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Pierre Ouellette and Stéphane Vigeant
 
''Conditional Factor Demands and Positive Output Effects: A Necessary and Sufficient Condition''
( 2017, Vol. 37 No.3 )
 
 
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 quasi-concavity of the production function.
 
 
Keywords: Output effects, cost minimization, Hessian matrix, conditional input demands, cost function, duality.
JEL: D2 - Production and Organizations: General
 
Manuscript Received : Feb 09 2017 Manuscript Accepted : Jul 08 2017

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