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Or as Tobin (1992) put it: "How Can Money Have Positive Value in Exchange?"

Money, however, is an embarrassment to value theory. According to standard theory, something can have positive value only if it generates positive marginal utility in individuals’ consumption or positive marginal productivity in the making of goods and services that do generate marginal utility. The embarrassing puzzle is sharpest for fiat money. All of its value comes from the fiat that makes it money. Fiat money has no intrinsic non-monetary source of value. It cannot be eaten or worn or be used in any other way that generates utility for consumers, except a few numismatists. Nor can it contribute to the production of things that consumers do value. It can be produced at zero social cost. Yet it is a scarce commodity for any individual agent. Why is it worth anything at all? That the institution of money is of value to the society as a whole as a public good does not automatically give it value to individuals in market exchanges.

Is there today any consensus answer to the above question?

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  • $\begingroup$ Look up Sunspot Equilibria. That should be helpful. $\endgroup$ – user28372 Aug 1 '20 at 3:42
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The answer, that can be found in greater detail in the following book

is quite simple. One has to create a positive marginal utility to the user. How one can achieve this aim? One has to create a positive demand for fiat money, which can be accomplished that taxes can only be paid with fiat money. Then it has a positive marginal utility, and the trick is done.

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  • $\begingroup$ You really think US$ would be worthless if the US didn't have taxes? $\endgroup$ – user253751 Jul 27 '20 at 19:28
  • $\begingroup$ @user253751 The situation with the US dollar is different. It has been covered by gold over decades, until the Nixon administration has abandoned the Bretton Woods systems. Hence, the dollar is by its origin not a fiat money. The situation is different for the introduction of the Chinese silver standard by the Ming dynasty (not to confuse with the Chinese silver yuan). Before that time the unit of account was based on rice, even taxes must be paid in rice. Then the Ming dynasty changed to the silver standard while requiring that taxes can be paid with silver coins. $\endgroup$ – Holger I. Meinhardt Jul 28 '20 at 6:59
  • $\begingroup$ Okay then. You really think the pound would be worthless if the UK didn't have taxes? $\endgroup$ – user253751 Jul 28 '20 at 9:51
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    $\begingroup$ @user253751 Currencies can hobble along without a government in places like war zones, but there’s also not a lot of alternatives. But in any developed country, do you think the currency would have much value for very long if the government stopped collecting taxes? In most cases, the fiscal deficit would run around 20% of GDP. $\endgroup$ – Brian Romanchuk Jul 28 '20 at 10:08
  • $\begingroup$ @user253751 The point with taxes is not crucial. The crucial part is of how one can create demand to an item that has per se no intrinsic value. And here taxes are a mean of achieving this goal for governments. Hence, it is about to impose a positive or negative marginal utility to create or destroy a market. If a market has been established for the pound and people find it useful for exchanging goods with it then they will have a positive marginal utility for it even all taxes have been abandoned later on. The pound becomes worthless when it has no utility for the consumers. $\endgroup$ – Holger I. Meinhardt Jul 28 '20 at 10:58
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I agree with Holger’s answer that taxes drive the value of a fiat currency, but there are some qualifications.

  • I think it is better to think of this as the question of the determination of the price level - why is at one level, and not multiplied by a factor of 10 or 100? Currency redenominations demonstrate that the price level is arbitrary. However, even a dead hyperinflated currency notes can have exchange value as a souvenir, so the value may not be zero.
  • We need to interpret “taxes” broadly. A country with large oil reserves could use oil exports to keep its currency value stable versus foreign ones, and this will then imply something about the domestic value.
  • Entities in an economy are embedded in a system of nominal contracts. These help lock the value of the currency for a period of time. But as hyperinflations demonstrate, this stickiness can disappear.
  • If we discuss the historical path, the developed countries’ currencies evolved out of pegged systems. However, saying that a country was pegged to gold decades ago does not tell us much about the current price level.
  • Some currencies can survive without a government, but that is typically in the case of war zones or similar.
  • I am discussing national currencies. Private currencies like Bitcoin exist, but they are of limited importance in commerce in the developed countries.

Returning to the question: is there a consensus? In a sense, yes. Take any developed country with an unpegged fiat currency, and then imagine the government setting taxes to zero. In most cases, that would imply a fiscal deficit of 20% of GDP or more. Very few economists would argue that this would not be highly inflationary. Beyond that, since there is disagreement about the inflation process, the details are disputed.

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Tobin appears wrong that "Fiat money has no intrinsic non-monetary source of value." See ELI5: What actually makes makes currency worth anything? : explainlikeimfive

One reason why fiat money has value, is that the government insists that people pay taxes, and the only payment of taxes they will accept is in their own currency. So, everyone has to earn or acquire enough in that currency to pay their taxes.

This r/explainlikeimfive comment by theelectricmayor answers your question. I edited punctuation and grammar.

Let's examine the idea that gold-backed money has value because gold has value. Does gold really have value?

Imagine you had a million dollars in gold coins, then all world governments and organizations vanished overnight. In this new Mad Max world, do you think you could walk over to your neighbor and buy some of his food with gold? After all what use is gold to him? He can't eat it, it won't protect him from the rain and it won't scare off wild dogs. It's just shiny metal that's too soft to be made into tools and frankly too heavy to lug around.

The reason a gold coin had value in the past was that, somewhere in every province was some powerful lord who had more food then he could ever eat, a big castle over his head and many guards with swords who knew how to deal with wild dogs. And with all of his needs well met, this lord could afford to trade some of his excess food or wood or swords for a pretty piece of metal to decorate his head with. So people used those gold coins in trade, because they knew that they could cash them out into something of true value (by trading with the lord of the castle), if they couldn't find someone that would accept them as a currency.

Of course, once more than a certain amount of gold coins circulates, gold coins in effect become a fiat currency, because the lord can only trade for so much gold before he run out of goods and there are only so many neighboring lords to try. So while this 'backing' of the gold currency existed it wasn't that robust. It would not survive a 'run on the bank' where everyone tried to cash out their gold coins at once.

Now let's imagine a different kingdom. This kingdom has fertile land and is protected from invaders because of the king's wise policies. Thus many farmers flock there to enjoy its bounty. However, in return for the use of the land, the king demands a yearly payment that can only be made using pieces of paper with the king's face stamped on them. The paper is worthless by itself, but because the chance to farm in this kingdom has value and you can't farm there without some of those papers, the papers gain value. People are willing to trade goods in exchange for these papers because then they can then can take a share of those fertile lands for a year. Indeed they now use the papers among themselves as a unit of value and even ask for it from outsiders — Those who wish to buy goods from those in the fertile kingdom now must obtain the paper its citizens value, which only makes the paper more valuable.

What I've just described is most fiat currencies. The USD (US Dollar) has a base value because taxes must be paid with it, and people are willing to pay those taxes because being a business in the US is more productive than being a business in a country like Somalia. In turn, US businesses deal in USD, so the value of US goods acts as an incentive to increase the value of the USD — if you want an American truck, you'll need to get USD. A neat example of this is OPEC who decided long ago that their oil would be indexed in USD. So the value of oil contributes to the USD's value, and since everyone wants oil, the value of oil provides a strong leg to 'prop up' the USD's value even if the US economy is doing poorly. This is why it is a financial concern when OPEC talks about switching to the Euro — it means the USD would be losing one of its pillars of value while the Euro would gain one.

So what's the value or promise of a fiat currency? Access to the economy of the country that issued it, as well as any satellites of that dollar economy.

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The value of fiat currencies may be derived from these facts:

  1. When a central bank issues new notes, they do not just dump it into the economy. To get the newly created cash into the economy, central banks buy already existing assets. In non-fiat systems, the central bank can only buy gold (therefore the currency is backed by gold). With non-fiat currencies they can buy whatever type of asset they deem appropriate, usually treasury bonds or foreign currencies. Therefore, non-fiat currencies are usually "backed" by bonds and other currencies.

  2. As some have pointed out, any currency always has some intrinsic value just because you will need it to pay your taxes. And if you refuse to pay them, you may end up in prison. But this is just a catalyst for people to start using a currency in a given economy. Many currencies have collapsed due to hyper-inflation (rapid loss of value of a currency) even while requiring high payments in taxes.

  3. A bigger reason why people may want to get money (giving it greater value) is because debt for individuals and corporations needs to be issued in a specific currency. And thus, it needs to be repaid in such currency. This also happens with many other contracts (lease agreements, rentals, employment contracts). This types of contracts create a specific liability for us that needs to be paid in a specific currency. Since almost all participants in an economy are tied to debt repayments or contracts with clear liabilities, almost everyone will be in search of money. Thus, increasing its value.

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Fiat money's value is not sustained on the president's figure or in a bank. The value of money comes from a common social agreement you and me participate of.

The money you have in paper or in the bank represents the debt we --the society-- have towards you. And we, as a society, agree in a symbol, which can be represented as a number on a computer server (the amount you see in your bank account when you check it on the internet), or a number printed in special paper.

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