Output learning and duality in joint production programs

Summary

Output learning is incorporated into a short-run static cost-minimizing model of the multiproduct, multifactor firm which employs a fixed-coefficients technology. The firm's output processes or activities are ultimately specified as functions of the activity variables themselves, thus rentering a generalization to a concave program. A Lagrange dual formulation is then used to obtain the indirect cost objective. Given that this optimal cost function is differentiable and satisfies a regularity condition, its price derivatives serve as input demand functions while its derivatives with respect to the minimum output requirements yield a set of (implicit) marginal costs or dual variables.