What makes our chequable demand deposits at banks media of exchange? The answer is: the clearing house, where circles of offsetting IOUs are cancelled out.
It is clearing houses that create money. Unless there is only one bank, where everybody banks, because it doesn't need a clearing house.
Nothing revolutionary here (except maybe a little bit right at the end). This is just me trying to get my head straight on something, following a discussion with JKH in the comments.
1. Amanda cuts Betty's hair for $20. Betty manicures Cathy's nails for $20. Cathy massages Amanda's back for $20. They pay for each other's services with currency. That currency is their medium of exchange. It flows around the Wicksellian triangle in the opposite direction to the flow of services. $60 in total transactions with currency.
2. Suppose Betty is temporarily short of currency, and gives Amanda an IOU for $20 in exchange for the haircut. And then pays off (buys back) her IOU a couple of days later for $20 in currency (maybe plus interest). I say that Betty's IOU is not a medium of exchange. Betty has merely postponed payment. Betty still needed to pay Amanda $20 in currency. Being able to buy on credit may reduce Betty's demand for medium of exchange, but it is not itself a medium of exchange. $60 in total transactions with currency.
3. Suppose Betty is temporarily short of currency, and gives Amanda an IOU for $20 in exchange for the haircut. Suppose Amanda gives Betty's IOU to Cathy in exchange for a manicure. And suppose Cathy gives Betty's IOU to Betty in exchange for a manicure. Betty then tears up her IOU to herself. They didn't need any currency at all. Betty's IOU was used as a medium of exchange. Betty is like a central bank, because everyone accepts her IOUs. $0 transactions in currency.
4. Suppose all three women are temporarily short of currency, and all three give their IOUs in exchange for services. And all three repay those IOUs with currency a couple of days later. There were still three transactions of $20 for currency. Again, I say that those IOUs are not media of exchange. $60 in total transactions with currency.
5. Suppose all three women are temporarily short of currency, and all three give their IOUs in exchange for services. After a couple of days, all three women meet together, in a place called a "clearing house". They add up each woman's debits and credits. Each has a credit of $20 and a debit of $20. They agree to cancel out the circle of offsetting debits and credits. They tear up the IOUs. They didn't need any currency at all. I say their IOUs are now media of exchange. $0 transactions in currency.
In that 5th case, what makes their IOUs media of exchange is the clearing house.
Now suppose that each of the three women starts a financial intermediary. She both borrows and lends. She sells her own IOU for $20 (she borrows $20), and uses that $20 to buy someone else's IOU (she lends $20).
Are their IOUs media of exchange? Are their financial intermediaries banks, that create money? That depends.
6. (same as 3). Suppose Bill uses Betty's IOU to buy carrots from Chris, who uses it to buy apples from Andy, who uses it to buy bananas from Bill. Then Betty's IOU is a medium of exchange. Nobody needed to use any currency at all. Betty runs a bank. All three men bank with Betty. $0 transactions in currency.
7. Suppose Bill uses Betty's IOU to buy carrots from Chris. Chris uses Cathy's IOU to buy apples from Adam. And Adam uses Amanda's IOU to buy bananas from Bill. But the boys don't like holding IOUs from girls with the wrong first letter in their names. Each boy banks with his own girl. Adam goes to Amanda and swaps Cathy's IOU for another one of Amanda's IOUs. Bill goes to Betty and swaps Amanda's IOU for another one of Betty's IOUs. Chris goes to Cathy and swaps Betty's IOU for another one of Cathy's IOUs. What happens next?
7a. (same as 2.) If the three women don't have a clearing house, Amanda gives Betty $20 to repay her IOU, Betty gives Cathy $20 to repay her IOU, and Cathy gives Amanda $20 to repay her IOU. You get as many currency transactions as if the three guys had used currency in the first place. The women's IOUs are not media of exchange. $60 in total transactions with currency.
7b. (same as 5.) The three women meet after a couple of days and cancel their IOUs in the clearing house. Nobody needed any currency at all. Their IOUs are media of exchange. The three women's financial intermediaries are banks. They create money. $0 transactions in currency.
But notice something that I fudged. The three women meet every "couple of days" and cancel out circles of offsetting IOUs in the clearing house. It matters a lot how frequently the clearing house meets.
Assume a stationary economy, but where the timing of discrete transactions is random. In one limit, as the clearing house meets less and less frequently, the percentage of gross transactions that need to be settled with currency approaches 0%, because they all net out. (It wouldn't be stationary if it didn't). But in the other limit, as the clearing house meets continuously, the percentage of gross transactions that need to be settled with currency approaches 100%, because none of them net out.
The extent to which chequable demand deposits are media of exchange depends on the percentage of transactions that net out in the clearing house, which is a negative function of how frequently the clearing house meets. In the limit, with continuous clearing, only one transaction is settled at a time, and none net out. All have to be settled with currency (i.e. reserves). So chequable demand deposits are not media of exchange, in the limit. But the velocity of circulation of reserves increases towards some very large number, as you approach that limit.
I think that's right.