Refutable implications of the firm model under risk
Curvature properties of the indirect utility function are shown to be necessary and sufficient for refutable behavioural postulates in the form of comparative static results, reciprocity relations, and restrictions on output and input responses for firm models under risk. These postulates are independent of onerous restrictions on risk preference, technology, or random variable distribution. As an exposition, the complete set of refutable implications for a multi-output firm operating under price risk is derived. At the data means, these implications are not rejected when they are tested using firm-level data, but both risk neutrality and constant absolute risk aversion are rejected. At individual observations, one implication is rejected almost as frequently as risk neutrality and constant absolute risk aversion.