Does the value of an intrinsically worthless (paper) money depend on the government's power to tax? I am going to answer this question from a quantity-theory perspective. The short answer is "yes". But the full answer is different from some other theories that also answer "yes".
Those of you who already understand the modern quantity theory of money will find nothing new in Part 1 of this post. I'm just trying to explain the standard story as simply as possible, without any math or jargon (I have even carefully avoided using the words "real" and "nominal"). You may find Part 2 more interesting.
The quantity theory of money says that the value of money depends on the quantity of money. If you double the stock of money, other things equal, the value of money will halve (i.e. the price of goods in terms of money will double).
Most quantity theorists recognise that prices of most goods don't adjust to equilibrium instantly. So it may take time for a doubling of the quantity of money to double prices.
(Strictly, the quantity theory only works for something like a paper money that is useless except as money. Because the monetary units don't really matter. If you add a zero to every $1 bill, so it becomes a $10 bill, and add a zero to all the prices, so $1 becomes $10, etc., then nothing has really changed in the economy. If you were in equilibrium before the change, you are still in equilibrium after the change. So you increased the stock of money tenfold, and each unit of money is worth one tenth its original value, and the equilibrium price level has increased tenfold. If money were gold, and dentists could use it, things wouldn't be exactly the same if you doubled the stock of gold and doubled all prices. Because dentists would use more gold to fix people's teeth, and the cost of getting your teeth fixed wouldn't exactly double.)
But the quantity theory also says a lot more than that. The current stock of money (the money supply) is not the only thing that affects the value of money. The value of money also depends on the demand for that stock of money (money demand). The demand for money is like the demand for an inventory. Money flows into and out of our pockets, so the amount we hold fluctuates hour by hour, but we demand to hold a certain average stock of money, because it makes shopping easier.
A doubling of the supply of money, if demand is initially unchanged, means that people are holding more money than they want to. They will try to spend or lend the excess. But if the total supply of money stays the same, even though each individual can spend or lend his money and pass it onto someone else, it isn't possible for all people to do get rid of their money this way. But their attempts to get rid of it by spending or lending are what causes the demand for goods to rise, and the prices of goods to rise. And when the price of everything doubles and people's money incomes and expenditures double, they will want to hold exactly double the amount of money for shopping, So prices adjust to make the demand for money double to match the doubled supply.
And that demand for money will depend on many things, including the cost of holding money. Because demand curves slope down, and the higher the cost of holding money, the less money you want to hold. You might spend the same amount of money per year, and earn the same money income per year, but you want your inventory of money to turn over more quickly, so you want hold a smaller stock of money on average. And the cost of holding money depends on how quickly that money is losing its value. (It depends on the expected rate of inflation, in other words).
And, just as the level of prices depends on the level of the stock of money, so the rate of change of prices over time will depend on the rate of change of the stock of money over time. The faster the stock of money is growing over time, other things equal, the higher will be the rate of inflation. So, the value of money today depends not just on the quantity of money today, but also on how quickly that quantity of money is growing over time.
Take two otherwise identical economies, with the exact same stock of money today, but the first economy has a growing stock of money and the second economy has a constant stock of money. The first economy will have a higher price level today, even though it has the same quantity of money today.
When governments spend money they must either get that money from taxes, or else borrow it, or else print it and increase the stock of money in circulation. Taxes reduce the stock of money in our pockets. For a given amount of government spending, and a given amount of government borrowing, the higher are taxes the smaller will be the amount of money printed and the slower will be the growth rate of the stock of money. And the slower the stock of money is growing over time, the higher will be the value of money today.
Take two otherwise identical economies, with the same quantity of money today, and with governments spending the same percentage of national income and neither country borrowing. But the first economy has taxes as a lower percentage of national income than the second. The first economy will have a higher price level than the second economy, even though they are otherwise identical, and have the same quantity of money today. Holding government spending and borrowing constant, higher taxes increase the value of money, because they reduce the growth rate of the money supply, reduce the rate of inflation, reduce the cost of holding money, increase the demand to hold money, and so increase the value of money.
There's a second way that taxes may affect the value of money, that is associated more with a Keynesian approach, but can nevertheless be incorporated into the quantity theory of money.
For a given level of government spending, and a given growth rate in the money supply, a reduction in taxes means the government has to borrow more. It has to issue more bonds. That increase in government borrowing may increase the equilibrium rate of interest on government bonds. If money pays no interest, but bonds do, then the foregone interest on bonds is the opportunity cost of holding money rather than bonds. So a reduction in taxes will cause an increase in the opportunity cost of holding money, reduce the demand for money, and so reduce the value of money.
Take two identical economies, with the same stock of money, and the same growth rate of money, and the same government spending as a percentage of income. If the first has lower taxes as a percentage of income than the second, the first will have a higher price level.
But this still leaves a puzzle. Paper money is only useful for shopping if it has value. If it has value, people will find it useful for shopping, and so there will be a demand to hold an inventory of money for shopping, and that demand (and supply) will determine its value. But if it didn't have any value at all, it wouldn't be useful for shopping, so there will be no demand for it, and so it won't have value.
There are two equilibria. In one equilibrium people leave the worthless bits of paper lying on the ground. In the second equilibrium people use those same bits of paper for shopping and they are valuable. Why are we in the second equilibrium, rather than the first?
Or, if there are red bits of paper and green bits of paper, what determines whether people will use the red, or the green, as money?
One possible answer to this puzzle is that the government requires people to pay the government 10 bits of green paper per year, as taxes. Does this answer work? Maybe, it depends.
If the government is spending 10 bits of green paper per person per year to buy goods, and collecting 10 bits of green paper per person per year in taxes, that means the government is using that green paper to do its shopping. But that does not eliminate the equilibrium in which green bits of paper are worthless. The government spends 10 bits of paper at the beginning of each year, gets nothing in return because the paper is worthless, and then at the end of the year people simply give the green bits of paper back to the government.
Hell, even I could do that. "Here are 10 bits of green paper per person. Unless I get all 10 back at the end of the year I will beat you up. How much will you give me for them?". "Nothing" is one possible answer, even if my threat is credible.
Let's try Plan B. "Here are 9 bits of green paper per person. Unless I get 10 back at the end of the year I will beat you up. How much will you give me for them?"
Plan B works. I have created an excess demand for the bits of green paper. 10% of the population will get beaten up, whatever happens. But each individual can avoid a beating by outbidding others for those bits of paper. The value of each bit of paper will be one tenth of the value of avoiding a beating for the person at the tenth percentile of the distribution of willingness to pay to avoid a beating.
And once the green bits of paper have value, people might also use them to do their own shopping, if they are more convenient to use than other media of exchange.
But Plan B only works because the government is trying to reduce the stock of money in circulation, by trying to collect more in taxes than it spends. Governments don't usually do this. When governments issue money, they normally do so because they want to spend more than they collect in taxes.
And Plan B only works because the intrinsically worthless paper money is now no longer intrinsically worthless. It is a convertible currency, at the margin. 10 bits are convertible into one avoided beating, and an avoided beating is a valuable good.
Plan B is therefore just a specific example where the puzzle is solved by supposing than an intrinsically worthless paper currency was initially, when first introduced, convertible into something intrinsically valuable. And it doesn't have to be the government that issues the money, or makes it convertible. And though people are likely to choose to use the same money that the government uses, it's also true that governments are likely to choose to use the same money their people use. The government is a big shopper, and one that has more powers than most. But the money people use isn't always the one issued by their own government, and in which they pay taxes.
Suppose that paper money is initially convertible into gold, or some other good that has at least some positive value independent of its use as a medium of exchange. Then people get used to using paper money as money. Even if convertibility is eventually suspended, and so the equilibrium where paper money is worthless becomes one possibility, people will continue in the second equilibrium, where the paper is valuable, simply because that's the equilibrium they are already in. It's a network effect, like speaking a particular language, or using a particular word processing program. I use Canadian dollars for shopping because everybody I shop with uses them too. And because we use them, they are valuable. And because they are valuable, we use them.
Plan B made me think of this: