Cryptocurrencies such as Bitcoin have seen their values gyrate over the past year, with the price of 1 bitcoin moving from $900 to nearly $20,000 in 2017, and then falling near $4,000 more recently. This has led some investors to write off cryptocurrencies as tools for speculation, not sustainable currencies.

But Linda Schilling of Ecole Polytechnique and University of Chicago’s Harald Uhlig seek to address some fundamental economic questions about cryptocurrencies. And in doing so, they describe in theory how cryptocurrencies could become less speculative and more like what Bitcoin creator Satoshi Nakamoto originally intended.

“In essence, we imagine a future world, where a cryptocurrency such as Bitcoin has become widely accepted as a means of payments, and where technical issues, such as safety of the payments system or concerns about attacks on the system, have been resolved,” they write.

It’s been a decade since Bitcoin entered the scene, after the pseudonymous inventor of blockchain, Nakamoto, published a 2008 white paper laying out the design of the system. A blockchain is a distributed digital ledger whose technology underpins Bitcoin trading. Nakamoto, whose identity remains secret, came up with the idea of a bitcoin, a digital reward that the software would generate for network users who win a competition to verify transactions on the blockchain by using computers to solve complicated mathematical equations.

Since then, as Bitcoin and several thousand copycat cryptocurrencies have attracted increasing interest and billions of dollars of investment around the world, academics have flocked to study the phenomenon.

Schilling and Uhlig used a mathematical model to posit a system like the one that exists in real life, “where a cryptocurrency competes with traditional fiat money for usage.” Their construct involves a central bank—the Fed—that manages inflation in dollars, while the supply of bitcoins constantly increases until it hits a limit imposed by Nakamoto. Bitcoin has no central authority, leaving no one to stop it from inflating.

If people are able to choose between dollars and bitcoins for their transactions, what is the fundamental price of bitcoins?

This hypothetical scenario is different in several key ways from today’s cryptocurrency environment. As currently implemented, cryptocurrencies face serious challenges: hackers sometimes break into digital coin exchanges and transfer cryptocurrencies to their own accounts, and holders of the currencies often prefer to speculate in their investment value rather than spend them on regular purchases, as Nakamoto intended. In the researchers’ model, these issues are resolved.

If people are able to choose between dollars and bitcoins for their transactions, what is the fundamental price of bitcoins? Schilling and Uhlig find that the bitcoin price expressed in dollars follows a martingale, a sequence where the expected future price of a bitcoin equals its present price. This means that people are just as willing to spend a bitcoin as they are to spend a dollar, because neither one is likely to appreciate against the other.

The researchers then derived an equation to explain speculation in bitcoins—and what could curb it. They point out that if people expect that the price of bitcoins will rise, they will hang onto their bitcoins rather than spend them. (In the real world, the transaction fees incurred when spending bitcoins may provide an additional reason for hoarding them.)

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But, they say, there are conditions under which bitcoin speculation should not happen. If the bitcoin price were expected to increase in value, buyers of goods may want to only use dollars for purchases and save their bitcoins. But then the sellers of goods, sharing the same expectations, would insist on receiving bitcoins rather than dollars. Equilibrium forces, therefore, rule out speculation in bitcoins.

The precise argument requires an assumption about the impatience of buyers and sellers. Of course, the future world where both dollars and bitcoins are equivalently used for transactions has not yet arrived, a possible explanation for why speculation in bitcoins currently exists.

The researchers also performed a series of calculations to demonstrate that it’s possible for the movements of bitcoins to also affect the Fed’s inflation targets for the dollar, and similarly that the Fed’s monetary-policy actions could influence the price of bitcoins. The study notes that these are preliminary findings.

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