Price Theory and Cryptocurrency

In a previous post, I alluded to Ben Klein’s paper on competitive fiat money. (As a quick note, I am going to refer to paper money that is not redeemable into some commodity as “fiat money” for ease of exposition.) In many ways, the paper was ahead of its time. What Klein was claiming could exist, a stable equilibrium of competing fiat currencies, was not something that had ever been observed. In this post, I’d like to examine Klein’s argument and discuss it in reference to something that seems a lot like his model: cryptocurrency.

As I discussed in my previous post on money, getting paper money to circulate as a medium of exchange is difficult. In theory, all we need is a network effect. I accept paper money because I expect everyone else to accept it from me in the future. Of course, this network effect is limited by what is known as “the last period problem.” If I know that there is some point in the future at which no one will accept the pieces of paper any longer, then I don’t want to accept those pieces of paper in the prior period. Through backward induction, no one will want to hold the pieces of paper today. One way to solve this last period problem is for the issuer to promise to buy back the pieces of paper for a fixed quantity of some commodity in the future. In that case, I know that I won’t be stuck holding a worthless piece of paper. I will have some valuable commodity.

But what do we mean by the last period problem? We know that the world will end one day, but that is not really what we mean.

A better example would be to think about reasons why there might be some “last period” in the future. When it comes to competitive fiat money, there is one common argument: hyperinflation.

The issuers of irredeemable paper money can print up nominal units of money and use them to buy real assets. The profit-maximizing behavior of firms might be to issue as many pieces of paper as possible in exchange for real resources. Hyperinflation results, but the real assets were nonetheless transferred to the issuer as a form of seigniorage.

Of course, in order to generate that seigniorage, the issuer must first get people to accept the pieces of paper. Yet, if people know that hyperinflation is a possibility, then they will never hold this fiat money in the first place and it will never circulate. There is a dynamic inconsistency problem. The issuer must promise to be prudent before creating hyperinflation all at once.

There are a couple of issues with this concern about competitive fiat money. First, this dynamic inconsistency problem is not unique to fiat money. Even redeemable paper money is subject to a similar problem. As I have shown elsewhere, in a world of complete markets and perfect commitment, redeemable paper money and the underlying commodity are perfect substitutes. However, if the issuer cannot perfectly commit to redemption, the probability that the issuer will renege reduces the value of the paper money.

The second issue is whether this dynamic inconsistency problem really exists. It is not obvious whether the issuer would want to create hyperinflation in its currency. Whether hyperinflation is advantageous depends on whether the profit from hyperinflation is greater than the present-discounted value of future profits in the absence of hyperinflation.

It is this second issue that Klein’s paper is really designed to address. Is hyperinflation the profit-maximizing strategy? We need to think about how issuers of fiat-type money might behave.

This is where price theory comes in. We know that people will be willing to hold a level of real money balances such that the marginal benefit generated from holding one more unit of the currency is equal to the marginal cost of holding that additional unit. We also know that a profit-maximizing issuer will produce an amount of currency such that the marginal revenue from issuance is equal to the marginal cost. Furthermore, in a competitive market, we know that the marginal benefit to the consumer is equal to the marginal cost of the producers. We can therefore think about an equilibrium in the market for money the same way we think about equilibrium in any other market.

One problem is that the marginal benefit of holding an additional unit of currency, given the price level, is hard to measure. These are primarily non-pecuniary benefits. However, one can measure the cost. As Brian and I have talked about before, when economists think about costs, they are thinking about opportunity cost. The opportunity cost of holding money is that one could have held some other asset instead. The marginal cost of holding money is therefore the nominal interest rate. Given that the marginal benefit is equal to the marginal cost, we now know the marginal value of that non-pecuniary benefit. It must be equal to the nominal interest rate.

For issuers of money, the marginal cost of issuing currency is increasing in the quantity of real money balances. This is because the issuer needs to invest in its brand name in order to get people to hold its currency rather than the alternatives. This requires advertising and anti-counterfeiting measures. If the issuer is a bank, as has conventionally been the case for private money issuers, there are also costs associated with intermediating loans and their brand of currency.

Thus, if there is a level of real money balances such that the marginal cost of producing those balances is equal to the nominal interest rate, it is possible that there is a unique equilibrium with finite real money balances (i.e., no hyperinflation).

But how do we know whether this is the unique equilibrium or under what conditions we might end up in this equilibrium if multiple equilibria are possible?

To answer that question, we need to think a little more carefully about the currency issuer’s profit maximization problem. I simply asserted that a profit-maximizing firm chooses a level of production that equates marginal revenue with marginal cost. However, that assumes that there is some maximum level of profit. It is possible that profit is strictly increasing in the quantity of real balances. In that case, hyperinflation is the dominant strategy for the currency issuer. The question we need to answer is under what conditions these scenarios might hold.

Let’s think about how consumers might respond to inflation under two scenarios. In the first scenario, consumers have perfect foresight about the rate of inflation, measured in terms of a particular type of currency. In the second scenario, consumers have to form expectations about the inflation rate.

In a world with perfect foresight, higher inflation is perfectly anticipated. As a result, the nominal interest rate will increase one-for-one with the inflation rate and the demand for real money balances will fall accordingly. This will not be profit-maximizing.

Now consider a world in which inflation is a surprise. In this case, the nominal interest rate will not adjust (or adjust sufficiently). The demand for real money balances will be above what they would be if consumers had correctly anticipated inflation and the issuer’s profit will increase. In this sort of environment, creating a massive, unexpected hyperinflation could be profit-maximizing. (While Klein himself casts doubt on this outcome, subsequent economists have disagreed.)

This brings us back around to the dynamic inefficiency problem. Issuers of the currency have an incentive to maintain stable values, until one day they don’t and they make a massive profit at the expensive of those holding the now worthless currency.

The historical evidence, up until this point, seemed to provide some support for the view that competitive fiat currency just wasn’t workable. The dynamic inconsistency problem seemed the likely culprit. That is, until cryptocurrency.

The emergence of cryptocurrency seems a lot like a system of competitive fiat currency. There are many cryptocurrencies that are not redeemable for any real commodity or asset. Yet, these cryptocurrencies have positive market values. Is this just an example of “sure this works in practice, but does it work in theory?”

My discussion of Klein’s model suggests the answer is no. The problem with competitive fiat money is the problem of dynamic inconsistency. The issuers have the incentive to make promises today and renege on those promises in the future. But the way that you solve dynamic inconsistency problems is by tying the hands of those who cannot perfectly commit to future actions. For policymakers, this often means forcing them to follow some stipulated policy rule. In private transactions, this often requires contractual solutions.

However, what cryptocurrencies have done is create a new type of solution. The supply of many cryptocurrencies are subject to some algorithm. Furthermore, the decentralized nature of these systems prevent “reneging” on the algorithm without approval of the many users of the cryptocurrency. Dynamic inconsistency therefore doesn’t seem like a problem. Without the looming dynamic inconsistency problem, these cryptocurrencies could continue to circulate as long as there is some network effect.

All of this is not to say that cryptocurrency will survive long-term or that it will be anything other than a niche asset. The potential for hyperinflation is not the only source of the last period problem. The fiat nature of some of these products might be outcompeted by those that offer some redemption in a particular real asset. It is also possible that future generations might not see the same value or potential in cryptocurrency as some in the current generation. If this becomes apparent, the value of these cryptocurrencies could fall rapidly toward zero.

Nonetheless, cryptocurrency represents a sort of test of Klein’s model, which was far ahead of its time.