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

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.