The objective of this study was to analyze the aggregate agriculture production function for the state of Minas Gerais. The analysis was accomplished in two phases. First, we separate the municipalities in terms of the productive efficiency, using the non-parametric approach of data envelopment analysis. In a second phase, a translog production function was adjusted for the efficient groups and for the inefficient ones, whose parameters were obtained by the ordinary least square method. This article indicates an analytic procedure that can subsidize the estimate of production functions more coherent with the reality, in the sense that relaxes the neoclassical assumptions that the firms are efficient. The results were coherent, once it was possible to separate the relatively inefficient municipal districts, to identify the difference in the partial elasticity of output and the elasticity of substitution between inputs in different groups. The conclusions indicated that is necessary to discriminate the production function in agreement with the level of productive efficiency and to calculate the elasticity of substitution in each point of the sample to test the regularity conditions in the production function.