/or production technology. It is important to note that small and medium size properties with a mean area of 262.98 ha predominate in the south region while large soybean properties with a mean area 701.78 ha predominate in the north region.

In Table 3, we notice that the higher frequency concentration of soybean producers in Mato Grosso do Sul (56.29%) are in the 0.80 –| 0.89 efficiency range. Therefore, if the economic efficiency of Mato Grosso do Sul’s soybean producers does not improve, future growth of soybean production in the state may be negatively stimulated, as new producers avoid cultivation of a crop with apparently low economic attractiveness.


4. Conclusions

In general, the studied soybean producers in Mato Grosso do Sul proved to be inefficient in the application of their productive resources; however, those from the state’s north region were operating nearer to the established efficiency frontier. This signalizes more favorable resource reallocation in the north state, possibly due to the economic efficiency improvements they have achieved through scale: the larger properties were concentrated in the state’s north. The differences observed between regions may also be due to land ownership regime, labor, mechanization, other technological advantages, and/or management.

The mean economic efficiency level achieved by the studied soybean producers was 80.28%. At first glance, this level is not low but indicates that additional productivity gain and/or production cost reduction may be obtained through more efficient utilization of productive resources. This would move these producers to their production frontier.

It was expected that Mato Grosso do Sul’s soybean producers would achieve better economic efficiency levels, that is, that they would operate very close to or on the production frontier established by this study. However, our results indicate that partial economic inefficiency in these producers’ productive processes has limited their ability to take advantage of available technology and obtain better economic results.

The verification of economic inefficiency among the studied soybean producers suggests that efforts should be made to improve performance in this segment. To be effective, these efforts will require that the producers have complete and current technical and economic information. If an improvement in economic efficiency does not occur, this segment’s low economic attractiveness may lead to negative production stimulation over the long term result.

In the attempt to improve Brazilian agricultural production, the determination of a production frontier that denotes rural agricultural producer economic efficiency would be of great utility for rural extension services and agricultural researchers. It would serve as a benchmark identifying those producers that are producing efficiently and those that need assistance.

From the business perspective of this study, our results indicate that public policy in Mato Grosso do Sul should be directing the transference of technology to the state’s soybean producers. This would be the most effective measure that government agencies could use to improve soybean production efficiency and insure the continued viability of this agricultural segment in Mato Grosso do Sul. The technology to improve soybean production efficiency is available; it just needs to be the field.

As a research suggestion, we believe that an efficiency analysis of all segments of the soybean productive chain would be worthwhile. Thus, other instruments to estimate the cost, profit, and production frontiers should be tested and used to measure the economic efficiency of rural enterprises.



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