Economic measures of capacity utilization: A nonparametric short-run cost function analysis

Measures of capacity utilization and capacity output are important metrics for evaluating firm performance. This is true whether capacity is considered from a cost accounting framework, an engineering standpoint, or an economics orientation. Ultimately, the crux of the capacity question is about resources not being used to their fullest extent. In an economics context, understanding where firms are producing on their average cost curve provides information about whether capacity utilization is greater than, less than or equal to unity. In real life, most firms are multi-output, multi-input in nature which makes estimation of capacity utilization and capacity output challenging if a cost based measure is desired. This is further complicated in a short run analysis incorporating multiple outputs and multiple fixed inputs where the relevant concept is the minimum of ray average cost. This paper develops appropriate mathematical programming models for measuring capacity utilization in the short-run for multiple-outputs and multiple fixed inputs. We offer a simple transformation that linearizes the non-linear DEA problem to estimate average, or ray average cost, and to determine capacity utilization and optimal output. The models are empirically tested on data from a number of U.S. electricity producers for the single output case, and a sample of dental practices for the multi-output case. Results show that for both industries, most firms were operating at less than full capacity, and needed to expand output to minimize their average costs.