Exact calibration of programming models of agricultural supply against exogenous supply elasticities

We develop a methodology to exactly calibrate quadratic programming models of agricultural supply against exogenous own-price supply elasticities. We show that calibration is only possible against certain sets of supply elasticities. For the case where one constraint is binding and the matrix of quadratic coefficients is diagonal, we derive the necessary and sufficient condition under which the calibration problem has a solution, and prove that it is then unique. We propose a general procedure to obtain implied elasticity equations in models of input allocation, and apply it to the constant-elasticity-of-substitution model with land constraint.