Optimization of inputs in a spatially variable natural resource: Unconditional vs. conditional analysis (Q1124520)

After providing a concise account of the development and use of the stochastic optimization of deterministic inputs in a spatially variable resource the differences between the conditional and unconditional approach are made convincingly clear. The successive inquiry into the comparative virtues of the conditional approach encompasses four distinct steps. Firstly, the economic optimization problem is formalized for a risk-averse, expected utility maximizing agent. Secondly, the underlying stochastic resource model and the parameters to be estimated as well as their estimators are identified for both approaches respectively. Particular attention is devoted to the form and estimation of the covariance matrix. Thirdly, the estimators for the expected value and the variance of the profit accruing to the agent are derived. Lastly, a numerical example containing the average long run estimators of the relevant distribution parameters as well as the optimal inputs and estimated profits for the unconditional approaches respectively is given. Additonally, the values for the case of certainty are calculated as benchmarks. From an economic point of view the key conclusion is as follows: Employing the conditional approach rather than the unconditional one warrants the additional mathematical effort if the distant-dependent autocorrelation coefficient is not negligable, since it makes better use of the information contained in the sample, thus reducing the variance of the average-yield estimator and enhancing the expected utility of a risk- averse agent. By the way of conclusion, the analysis of the optimal number and spread of samples are pinpointed as important future research topics.