Monetary Policy in Private Money Economies

We develop a variant of the Lagos and Wright (2005) model to study the role of real assets as media of exchange (private money). There is productive capital in the model that is controlled by an asset fund that finances itself by issuing claims against the capital stock. Although the claims are freely traded in a competitive secondary market, asset fund manager controls 1) the number of claims outstanding, 2) the dividends paid out to claim holders and 3) the fee charged for participating in the asset fund. Our main results are as follows. The first-best allocation can always be replicated by the fund manager. Doing so requires that the private money supply grows in equilibrium and the fee must be positive. In this case, introducing fiat money does not improve the allocation hence it is not essential. We show that the fee charged by the asset fund plays the same role as lump-sum taxation by a government running the Friedman rule. However, if the fee is constrained to be zero, then the first best allocation cannot be obtained while the second best policy still requires a positive growth rate in the number of claims. In this case, a fiat object controlled by the government may be essential.