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.
Part 1.
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.
Part 2.
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:
Worthwhile Canadian Initiative 
rogue:
An increase in the demand for money is like a decrease in the supply of money. Both cause an excess demand for money (people want to hold more money than they have), and that causes recession and deflation. That was what was happening in my response to your question.
Thanks Nick. I’ll have a look at what Mike Sproul has written on the backing theory, and if I have an explanation that is not old hat, I’ll put it on my blog.
Nick, it’s true it’s all the same whether it’s an increase in the demand for money or a decrease in the supply of money, they’re both inflation. But the result could still mean a decrease in velocity. The resulting high prices could just be that the increasingly few transactions are clearing at the ever increasing price. If the money stock keeps increasing, this supports an increasing price level even though the velocity and the volumes may already be decreasing.
“You could correctly say that the unemployed are trying to “buy” money. But, and this is important, because it is why money is different, that does not mean the unemployed want to hold more money. They don’t want to hold money. They want to buy money, then immediately sell it again, to buy food, clothes, furniture, etc.”
Or you could correctly say that the unemployed DO want to hold money but they dont have enough of it to hold it because they need all of what they get just to stay alive.
Gizzard: Yes, but the important question is this: if others did sell their money, by buying the unemployed’s labour, would the unemployed hold that money or spend it? OK, it’s probably some of each. I think they would mostly spend it, which means they are buying the labour of other unemployed. So the process doesn’t stop at the first round, it continues, through a “monetarist multiplier”.
Back to the original debate, more commentary from Dr. Wray, going a bit beyond taxes initiating the value of money-
“To go further, let us say government monopolizes the water supply (or energy supply, or access to the gods, etc); it can then name what you need to deliver to obtain water (energy, religious dispensation, etc). In that case, if it says you must obtain a government IOU, then you want government IOUs—currency—to obtain water in order to avoid death by dehydration. In early 19th century England, almost all activities necessary to keep your family alive were illegal by dictate of the crown. You had to pay a fine after you killed game to feed your family. You needed the crown’s currency to pay the fine—hence “fees drove money”. You get the picture.”
http://neweconomicperspectives.blogspot.com/2011/07/response-to-blog-8-more-on-taxes-drive.html
wh10: thanks for posting that.
But Dr Wray is assuming that the monopolist reduces the supply of water to 9 litres per year when the demand is 10 litres per year. OK, that will make water scarce, and valuable.
But that would mean that the government spends 9 bits of paper per year and taxes 10 bits of paper per year. So it has taxes higher than spending. This creates two issues:
1. If the government can have taxes higher than spending, why does it resort to paper money? It could do the same with gold, or whatever.
2. This means that the stock of paper money is falling over time. That is certainly not what has happened, historically. It has been growing over time. Governments spend 11 bits of paper, and tax 10.
(I may not be responding to comments for a few days).
wh10: if you have the time, I would be grateful if you could suggest this response to Randall Wray. If it does indeed apply to his argument. I tried to read his posts quickly, but I need to go to bed, so can’t read it properly. And I may not be on the internet for a few days.
“It’s weird. We want the people to fear inflation but we don’t want the policymakers to fear inflation.”
Most average joes spend every penny of the money they hold, do you really need them to fear inflation?
Perhaps you meant you want the ‘people’ that hold money to fear inflation? These same ‘people’ seem seem to have much sway over whether policy makers fear inflation. Maybe call them savers instead of people?
Why force savers to spend if they don’t want to? Is there some economic justification, besides making your economic theory work?
MMT allows for people to save and not need to spend by providing unlimited NFA. It seems your biggest fear is that savers might build up large savings and then actually start to spend uncontrollably.
Anyway it might help the national debate if both savers and people acknowledge the fear is hyperinflation, not running out of NFAs or bumping into a debt limit.
“But Dr Wray is assuming that the monopolist reduces the supply of water to 9 litres per year when the demand is 10 litres per year. OK, that will make water scarce, and valuable”
Why only 9? Might someone not want to save an extra liter, so that water still has value ever if 10 were made available? Might another household be created each accounting period requiring another liter to be added to supply?
Will do!
Nick
Thanks for the detailed response.
Yes money is wierd. Most people think of it like a commodity but its not. It simply prices commodities and has some value as a useful fiction.
In your story are bond holders people, whom you want to fear inflation or are they govt whom you dont want to fear inflation? If bond holders fear inflation they will, according to all your monetarist models, make things worse by demanding higher interest rates raising “borrowing” costs ( I dont buy the idea that our govt borrows money but Ill use that term just for those of you who do). If they dont fear inflation and keep purchasing low interest debt ad infinitum then……… MMT is correct it seems.
“But money is not like land, or bonds. Money is really weird. At least at times like now, when there’s lots of output and labour that firms and unemployed workers want to sell but can’t, because they can’t find buyers.”
Agreed, but I would add they cant find buyers in the private sector. They COULD find it in the public sector if we didnt have this unwarranted aversion to govt employment as a bridge to private sector employment.
Treating money like its a zero sum game is a large part of our problem I think.
Sorry I’m late to the party Nick:
How about plan c: government gives the money to the banks. The banks loan out the money, 10 bits of green paper, and demand back 11 bits of green paper. Not only will this create an excess of demand, but it will allow government to spend more than it issues, as long as the excess of demand is maintained. And the banks are the ones that come beat up the ones short of their green bits of paper. As you point out, there always will be some peple short of the green bits of paper.
Check out: http://anamecon.blogspot.com/2010/11/banks-are-forcing-debt-on-rest-of-us.html
Gizzard. In any Keynesian model, for example, an increase in expected inflation may (depending on the central bank response) increase nominal interest rates, but will lower real interest rates (unless the economy is at full employment). An increase in expected inflation will increase AD, output and employment. Same in monetarist models, if we are in a short run recession. Hard to explain this fully, without diagrams, etc. But you really MUST distinguish real vs nominal interest rates. MMTers need to be clear on this. “Bond holders” are people.
Greg: but that’s not a tax, which is involuntary. Suppose I said: “here are 10 bits of paper. If you take them, and don’t give me back 11 next year, I will beat you up. If you don’t take them, I will not beat you up, even if you don’t give me back any.” Nobody will take my offer. Unless of course the bits of paper already have value.
Nick
When you use the term real interest rate you are referring to a natural rate of interest no? I understand that its not universally accepted that there IS a natural rate of interest.
If you are talking about the nominal rate minus the inflation rate, the inflation rate is in essence a nominal variable itself that is quite divergent in how it can be determined.. is it not. I understand that there is some agreement to the measurement of inflation but even inflation is a nominal variable is it not? In fact, inflation must be nominal because inflation is only measured in the same units as money.
I don’t believe in “and the a miracle occurs” science. Inflation is like price controls, it systematically misleads people about price relation — it does so because the growth of money MUST take place a particular places in the economy, but no one can know everything about this, or all or the effects on relative prices and quantities (particularly productionand use of time consuming production goods).
To ubderstand causation, stop thinking in terms of magic.
Nick writes,
“Greg: In a steady, fully-anticipated, inflation.”
There is No Such Thing. Inflation by definition is Not fully anticipated, or perfectly steady in it effects.
It begs the question to assert “a steady state” my counter-example assumes isn’t possible or actual.
Assume magic and “a miracle occurs” only reveals the scientific poverty of the “case” against my point and causal example.
Make that:
“I don’t believe in “and then a miracle occurs” science.
Nick,
While I not entirely convinced by Mike Sproul’s defence of the real bills doctrine on his website, it does highlight the need to explain the “hot potato” effect of money rigorously. Do you (or any other reader) know if this has been done please?
Nick said:
“Greg: but that’s not a tax, which is involuntary. Suppose I said: “here are 10 bits of paper. If you take them, and don’t give me back 11 next year, I will beat you up. If you don’t take them, I will not beat you up, even if you don’t give me back any.” Nobody will take my offer. Unless of course the bits of paper already have value.”
The bank can say: “I will give them value. I will make sure you will be able to buy- a used car from my friend the used car dealer, who will be able to take the bits of paper and buy from my friend the farmer, who will pay you for your labor in these bits of paper which you will work for because to you they now have value… Im not sure how token economies started, way back when, but I doubt the first medium of exchange was gold. How did cowrie shells take on value? It wasn’t because of taxes.
“a steady, fully anticipated inflation” … isn’t inflaftion and isn’t a phenomena of the real world.
If your “model” stipulates “a steady, fully anticipated inflation” you model isn’t allowing us to even think of inflation much less understand it or model its causal effects.
In a gold money system, the growth of the gold supply out of mines in the new world changes all relative price relations and changes the time structure of production at particular places in the economy, and also changes consumption and production decisions by different people.
In different sorts of banking / money regimes similar effects take place, depending on were new money enters the economy, where it didn’t before, and depending on how it interconnects with credit and leverage elements.