Money as a mechanism to intersubjectively compare entirely subjective preferences

Purpose: This article contributes a money model that let us understand under which conditions money allows to interpersonally compare the entirely subjective material preferences of different economic subjects. Methodology: We proceed in several steps. First, we provide a graph-based model for the infinitely scaling network of economic relevant interactions, which resolves the issue that the nodes (economic subjects) and the edges (economic interactions) of this graph cannot be modelled independently. It rests on the role concept, where roles can compose externally to an interaction (an edge) and internally to a coordinating subject (a node). Second, we choose the preference concept and its possible representation by a utility function to model how an economic subject takes its decisions. Then we introduce two complementary roles of buyer and seller together with two different ways to compose both, namely 'externally' to a trade and 'internally to a trader. We provide a simple utility representation that is 'compositionally consistent' as we defined it for both compositions. In fact, we prove that this utility representation is the only one with this property. Findings: In this money model, interpersonal comparison of subjective material preferences is possible under the following conditions: (1) The decisions of an economic subject in a trade can be modelled by a preference model where preferences are expressable as utility. And (2) all buyers have the same total budget and the same access to the same set of alternatives. Value: Since the (now disproved) conviction that one cannot compare subjective preferences interpersonally had significantly shaped economic theory in the past, the authors assume that the (now proven) fact that money allows exactly such a comparison under certain conditions will shape economic theory and practice in the future as well.