economics: how does more money get put into circulation?

According to the US Federal Reserve, there is about $1.4T in circulation these days. Presumably the amount in circulation was much less than this back in 1792, when the US Mint first started minting currrency.

It seems that every currency transaction must be a zero-sum exchange: the “+” in my ledger must always equal the “-” in your ledger, and vice versa. That being the case, how does the amount of cash in circulation ever get increased?

Well, if you’re talking about physical currency–the US Mint prints money. Some of that is to replace bills that get removed from circulation because when they get to the bank they’re considered too worn and damaged to continue on. But if somebody (the Federal Reserve) approves increasing the amount in circulation, then newly printed notes are used to pay out a tiny fraction of government expenses… I think.

When the Federal Reserve wants to expand the money supply, it creates more dollars and then buys things with them. In the past, the Federal Reserve would typically buy US Treasuries, but currently they also have quite a bit of mortgage-backed securities on their balance sheet as well. Conversely, when the Federal Reserve wants to shrink the money supply, is sells assets it owns and destroys the dollars it receives from the sales.

Does this mean that the Federal Reserve’s expenditures exceed its budget (in years during which it seeks to expand the money supply)?

The Federal Reserve has a budget, but not in the way a household does. It can have no fixed number as an outside target. It does not run into debt when it changes the money supply in either direction. Its assets exceed liabilities, though. Better to think of it as a force outside the system, like the sun, whose output affects temperatures on the earth.
The actual budget and net worth of the Fed can be found on Wikipedia.

There is the well known multiplier effect when a bank loan is made. When you have a bank account that money is still counted as a “+” in my ledger, but when the bank takes that money (combined with other people’s) and makes a loan to some dude and that dude buys a house with that money, that money is accounted as “+” on the ledger of the guy that dude bought the house from, too.

Creating new dollars and buying securities (Open Market Operations) to expand the money supply are not considered a budget items; they are asset swaps. On its balance sheet, the Federal Reserve will list the estimated value of purchased securities as assets, and it will list the dollars used in the purchase (which were created and are now floating in the general money supply) as liabilities. But it doesn’t consider these action to be true expenditures. They aren’t using their income to buy these securities; they’re creating brand new money to buy them.

Of course, the Federal Reserve has income and expenditures like any other bank. It pays employees, has facilities, runs equipment, etc… These expenditures are paid using the interest income it receives from its assets, and with any capital gains income from Open Market Operations.

For physical currency, the short answer is that the Treasury prints/mints it, and then sells it to banks. They have printed/minted more than they’ve bought back and destroyed (including the relatively small amount otherwise destroyed) since 1792, so there’s more physical currency in circulation.

But, there’s a big difference between ‘physical currency’ and ‘money supply’. Pretty obviously, since the banks aren’t buying physical currency with other physical currency. And I’m willing to bet the amount of money you spend in a month is vastly larger than the amount of physical currency you handle. https://en.wikipedia.org/wiki/Money_supply is a start.

The money supply mostly increases through fractional reserve banking (banks loan out part of their deposits, which increases the money supply).

Answers have been accurate but let’s add some spice to make it easier to understand and more memorable.

The Federal Reserve has an accounting computer.

The core equation of accounting is: ASSETS - LIABILITIES = EQUITY. In other words, the value of what you own minus what you owe to other people equals your networth.

Now here’s where the magic happens. The Congress has declared that the liabilities of the Fed are the currency of the realm. Anybody can write a liability. I can write an IOU that says “I owe you one trillion dollars”. I’ve done this before. I wrote it and signed it and put it in my pocket to feel all special. But for real business operations, the trick is getting other people to accept your debt in exchange for other stuff that’s valuable. The Fed doesn’t have this problem because the Fed is part of the government.

When the Fed wants to issue money, they hand out IOUs. Because the Fed is a central bank, this is done through the banking system itself. The Fed can say to the banks “Hey banks, I want to buy one trillion dollars worth of assets from you.” And the banks will say, “Yeah okay, sounds cool.” So the Fed gobbles up the trillion dollars of assets and issues to the banks a trillion dollars of IOUs on its accounting computer.

ASSETS: 1 trillion
LIABILITIES: 1 trillion (computer)

Those liabilities are called United States dollars.

We’re ignoring all the other stuff that’s on the balance sheet at present just to focus on this transaction to make it simpler. Just this one transaction. And you can see, it’s just double-entry accounting. The Fed has purchased more assets which is must record, and simultaneously it has created more liabilities to give to banks in order to pay for those assets. Pretty simple. That is the first step of the process. This operation increased the monetary base of the US.

Right now that new money is still on the computer. Banks can have accounts at the Fed but private people like me and you do not. You’re asking about currency in circulation, and we are almost there. Those “liabilities” on the computer are basically the same stuff as green cash, as far as the Fed’s books are concerned. What this means is that those computer entries will be turned into green cash whenever the banks ask for it. It’s already green cash, it’s just being stored on computer instead of in a vault. So the banks just have to contact the relevant person and say hey, I’d rather have the actual physical green instead of the computer green. And the Fed is all like, no problemo. Other parts of the government are contacted in order to print up the cash, and that’s it.

ASSETS: 1 trillion
LIABILITIES: 0.5 trillion (computer), 0.5 trillion (printed cash)

The cash gets delivered in armored cars to the bank, where it’s placed in the local vault. And then customers of the banks like you and me make withdrawals when they want cash money. That’s how the physical cash leaves the banking system and enters the wider world. The 1.4 trillion dollars in circulation cited in the OP the stuff outside the banking system. It is still listed as a “liability” of the Federal Reserve on the books, but of course, it does not work like any other liability in existence.