The use of prior information on supply elasticities to calibrate programming models of agricultural supply has been advocated repeatedly in the recent literature (Heckelei and Britz 2005). Yet, Mérel and Bucaram (2009) have shown that the dual goal of calibrating such models to a reference allocation while replicating an exogenous set of supply elasticities is not always feasible. This article lays out the methodological foundation to exactly calibrate programming models of agricultural supply using generalized CES production functions. We formally derive the necessary and sufficient conditions under which such models can be calibrated to replicate the reference allocation while displaying crop-specific supply responses that are consistent with prior information. When it exists, the solution to the exact calibration problem is unique. From a microeconomic perspective, the generalized CES model is preferable to quadratic models that have been used extensively in policy analysis since the publication of Howitt’s (1995) Positive Mathematical Programming. The two types of specifications are also compared on the basis of their flexibility towards calibration, and it is shown that, provided myopic calibration is feasible, the generalized CES model can calibrate larger sets of supply elasticities than its quadratic counterpart. Our calibration criterion has relevance both for calibrated positive mathematical programming models and for “well-posed” models estimated through generalized maximum entropy following Heckelei and Wolff (2003), where it is deemed appropriate to include prior information regarding the value of own-price supply elasticities.