Monetary policy implementation and pass-through

I provide a simple general equilibrium model of monetary policy implementation and pass-through for undergraduate and graduate teaching. Besides a household and a firm, the model features a continuum of commercial banks, a government, and a central bank. The household uses deposits and cash to transfer resources over time. Monetary policy is implemented with open market operations and interest on reserves policies. I show that open market operations affect the money market rate, the government bond yield, and the deposit rate through changes in the insurance yield on reserves. At the interest rate floor, the insurance yield is zero. Therefore, open market operations become ineffective when reserves are ample. By contrast, interest on reserves policies change interest rates even at the interest rate floor. In addition, I find that expansionary monetary policies decrease expected commercial bank profits. Also, they increase household cash holdings in a monotonic, but non-linear fashion.