Testing for production with complementarities

Suppose we observe a finite number of input decisions made by a firm, as well as the prices at which those inputs were acquired.  What conditions on the set of observations are necessary and sufficient for it to be consistent with a firm choosing inputs to maximize profit, subject to a production function exhibiting production complementarities?  In this paper, we develop an axiomatic characterisation of this hypothesis and also develop a test that can be easily applied to finite data sets.