On the Normalization of Dimensioned Variables in Ecological Economics

The fundamental concern of ecological economics is to accurately model all aspects of the economy–ecosystem interaction problem — the myriad ways in which the economic and ecological systems are connected to each other. Almost all the monetary and physical variables used to describe economy– ecosystem interactions are dimensional in nature. The exact cardinal value taken by dimensioned variables is contingent on the particular measurement unit used. While several papers on the subject have pointed to the care required in using dimensioned variables in ecological economics, there is little consensus on how dimensional variables must be incorporated in economy–ecosystem interaction models (Mayumi and Giampietro 2010; Malghan, 2011; Chilarescu and Viasu, 2012; Baiocchi, 2012; Mayumi and Giampietro, 2012). Mayumi and Giampietro (2010) inaugurated the debate by making the provocative claim that many models in economics and ecological economics that make use of transcendental functions like the logarithm are fundamentally flawed when these functions use what are apparently dimensioned variables. Malghan (2011) claimed that several popular biophysical sustainability indicators are dimensionally inconsistent because they neglect the ̳qualitative residual‘ that is the defining characteristic of any social–ecological system (Georgescu-Roegen 1971). In a brief comment, Chilarescu and Viasu (2012) showed that the critique that a neoclassical production function (Arrow et al., 1961) is dimensionally inconsistent does not consider that the parameters of a production function are dimensioned variables, too. Thus, in the familiar Cobb-Douglas
On the Normalization of Dimensioned Variables in Ecological Economics

The fundamental concern of ecological economics is to accurately model all aspects of the economy–ecosystem interaction problem — the myriad ways in which the economic and ecological systems are connected to each other. Almost all the monetary and physical variables used to describe economy– ecosystem interactions are dimensional in nature. The exact cardinal value taken by dimensioned variables is contingent on the particular measurement unit used. While several papers on the subject have pointed to the care required in using dimensioned variables in ecological economics, there is little consensus on how dimensional variables must be incorporated in economy–ecosystem interaction models (Mayumi and Giampietro 2010; Malghan, 2011; Chilarescu and Viasu, 2012; Baiocchi, 2012; Mayumi and Giampietro, 2012). Mayumi and Giampietro (2010) inaugurated the debate by making the provocative claim that many models in economics and ecological economics that make use of transcendental functions like the logarithm are fundamentally flawed when these functions use what are apparently dimensioned variables. Malghan (2011) claimed that several popular biophysical sustainability indicators are dimensionally inconsistent because they neglect the ̳qualitative residual‘ that is the defining characteristic of any social–ecological system (Georgescu-Roegen 1971). In a brief comment, Chilarescu and Viasu (2012) showed that the critique that a neoclassical production function (Arrow et al., 1961) is dimensionally inconsistent does not consider that the parameters of a production function are dimensioned variables, too. Thus, in the familiar Cobb-Douglas