Warren Mosler and other MMTers have emphasized for decades that “the currency is a public monopoly,” which means that, just as the monopolist sets the price of its product, the government has pricing power over the currency. For MMT this doesn’t come from setting the quantity of money or something like that, but rather by specifying what you have to do to get the money from the government — that is, the prices government pays when it spends money into the economy (or the collateral demanded when it lends). If government pays its workers $15 per hour for basic labor, then it is implicitly stipulating that you need to do 1 hour of work to get 15 dollars from the dollar-monopolist.

A paper by Pavlina Tcherneva puts this on a mathematical footing, demonstrating several scenarios and several kinds of fiscal policy using this notion. However, her model takes it as given that it’s possible for the government to set prices, and demonstrates the results. I thought it would be neat to make a toy model that asks whether or not government really has the power to do this, given some fairly loose conditions. So that’s what this article is about.

In particular, I want to get at the question of whether or not private markets are compelled to move towards prices government sets — can the private sector not simply ignore what the government does? In this model below, I’ll have a very simplistic government and private sector, and we’ll observe the dynamics between them.

Disclaimer that should come attached to any model: this is a toy, a thought-exercise, and shouldn’t be taken to be perfectly reflective of the real world. No model ever offers conclusive “proof” of anything, and neither does this. But it can still be a useful, elucidating exercise.

The Model

Our model works as follows. Time occurs in discrete steps. The government sells fiat money into the economy (for labor or goods), and then once in the economy, it can be “resold” by private sellers. The government collects money out of the economy when taxes are paid. We will accordingly deal with two prices: the price that the government offers, and the price that prevails in the private “resale” market. Both of these are the price of money in terms of real things, e.g. how much labor you have to do to get one dollar. The question will be whether its possible for the prevailing market price to be different from the government price in the long run.

With money supply M, government spending G, and taxes T, the “law of motion” for the money supply is:

The (flow) demand for fiat money each period is

where D is a decreasing function of the price of money, meaning that as a unit of money becomes harder to get (deflation), demand for it drops off.

The supply of fiat money in the private resale market is

where k is a function that increases as the price that money commands in the private market increases. This specification means that the supply of money in resale markets will be zero when the money supply is zero, so that’s good. Otherwise, k is sort of like a ‘spending velocity of money’ ¹.

The next equation specifies how many transactions happen in the private resale sector each period

R is the size of resale transactions (measured in dollars), p^g is the price of fiat money that the government stipulates, p^f is the price in the private markets, and H is the Heaviside Step Function, which takes on the value 1 if p^g ≥ p^f, and otherwise is zero. The “Min” part says that if supply is less than demand then supply determines R, while if demand is less than supply then demand determines R. (In other words, the “short side rules.”) The H part tells us how the price competition plays out: if the government is charging a better price than the private market (you can get the same amount of dollars with less labor), then the private market will lose all buyers, and the demand that resalers see will go to zero.

Next we specify the government’s fiscal policy. Government spending is given as

which is that the government fills whatever demand the private market isn’t filling, at its fixed price of p^g — this is basically a Job Guarantee. We will take tax collections as totally exogenous.

And finally, the adjustment process, given by

This governs how the private market price of money adjusts over time. To get the current price that the private sector will charge, we take the previous price and multiply by this complicated-looking adjustment factor. r is the rate of adjustment, i.e. how reactive the market price is to imbalances between supply and demand between periods, and the term in square brackets represents the imbalance in the private market. D times H works the same as above, being equal to the market demand when the private price is below the government’s and zero otherwise. The delta symbol is the ‘Kronecker delta’ which takes on a value of 1 if the government price was equal to the private price, and zero otherwise.

When the private price is above the government price, so that there are no buyers in the private market, this term reduces to just -S, indicating that prices need to drop sharply to bring buyers back in. When the private price is below the government price, then this expression becomes D-S, indicating that the price needs to rise if demand is above supply and fall if supply is below demand. Finally, in the case where both prices are equal, this expression is D-S-G, indicating that even if private supply is insufficient, there is no pressure to raise prices because government selling of money fills the gap at the same price².

The Steady-State

Obviously, by design the prices in the two markets don’t have to be equal in every period. The question is what happens in the long-run: is there a long-run steady-state solution where the private price is different from the government price? To figure this out, we have to find the steady-state.

To begin with, in the steady-state the money supply should be unchanging, which means the government’s budget is balanced.

Additionally, prices should be unchanging in the steady-state, giving

As before there are three cases, depending on the relationship between p^g and p^f. We can reject as trivial the case where the government’s price is permanently better than the private price: this gives -S=0, which should only be true if M=0 — a very uninteresting economy.

In the next case, suppose that the two prices are equal. This gives D-S-G=0. If we were to specify a form for the demand and supply functions, this would allow us to solve for an equilibrium money supply too.

However, the real action comes when we consider the case where the private price is permanently below the government’s price — is this possible? In that case, the condition above would give D-S=0, implying that D=S, which is also equal to R. Because we know that G=D-R, this gives us that G=0. But because in the steady-state G=T, this can only be true if T=0.

In other words, within the model, the steady-state where the private price is below the government’s price is only possible if taxes and government spending are zero. Otherwise, in the long-run, the private market price level moves towards the price level set exogenously by government³.

Discussion

The key feature of this model is the price competition between the private sector and the government, and the fact that the government doesn’t have to blink while the private sector does. If the government is paying better than the private sector, then not only will private sales drop to zero, but the large increase in the money supply from the increase in government spending will further hurt private sellers, increasing supply while they face zero demand, forcing them back to the table, to bring their price down to match the government’s.

On the other hand, when the private price of money is more attractive than the government’s, the private sector might enjoy its money-sales boom but this is only temporary: with government spending dropped to zero, taxes are slowly draining the money supply, reducing private supply capacity, until demand outstrips supply and prices are forced back up to match the government’s offer.

The result is that if taxes are above zero then the government has market power to determine the price level, and private prices are attracted towards the prices that government pays. This actually tracks certain results in mainstream Industrial Organization and Antitrust economics, which argues that if there is something that reduces the stock of durable goods available to be resold, eg. depreciation or taxes in our case, then the production monopolist will retain pricing power.

In the real world of course it’s a lot more complicated: administered prices means that most prices really aren’t that sensitive to imbalances in supply and demand; and, the government isn’t providing money on an on-demand basis, because we don’t have something like a Job Guarantee (yet). But we can conduct somewhat more realistic thought experiments illustrating the point too. For example, if the government announced that it was just going to pay all of its suppliers and workers 10 times the prices it paid last year, does anybody doubt that there would be inflation as a result?

David Andolfatto on Twitter asks why the government unique in this respect. Why can’t Amazon do the same thing? Of course it can try, but as per above, private entities eventually have to blink while the government doesn’t. If Amazon starting paying everybody 10x what it paid them last year, it would see its costs increase 10x, while (initially at least) its revenues would be unchanged. Suddenly they’re taking a huge loss, that they won’t be able to finance forever, in a way that the government could do because it’s the currency-issuer (and even if revenues started catching up, it would be very slow and painful). And, if the government didn’t agree to raise prices as the effects of Amazon’s experiment rippled through, then just as in the model, government spending would drop to zero, depressing the economy, hurting Amazon’s profits even more. This could be long and painful, but eventually they’d have to blink.

In real life, the government does not typically try to oppose inflation by holding steady on prices in this way. As Mosler has argued, it could do this, but it’s probably bad policy, because the collateral damage would be severe: in our modern administered price markets, it takes a very large, severe drop in demand to bring prices down. Instead, the better policy might be to manage the pressures within the private economy that lead to private suppliers requesting higher prices. That includes, but is not limited to, demand management policy, robust antitrust to keep markets competitive, and possibly incomes policies or corporate governance reforms to prevent spiraling conflict inflation.

Conclusion

This model demonstrates the possibility of a key claim of MMT, namely that government is price-setter for its currency, acting through the prices it pays when it spends or lends. The purpose of the model isn’t to suggest policy or prove anything, only to demonstrate the plausibility of MMT’s theory of the price level: given a very loose set of assumptions, we can build a model in which the price level in the private markets tends in the long-run towards prices set exogenously by government.

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¹ While this shouldn’t be seen as MMT endorsing the quantity theory of money, Mosler has previously argued that if the definition of “money” is broadened to include all government liabilities, as we’re doing here, then QTM makes a bit more sense.

² When supply is insufficient but the private price is below the government price, then the government will still sell to fill in the gap, but this provides leverage to private sellers to raise their price, hence why the G term vanishes in this case.

³ Whether and how the model actually converges to this steady-state if it starts outside of it depends heavily on the specification of the demand and supply functions, and on the value of the parameter r. Some simulation experiments showed that certain specifications tend smoothly towards this long-run steady state, while others lead to oscillation around it or even chaos. But if the model starts here, it will stay there.