How can the Fed affect the money supply by using the discount rate?
The Federal Reserve (the Fed) can affect the money supply by using the discount rate because it will affect the amount of lending that goes on in the economy.
The discount rate is the interest rate that the Fed charges banks that want to borrow money from it. The interest rate that the Fed charges then affects the interest rates that banks themselves charge. The interest rate that banks charge is, in essence, the price that people and firms must pay to borrow money from the banks.
Basic economic laws tell us that when the price of something goes down, people will buy more of that thing. In this case, when the price of borrowing money drops, people will borrow more of it. When people borrow more money, the supply of money increases. That is because every time people borrow money, they in essence make more of it. If there is $1,000 in a bank and I borrow that $1,000, the money supply has increased by $1,000. The original $1,000 is still in the bank and whoever it belonged to can still come and get it. At the same time, I have $1,000 that did not previously exist. This means that the bank and I created $1,000 in new money when I borrowed money from them.
Thus, if the Fed decreases the interest rate, it increases the supply of money. If it increases the discount rate, it raises the price of borrowing and the money supply drops.
Adjusting the discount rate is one of the primary tools by which the Fed can control the money supply. The Federal Reserve itself defines the discount rate as "the interest rate charged to commercial banks and other depository institutions on loans they receive from their regional Federal Reserve Bank's lending facility." Banks have to borrow from time to time from the Federal Reserve to keep their cash reserve at levels mandated by the Fed itself. So by raising the discount rate, the Fed makes borrowing money for banks more expensive. This, in turn, incentivizes banks to keep their cash reserves high, which they can in turn do by raising interest rates, both on loans to consumers and on savings accounts (this incentivizes people to deposit their money in savings accounts, which gives banks more money in reserve). So by raising or lowering the discount rate, the Fed can basically force banks to keep more money in reserve, which lowers the amount of money in circulation—the money supply. It can do the opposite by lowering the discount rate. There are other tools the Fed can use to implement monetary policy, but the discount rate is, for the reasons we see here, perhaps the most powerful one.