When I teach monetary economics, one of the topics I discuss is coexistence of money and higher-return assets. My list of potentially serious explanations includes (i) a structure of Shapley-Shubik trading posts that gives a special role to one object (see Krishna [1] for an argument that a structure of posts that favors a low rate-of-return object is not robust); (ii) Zhu-Wallace [6], which, as carefully described by Lagos, divides the gains from trade in pairwise meetings between buyers and sellers in a way that can favor the holding of a low rate-of-return object; and (iii) the possibility that the higher-return assets are counterfeits (see, for example, Li et. al. [4]). Here, after setting out the Lagos idea in a simple way, I explain why I will not add it to this list. Because the main idea applies to any model, I set it out against the background of the alternating-endowments model (see [5]). There is one good per discrete date, a unit measure of people, and each person maximizes expected discounted utility of consumption with discount factor β ∈ (0, 1) and period utility function u: R++ → R, where u is twice differentiable and u ′ ′ < 0 < u ′.

A random‐matching model of money is used to deduce the effects of a once‐for‐all change in the quantity of money. It is shown that the change has short‐run effects that are predominantly real and long‐run effects that are in the direction of being predominantly nominal provided that the change is random and people learn its realization only with a lag. The change in the quantity of money comes about through a random process of discovery that does not permit anyone to deduce the aggregate amount discovered when the change actually occurs.

In "The Inefficiency of Interest-bearing National Debt" (J.P.E. [April 1979]), we argued that private sector transaction costs are needed in order to explain interest on government debt. It follows that if the government's transaction costs do not depend on its portfolio, then, barring special circumstances, an open-market purchase is deflationary and welfare improving. In this paper we show that this result can survive a potentially relevant special circumstances: reserve requirements which limit the size of insured intermediaries.

[In "The Inefficiency of Interest-bearing National Debt" (J.P.E. [April 1979]), we argued that private sector transaction costs are needed in order to explain interest on government debt. It follows that if the government's transaction costs do not depend on its portfolio, then, barring special circumstances, an open-market purchase is deflationary and welfare improving. In this paper we show that this result can survive a potentially relevant special circumstances: reserve requirements which limit the size of insured intermediaries.]

The coexistence of money and default-free interest-bearing government bonds is explained by transaction costs; the private sector absorbs money with less real difficulty than it absorbs bonds. Under the assumption that the costs of issuing money and issuing bonds are identical, it follows that the presence of government bonds is inefficient. Further, the steady-state inflation rate is higher with bond financing of a given real deficit because there is less net output, less real saving, and hence the need for the government to inflate faster. This is demonstrated in a version of Samuelson's pure consumption-loans model.

The coexistence of money and default-free interest-bearing government bonds is explained by transaction costs; the private sector absorbs money with less real difficulty than it absorbs bonds. Under the assumption that the costs of issuing money and issuing bonds are identical, it follows that the presence of government bonds is inefficient. Further, the steady-state inflation rate is higher with bond financing of a given real deficit because there is less net output, less real saving, and hence the need for the government to inflate faster. This is demonstrated in a version of Samuelson's pure consumption-loans model.

[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.]

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.