I don’t think this would be categorized under the common theories of market failure taught to undergraduates, but anybody who holds the following opinion thinks that the market produces sup-optimal outcomes. Writes Matthew Zeitlin (H/T Bob Murphy),

Goodhart points out, however, that Menger is just wrong about the actual history of physical money, especially metal coins. Goodhart writes that coins don’t follow Menger’s account at all. Normal people, after all, can’t judge the quality of hunks of metal the same way they can count cigarettes or shells. They can, however, count coins. Coins need to be minted, and governments are the ideal body to do so. Precious metals that become coins are, well, precious, and stores of them need to be protected from theft. Also, a private mint will always have the incentive to say its coins contain more high-value stuff than they actually do. Governments can last a long time and make multi-generational commitments to their currencies that your local blacksmith can’t.

The problem with this theory is that it doesn’t explain how governments know the weight of the coins they ought to mint. The demand for money, while forward looking, has to have some basis in the present (or near past), because it’s only by looking at prices that we can calculate the amount of money we’d like to hold. This is how I understand Mises’ regression theorem, which was an attempt to solidify Menger’s theory of the origins of money. Commodities such as gold were first traded as non-monetary goods, and as their exchange spread gold became more liquid and people began demanding it for this liquidity. But, as aforementioned, this demand had to find some basis in present prices, otherwise people have no idea how much money they ought to demand.

What this suggests is a degree of simultaneity between the formation of money prices and the emergence of said money. Government can mint currency, but it has to have some basis to calculate in what weights coins ought to be minted, which is dictated by the public’s demand for money. Thus, it makes more sense to assume that government could only begin to mint currency once demand for this currency already existed, meaning after the emergence of money. The chartalist theory looks at this exactly backwards, and for this reason I can’t make much sense of it (although it’s true that government’s demand for money, through taxation, adds to the liquidity of money and therefore has some role in explaining currency formation).

The whole misaligned incentives of private mints point is nonsense. All firms have an incentive to cheat their customers. What makes this unprofitable is competition, which is precisely why we’d want the market to provide currency. It’s the government that has the history of debasing its currency and driving better, private currencies off the market (by guaranteeing the same exchange value for bad currencies — this is the gist of a modern interpretation of Gresham’s Law). It also overlooks the fact that there are plenty of historical examples of the market providing methods of checking the quality of coins and currencies. For example, during the American free banking era newspapers would publish the values of different currencies daily. This is also one reason why money substitute tends to circulate more than commodity money.

This being said, I actually don’t find much fault (although one potential big one) in the following paragraph (although it’s ironic that the author mentions seigniorage, but doesn’t include this in his analysis of private minting),

But why oversee money creation in the first place? This brings us to the second theory of money, which Goodhart calls the “C View,” standing for “cartalist” (chartalist is a more common spelling). To simplify radically, it starts with the idea that states minted money to pay soldiers, and then made that money the only acceptable currency for paying taxes. With a standard currency, tax assessment and collection became easier, and the state could make a small profit from seiginorage.

Before the commodity currencies we’re all familiar with (e.g. gold, silver, et cetera), societies used all kinds of different commodities for money — cows, wheat, chickens, stones, et cetera. I don’t think it’s a stretch to argue that early governments paid salaries in commodities like gold and silver, adding to the liquidity of these goods. Then, subsequently, society in general began to demand these commodities for their liquidity, instead of market alternatives.

The major problem I see with this theory is that it seems somewhat inefficient for governments to collect taxes in a commodity that isn’t widely traded by society. I can’t see how many people could pay their taxes, especially if commodities like gold and silver weren’t widely traded prior to this hypothetical political decision. Instead, it makes more sense for a government to collect taxes using a common good that is already widely traded. So, as I wrote above, I can see how government can make something more liquid, I’m not sure it makes a lot of sense to claim that this liquidity is due to government at first, or that government demand for this commodity as money preceded market demand.

Regarding Zeitlin’s evidential claims, he looks over the fact that any new currencies introduced by government (to pay for wars through seigniorage) have to have some basis for forming prices. Without prior prices, society would have no clue as to what these prices should be. New currencies must use prices defined by former currencies to operate, and these former prices are linked to the new currency through some exchange value between the two currencies (defined either by the market or by the state, the latter being pretty common historically).

In short, the chartalist theory of the emergence of money simply doesn’t make a lot of sense. Menger’s is more intuitive and internally coherent.

Edit: The second to last paragraph shows the relevance of Mises’ regression theorem. He was interested in proving why the requirement of recent prices doesn’t lead one into an infinite regression. The value of the first currencies was decided overtime by the trading of non-monetary commodities, so that exchange rates steadily developed as some goods became more widely traded than others.