Conditional Factor Demands and Positive Output Effects: A Necessary and Sufficient Condition
Résumé
The duality between cost and production functions has been thoroughly studied and is well-known. A given set of
assumptions on the technology implies a set of restrictions on the Jacobian of the cost function and on a subset of its
Hessian matrix. The vector of second derivatives of the cost function with respect to the input prices and the output
has not been fully characterized, however. In this note, we present a necessary and sufficient condition to ensure that
the components of this vector are all strictly positive. That is, we specify the condition for all conditional demand
functions to be simultaneously increasing in output. This condition is interpreted as a strengthening of the quasiconcavity of the production function.