In response to the subprime crisis in 2008, central banks lowered their short rates rapidly, but came up against the zero-interest rate floor. To ensure the liquidity of the financial system, they then decided a Quantitative Easing policy of buying securities massively, mainly government bonds. Their balance sheets began to swell, reaching historically unprecedented levels of 8960 billion USD for the Fed, 8500 billion euros for the ECB. Then, in 2022, when the world was confronted with an inflation that took central bankers by surprise, they embarked on a rise in short rates that was unprecedented in its speed and force. Inflation has receded, and while the markets are only thinking of lower rates, central bankers are wondering what to do with the large stocks of securities they are holding. In today's jargon, how do you reconcile lower rates with a necessary quantitative tightening? And, if we look to the future and broaden our perspective, what use should be made of the two instruments now available to central banks: interest rates and quantitative monetary policy? How can we get away from the current sequential vision: first, act on rates (downwards in 2008, upwards in 2022), then, in a second phase, implement a quantitative policy (upwards in 2009, downwards in 2024)? In this paper, we attempt to provide an answer to this very legitimate question. We develop a simple, general equilibrium model, which can be solved analytically, to understand and analyze monetary policy from an "operational" point of view. The aim is not so much to describe the macroeconomic ecects of monetary policy as to study what is often referred to as the "plumbing" or "piping" that a central bank must consider when implementing the decisions it takes to stabilize the economy or ensure financial stability. [...]
