Assume that the banking system has total reserves of \(100\) billion. Assume also that required reserves are 10 percent of checking deposits and that banks hold no excess reserves and households hold no currency. a. What is the money multiplier? What is the money supply? b. If the Fed now raises required reserves to 20 percent of deposits, what are the change in reserves and the change in the money supply?

The required reserve ratio is a central banking regulation that sets the minimum fraction of customer deposits and notes that each bank must hold as reserves, rather than lending out. In our exercise, the initial required reserve ratio is 10%, which dictates that banks must keep \(0.10 for every dollar of deposits as reserves. When the Fed, which is the central bank in the United States, increases this ratio to 20%, it means that banks are now required to hold \)0.20 for every dollar of deposits.

Understanding this ratio is crucial because it directly impacts the ability of banks to create new money through lending. A higher required reserve ratio means banks can lend fewer funds, consequently reducing the money supply in the economy. Conversely, a lower ratio would allow banks to lend more, increasing the money supply. This mechanism is used by central banks to control inflation, manage economic growth, and stabilize the financial system.

The money supply represents the total amount of monetary assets available in an economy at a specific time. It includes cash, coins, and balances held in checking and savings accounts. Simplifying the concept from our exercise, the money supply can be expanded by banks as they use deposits to make new loans.

The money multiplier effect arises from the fact that banks can lend out a portion of their deposits while retaining the minimum required reserve. Initially, with a 10% reserve ratio and \(100 billion in reserves, the potential money supply is \)1000 billion. However, when the reserve ratio is increased to 20%, the same amount of total reserves could only support a money supply of \(500 billion, substantially lowering the potential for new money creation by \)500 billion from the initial scenario. These changes demonstrate the sensitive balance between the reserve ratio and the liquidity available in the economy.

Banking system reserves are the currency deposits that financial institutions must hold in their vaults or with the central bank. They play a pivotal role in the monetary system by ensuring that banks remain solvent and minimizing the risk of a bank run.

In the example from our exercise, the total reserves of the banking system amount to $100 billion. This reserve base can either be increased by monetary policy decisions of the central bank or through the accumulation of more deposits over time. Importantly, the reserves held do not change with the adjustment of the required reserve ratio; rather, the ability for banks to leverage these reserves in creating loans is what's altered. With a higher required reserve ratio, banks have less capacity to use their existing reserves for lending purposes, effectively tightening the money supply.