[A post for Alex Douglas.]
Here are two closely related questions, about Chartalism and the relation between stocks and flows of money.
1. How can intrinsically worthless bits of paper be a valuable asset that gets used as a medium of exchange?
One answer is that the government forces us to pay taxes with those intrinsically worthless bits of paper, which creates a demand for those intrinsically worthless bits of paper.
There's a problem with that answer. Taxes are a flow; they have the units $/time. Taxes create a flow demand for intrinsically worthless bits of paper. But there is a stock of intrinsically worthless bits of paper; and that stock has the units $. And if that stock of paper is strictly positive and increasing over time, as it usually does, that means the flow supply of new paper created must exceed the flow demand for paper to pay taxes. So if flow supply exceeds flow demand, why doesn't the market price of those intrinsically worthless bits of paper fall to zero?
If intrinsically worthless bits of paper paid interest, or appreciated over time, and so gave the same rate of return as other assets, there would be a stock demand for those intrinsically worthless bits of paper. Matching that stock demand to the stock supply could give us a positive equilibrium price, just like any asset, even if the stock was increasing over time. But paper currency usually does not pay interest, and usually depreciates over time. Indeed the Bank of Canada, which issues the intrinsically worthless bit of paper (OK, plastic) in my pocket, promises it will do its best to ensure they depreciate over time at 2% per year. And sometimes currency is expected to depreciate much more quickly than that, and yet people still want to hold it at some positive price. So why do I have a stock demand for that paper? Why don't I hold my wealth in some other asset instead, then pick up some of those worthless bits of paper off the growing pile littering the streets just before the government stupidly insists I must give it some?
Suppose we did have a theory of the stock demand for money. For example we could say that monetary exchange is more convenient than barter exchange, and that it is very inconvenient to spend money immediately after it enters our pockets, so we want to hold a stock of money temporarily despite it paying no interest and depreciating in value. The convenience yield of a stock of medium of exchange offsets the loss of interest and depreciation. Putting that stock demand for money against a limited stock supply of money there will be an equilibrium in which money has a positive value. (And yes, there may be a second equilibrium in which it has zero value and so cannot be used as a medium of exchange and so has no stock demand; and we are still waiting to see if Bitcoin for example stays in the first or collapses to the second equilibrium.)
If the government forces us to pay taxes in labour (like a military draft) we won't use labour as a medium of exchange. Labour doesn't work very well for that purpose. But if we have a stock demand for bits of paper to use as a medium of exchange, and if the stock supply were limited, those bits of paper could have positive market value even if we paid all our taxes in labour.
The flow demand for money to pay taxes is neither necessary nor sufficient to explain why a stock of intrinsically worthless bits of paper have positive value. Nor why they are used as medium of exchange.
Now it is true that the government is very influential in deciding what good will be used as money. Because each of us wants to use the same medium of exchange as the people we trade with. If everyone I trade with wants to be paid in those intrinsically worthless bits of paper, I will use that paper to buy food and clothes as well as to pay taxes. There's a strategic complementarity in what we choose to use as money. And governments are big players in the money game. So if the government uses something as money, there's a good chance the rest of us will all follow its lead. Just like when the government switches to Daylight Saving Time most of us just follow along. But it doesn't always work. The Cuban government tried to ban the use of US dollars, but failed.
2. What is the relation between the flow of monetary expenditures and the stock of money?
Purely as a matter of accounting identity, we can define Velocity of circulation as the ratio between the flow of monetary expenditures and the stock of money. Velocity has the units (1/time). Velocity reconciles flows of monetary expenditures ($/time) and stocks of money ($).
But velocity is not just an accounting relationship between flows and stocks. I can choose the velocity of circulation of the money I hold. I can choose to spend it very quickly after I receive it, or I can choose to spend it very slowly. So can every other individual. So any theory which has a stock of money and a flow of monetary expenditures must implicitly also be a theory of individual choice of velocity. Does that implicit theory of individual choice make sense?
Suppose for example you have a theory which says that government expenditure creates money and taxes destroy money. So that a government deficit means that the stock of money is growing over time and a surplus means the stock of money is shrinking over time. Also suppose that same theory says that there is a relationship between the level of government deficit and the level of monetary expenditures. But that means that a government deficit that is constant over time means the stock of money is growing over time relative to the level of the flow of monetary expenditures. And purely as a matter of accounting identity that means velocity must be falling over time, towards zero. And a budget surplus must mean velocity is rising over time, without limit.
Why would individuals choose to have velocity falling over time towards zero or rising over time without limit? Do those choices make sense?
The simple textbook's ISLM model has a clear and simple answer to those questions. It says that velocity is a positive function of the opportunity cost of holding money, so if money always pays 0% interest, a rise in the rate of interest on other assets will cause velocity to increase. You might not agree with that answer, but it is an answer.