Estimating Elasticities of Substitution in African Crops

Abstract

This paper examines cross price elasticities of substitution for labor, capital, and fertilizer for the agricultural sector in Africa with a translog production function. The data are from the Food Agricultural Organization and World Development Indicators Database. The elastisities are calculated directly from the estimated parameters of a production function. Those elastisities include the Allen Substitution Elasticity (AES), factor price substitution elasticity, and Hicks elasticity of complementary (HEC). Allen elastiticies of substitution of all inputs are positive. Results show that only labor and capital are complements among the inputs in HEC and factor price substitution elasticities. Own price elasticities for labor, capital, and fertilizer are inelastic. Labor is the most sensitive of the inputs to input prices. Furthermore, HEC shows that fertilizer demand is elastic with respect to the capital price and inelastic with respect to the wage.