Decompositions of Profitability Change using Cost Functions

Profitability at a period of time is defined as the value of outputs produced by a production unit divided by the corresponding cost. Using some earlier work by O’Donnell, the paper provides a decomposition of profitability growth over two periods into various explanatory factors. The explanatory factors are: the change in the production unit’s cost efficiency, an index of output price growth, returns to scale, technical progress and an index of input price growth. If output prices for the production unit are not available, the paper suggests that marginal costs could be used as prices to weight outputs in each period. Using marginal or average costs to weight outputs leads to a methodology for evaluating the productivity performance of nonmarket production units that is similar to the methodology suggested in the Atkinson report.