The Lagos‐Wright model—a monetary model in which pairwise meetings alternate in time with a centralized meeting—has been extensively analyzed, but always using particular trading protocols. Here, trading protocols are replaced by two alternative notions of implementability: one that allows only individual defections and one that also allows cooperative defections in meetings. It is shown that the first‐best allocation is implementable under the stricter notion without taxation if people are sufficiently patient. And, if people are free to skip the centralized meeting, then lump‐sum taxation used to pay interest on money does not enlarge the set of implementable allocations.

SEVERAL ECONOMISTS2 have argued that if individuals correctly perceive the rate of inflation so that their expectations are rational, then deterministic models of money and economic growth are unstable. In this view, points on the steady state equilibrium paths examined by Tobin [9] and others are saddlepoints, there being a tendency to diverge more and more from such a path as time elapses if the system is not initially on the path. The source of instability is understood most easily in the context of a model in which money is neutral, with real growth and capital accumulation both being exogenous with respect to the money supply and price level and, moreover, with both equaling zero. Time is continuous. The price level P and money supply M are assumed at each moment to satisfy the demand function for real balances

Two competing monetary policy prescriptions are analyzed within the context of overlapping generations models. The real-bills prescription is for unfettered private intermediation or central bank operations designed to produce the effects of such intermediation. The quantity-theory prescription, in contrast, is for restrictions on private intermediation designed to separate "money" from credit. Although our models are consistent with quantity-theory predictions about money supply and price-level behavior under these two policy prescriptions, the models imply that the quantity-theory prescription is not Pareto optimal and the real-bills prescription is.

Alternative monetary policies are analyzed in an ad hoc macroeconomic model in which the public's expectations about prices are rational. The ad hoc model is one in which there is long-run neutrality, since it incorporates the aggregate supply schedule proposed by Lucas. Following Poole, the paper studies whether pegging the interest rate or pegging the money supply period by period minimizes an ad hoc quadratic loss function. It turns out that the probility distribution of output--dispersion as well as mean--is independent of the particular deterministic money supply rule in effect, and that under an interest rate rule the price level is indeterminate.

Previous work on the denomination structure of currency treats as exogenous the distribution of transactions and the denominations held by people. Here, by way of a matching model, both are endogenous. In the model, trades in pairwise meetings alternate in time with the opportunity to freely choose a portfolio of denominations and there is a trade-off between the benefits of small-denomination money for transacting and the costliness of carrying a large quantity of small-denomination money. For a given denomination structure, a monetary steady state is shown to exist. The model implies that too small denominations are abandoned.