Productivity Measurement and the Environment

The materials balance tells us that matter cannot be created or destroyed. The mass contained in inputs must either be contained in the outputs or contained in residuals. Residuals are discharged to the external environment and are pollutants if harmful effects arise. Damages are measured by the willingness to pay for environmental qualities. Static productivity is measured by a ratio of an output index, subtracted damages measured in money, on a multifactor input index. Static productivity will decrease when considering damages, but the social productivity change may go both up and down. A model considering both desirable and undesirable outputs should contain two types of relations: a production function for the desirable outputs, and one for the undesirable outputs. One way of doing this is to specify the functions to have the same set of inputs. This is the factorially determined multi-output model of Frisch. Productivity change measures can be calculated for each type of output separately using a Malmquist index.