This paper studies a stationary, pure exchange overlapping generations model with a particular kind of randomly generated pairwise-trading pattern. This model, in contrast to the usual overlapping generations models, has the following implications. As regards existence, it is shown that a standard boundary condition on preferences is sufficient to imply the existence of a stationary monetary equilbrium. As regards properties of the equilibrium, for some specifications, my model has a stationary equilibrium in which claims bear a higher rate of return than fiat money. It is also proved that this stationary equilibrium is conditionally Pareto optimal.
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