Symmetry and reversibility in social exchange

In this paper, the equilibrium properties of Coleman's (1973) model of social exchange are explored as a prelude to making interpretations about the dynamics implicit in static models of exchange in general, this model in particular. The model is first presented in the conventional way—as an exchange condition embedded within more general equilibrium conditions, and the subsequent analysis of the model is enriched by examining its equilibrium at aggregate as well as disaggregate levels and by interpreting the model as a set of flows or networks. Its equilibrium properties are then described. First, it is shown how a model in which the exchange condition is a function of its equilibrium, defines an equilibrium which is reproducible and reversible in the stochastic sense. Tests for reversibility are given which show how the equilibrium conditions can be computed from inspection of the data set. Second, an underlying flow structure to the model is assumed, and it is shown how equilibrium in this structure is equivalent to the exchange condition being met. This produces symmetric flows or equal exchange at the aggregate level and a reversible equilibrium. The real interest in this analysis is on how near an actual system is to such equilibria and thus a set of accounts measuring such departures from equilibrium in terms of aggregate and disaggregate flows is presented. Finally, a test example based on the data used by Michener, Cohen and Sorensen (1977) is presented to illustrate the concepts of proximity to structural and reversible equilibria.