O objetivo desse trabalho é analisar as inter-relações entre os principais insumos utilizados no processo produtivo da soja e as suas possibilidades de substituição, através dos conceitos das elasticidades-preço da demanda, de Allen e de Morishima. O referencial teórico do estudo é o da teoria da dualidade da função custo e da função de produção. Os dados são provenientes de uma pesquisa de campo realizada nos cinco principais estados produtores do País. Químicos, capital, terra, mão-de-obra e outros custos foram as variáveis analisadas. As elasticidades-preço cruzadas mostraram que há complementaridade entre os fatores mão-de-obra e capital. As elasticidades de substituição parcial de Allen indicaram substituição entre a maior parte dos fatores de produção. Houve uma forte relação de complementaridade entre os fatores capital e mão-de-obra e de substituição entre os fatores químicos e mão-de-obra. Na classificação de Morishima, capital e mão-de-obra são complementares quando o preço de capital varia e substitutos quando varia o preço do fator mão-de-obra. This paper analyzes the substitution relations between the main inputs used in soybean production in Brazil, through the estimates of Allen and Morishima substitution elasticities. The theoretical approach used is the production/cost duality. The data was obtained from field research in the five main production states in the country. Chemicals, capital, land, labor and other costs were the variables under study. The estimated cross-price elasticities pointed to complementary relations between labor and capital. The Allen partial substitution elasticities showed substitution between most of the production factors, but a strong complementarity relation was found between capital and labor. In the Morishima elasticity of substitution concept capital and labor were found to be complements when the price of capital varies and substitutes when the price of labor varies
Economies of scale and factor substitution in the brazilian soybean production The main objective of this paper is to estimate a translog cost function for the soybean production activity in Brazil, to infer about the existence of scale economies in the sector. We use cross-section data obtained through a field research undertake during the period of September to December 2004, in a sample of 218 soybean-producing units in the main producer states in Brazil. The paper also addresses a socioeconomic characterization of the surveyed units and analyses substitution possibilities between inputs. The sample reflects regional detail of production structure, with smaller producers concentrated in Southern Brazil and larger producers concentrate in the Center-West region. The elasticities of derived demand showed complementary relation between labor and capital. The Allen partial elasticities of substitution show substitution between most of the production inputs. Capital and labor are complements and chemical and labor are substitutes. In terms of Morishima elasticity of substitution capital and labor are complements when capital price varies and they are substitutes when labor price varies. The economies of scale estimates point to an optimal scale of production around 12 thousand ton that could be produced in an area with approximately 4,000 hectares. The results suggest that the presence of scale economies could be determining a new production structure for the sector in Brazil. And finally, the evidence found also suggests that some aspects of the small production system work to reduce the importance of these scale economies, and are determinant to keep the small-scale operations in the traditional regions in the short run.
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