The Optimum Quantity of Money with Borrowing Constraints

Abstract

We characterize the optimal anticipated monetary policy in economies where agents have precautionary savings motives due to random production opportunities and the presence of borrowing constraints. Non storable production makes intrinsically useless outside money valuable to insure consumption. We show that the choice of the optimal money growth rate trades off insurance vs. incentives to produce: an expansionary policy provides liquidity to borrowing constrained agents, while distorting production incentives. The joint presence of uncertainty and borrowing constraints implies that the Friedman rule leads to autarkic allocations. For utility functions with log concavity (or more) we show that the optimal constant money growth rate is strictly positive and finite. Considering state-dependent policies allows us to decouple, at least partially, the insurance motive from the production incentive. The optimal state-dependent policy prescribes expanding the money supply in recessions and contracting it in expansions: on average, the optimal state-dependent money growth is negative

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