A random variable of economic interest is sometimes an identity function of two or more separate variables; for example, crop income per acre is the product of price and yield. This article presents a method for partitioning the variance of such a random variable into components that can be associated with the separate random variables in the identity and interactions among them. Under some statistical assumptions on the variables involved, the converse of the partitioning procedure is useful for deriving the variance of a random variable from the moments of the separate variables of the identity.
Many studies have concentrated on the optimal location of cattle feeding. Two major limitations of such studies have been (1) reliance on a single demand function for beef and (2) failure to consider existing slaughter capacities. By utilizing separated or split‐demand functions for beef and explicitly accounting for present regional slaughter capacity, quite different patterns of beef feeding emerge. In comparison with actual feedlot locations, the models used showed considerable improvement over most previous models. More importantly, results compare favorably with recent trends in the location of cattle feeding.
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