Primal and Dual Capacity Utilization: An Application to Productivity Measurement in the U.S. Automobile Industry

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Abstract
Capacity utilization measures have traditionally been constructed as indexes of actual, as compared to “potential,” output. This potential or capacity output (Y*) can be represented within an economic model of the firm as the tangency between the short- and long-run average cost curves. Economic theoretical measures of capacity utilization (CU) can then be characterized as Y/Y* where Y is the realized level of output. These quantity or primal CU measures allow for economic interpretation; they provide explicit inference as to how changes in exogenous variables affect CU. Additional information for analyzing deviations from capacity production can be obtained by assessing the “dual” cost of the gap. In this article the definitions and representations of primal-output and dual-cost CU measures are formalized within a dynamic model of a monopolistic firm. As an illustration of this approach to characterizing CU measures, a model is estimated for the U.S. automobile industry, 1959–1980, and primal and dual CU indexes are constructed. Application of these indexes to adjustment-of-productivity measures for “disequilibrium” is then carried out, using the dual-cost measure.

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