### A method for calibrating input (and output) price elasticities

#### Abstract

We propose a theoretically consistent method for calibrating input (and output) price elasticities (of agricultural crops) from a minimal set of given estimates. Our review of production theory suggests three starting points for the exercise: (a) inputs and outputs have to be classified by input nonjointness, (b) production functions may be assumed to be linearly homogeneous, and (c) given an *n* x *n* (symmetric) matrix of elasticities, which has *n(n*+1)/2 distinct cells, the values of *n*(*n*-1)/2 of the distinct cells must be known to solve the n unknown elasticities. Exploiting Shephard’s Lemma and Euler’s Theorem, we work out the method for a cost function with four inputs. We also provide a numerical example involving a 9 x 9 matrix of a multiple-output profit function.

Classification-JEL: C63, D21, Q12

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