Bisymmetry and Consistent Aggregation: Historical Review and Recent Results
János Aczél · 2019
The problem of consistent aggregation asks, for example, whether the aggregate of maximal outputs of several producers in an industry may be determined by the aggregates of their (microeconomical) inputs through a macroeconomical production function. This turns out to be equivalent to a functional equation, that of rectangular generalized bisymmetry. Nevertheless, the two topics evolved from 1946 till now with rather little contact. We present this history and the solution of the relevant functional equation on general sets and apply the results to intervals of real numbers. Interpretation, representativity considerations, and compatibility and incompatibility examples follow.