Banking in a matching model of money and capital

We introduce banks in a model of money and capital with trading frictions. Banks offer demand deposit contracts and hold primary assets to maximize depositors' utility. If banks' operating costs are small, banks reallocate liquidity eliminating idle balances and improving the allocation. At moderate costs, idle balances are reduced but not eliminated. At larger costs, banks are redundant. A central bank policy of paying interest on bank reserves can reverse inflation's distortionary effects, and increase welfare, but only when costs are small. The threshold levels of banks' costs increase with inflation, suggesting inflation and banks' utilization are positively associated.