This paper develops a method to jointly estimate crop yield elasticities and area elasticities with respect to output prices based on a theoretically consistent model. The model uses a duality theory approach for the multi-output and multi-input firm, and introduces uncertainty in the level of target output which conditions the cost minimization problem, in the output prices and in the conditional input demand functions. The underlying production technology is conditioned on fixed inputs, both allocatable and non-allocatable. Up to our knowledge, there have been no theoretical developments of this type of models for multioutput technologies. Our approach is also novel because no previous model of this type has introduced the effects of allocatable fixed inputs. We provide an empirical application of this theoretical framework using State-level data and approximating the dual cost function by a normalized quadratic flexible functional form. We derive expressions for the elasticities of interest conditional on the function specification assumed.