We evaluate optimal monetary policy in an economy where agents face random oscillations in their production opportunities which fluctuate between productive and unproductive periods. The economy is populated by agents of two types defining their productive state. Types are assumed to be perfectly negatively correlated, so that at each point in time only one type is productive. As in the seminal work of Scheinkman and Weiss (1986) agents face a borrowing constraint: since the state is not observable agents cannot issue private debt. Because of this market incompleteness, money (an intrinsically useless object) may serve a fundamental insurance role and be valued.
We extend Scheinkman and Weiss’s analysis, which assumes a constant money supply, by letting the government choose a perfectly anticipated monetary growth rate, implemented through lump-sum money transfers. As in Levine (1991) we assume that the government does not know which agent is productive, so that the transfers are equal across agents. In this economy money is the only savings instrument: an unproductive agent consumes exchanging money for goods with the productive agent.
As the state can be reversed, the value of money is positive for productive agents too, who are hence willing to trade their production for money. A known feature of the Scheinkman-Weiss economy is that rich productive agents will be relatively less interested in trading goods for money. It follows that trade volumes, aggregate production, and the price of money depend on the distribution of wealth (i.e. shares of money holdings) which evolves through time following the history of shocks.
We provide an analytical characterization of the price of money and aggregate production, as functions of the money growth rate parameter and the wealth distribution. Moreover, we characterize the dynamics of the wealth distribution as a function of money growth and the history of shocks. These objects give a complete description of the dynamics of this economy.
Since the money growth rate affects the distribution of wealth, monetary policy has real effects and the choice of the optimal anticipated policy involves a tradeoff between two margins: the first is that a monetary expansion provides insurance to agents who incur in a long spell of unproductive periods, and end-up having low money holdings and little consumption. The second margin is the classic cost of inflation: an expansionary policy lowers the return on money, lowering productive agents’ incentives to produce in exchange for money. The choice of the optimal money growth rate trades off insurance vs. production incentives.
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The Optimum Quantity of Money with Borrowing Constraints
