Estimating the Marginal Cost of Operating a Service Department When Reciprocal Services Exist.

Abstract ABSTRACT: Prior work has examined models in which the reciprocal cost allocation method yields allocation rates that are equal to the marginal costs of operating service departments. We extend this work by analyzing more general production functions for service departments and by incorporating uncertainty. The results demonstrate that the allocation rates derived from the reciprocal cost allocation method are random variables that, in general, are not equal to the expected marginal costs of operating the service departments. In particular, the reciprocal cost allocation rates are biased estimates of these expected marginal costs if any of the service departments operate at a point on their production functions at which the marginal physical product is not equal to the average physical product of their inputs. We also analyze three econometric procedures that provide consistent estimates of the marginal costs. The simulation results indicate that the standard deviations of these estimators are considerably larger than those of the reciprocal cost allocation rates. Because the estimates of the marginal costs provided by the reciprocal cost allocation method have a greater degree of bias, but a lower standard deviation than the estimates provided by the other methods, none of the methods provide estimators that are unambiguously best. Factors that affect the magnitudes of the bias and relative efficiency of the reciprocal cost allocation rates are also discussed.