Optimizing Production under Uncertainty: Generalisation of the State-Contingent Approach and Comparison of Methods for Empirical Application

In a recent paper Rasmussen (Rasmussen 2003) derived criteria for optimal production under uncertainty based on the state-contingent approach developed by Chambers and Quiggin (2000). While the criteria in the 2003-paper were derived for the one variable input case, and for different types of input, the present paper generalises the results to the multi-variable input case. It is further shown that with the output-cubical technology as the basic model, any type of input may be analysed as a special case within the general model framework developed. The main part of the paper is devoted to the problems of empirical application of the State-contingent approach. To empirically apply the optimization criteria derived, one needs specific functional forms of both the state-contingent production functions and the utility function based on state-contingent income measures. The paper shortly reviews the empirical approach normally taken when using the well-known Expected Utility (EU) model and this approach is in turn compared to the more general approach potentially available in the state-contingent model. Comparisons show that the potential benefit of the state-contingent approach compared to the expected utility model is limited by the empirical opportunities. Thus, it is unrealistic to expect production functions to be estimated for all possible states of nature. State-contingent production functions therefore, have to be considered as stochastic production functions. In this case, it is not obvious whether the state-contingent approach is better than the expected utility model, and it is proposed that this is further investigated using Monte-Carlo simulation.