This paper demonstrates the existence of a unique solution of the PMP problem when both observed output quantities and limiting input prices are taken as calibrating benchmarks. This version of PMP avoids the use of a user-determined small positive number ε originally introduced for guaranteeing that the dual (shadow) price of binding input constraints be positive. Furthermore, the paper shows how to obtain endogenous output supply and input demand elasticities that match available information about them in the form of previously estimated parameters for an entire region or sector. The framework is applied to a sample of farms also for the case that admits no production for some of the crop activities. The calibrating solution is very close to the observed values of output quantities and input prices. The calibrating model does not use the matrix of fixed technical coefficient and reproduces identical calibrating solutions.