# Cryptocurrencies and Bubble Wealth

Americans now hold over \$1 trillion in cryptocurrencies. Has \$1 trillion in wealth been created? From the standpoint of economic theory, the answers is no. The wealth of a society consists of its real assets that produce consumable goods and services. Unless a cryptocurrency provides some type of convenience yield how could it create wealth? On the other hand, everyone who holds the currency thinks of its as wealth because it can be sold and converted into consumption. This short note takes a step in resolving the apparent paradox by presenting a very simple numerical example of the operation of what I call Bubble Wealth.

The example begins with an “economy” that consists of three individuals: A, B, and C. At the outset in period 0, the wealth of each of them consists of 10 units of a “stock” that pays out in terms of future consumption. Consequently, both the aggregate social wealth, the claims to future consumption, and the perceived social wealth, calculated by summing the perceived wealth of all the individuals, are both 30 units as shown in the exhibit below.

In period 1, individual A invents a digital coin denoted by Coin. This Coin provides the owner with no rights to future consumption and pays no interest, but it is designed to trade freely. At this point, there is still no difference between actual and perceived social wealth.

In period 2, A sells Coin to B for one unit of stock. After the trade closes, A owns 11 units of stock, B owns 9 units plus Coin, and C still has 10 units. The aggregate social wealth remains 30 units, but the perceived wealth has risen to 31 because B believe Coin is worth at least the 1 unit that he paid for it. The results are shown in the table below.

In period 3, C buys Coin from B for 2 units based on the belief that its price will rise in the future. As shown in the exhibit the holdings are now: 11, 11, and 8 + Coin. The perceived wealth has increased to 32 because C concludes that Coin is worth at least the 2 units that he paid for it.

In period 4, the investors recognize that Coin has no value in terms of future consumption and the price collapses. The perceived social wealth drops back to the actual social wealth of 30. The net effect is the transfer of 2 units of stock from C, who was left holding the bag when the collapse occurred, to A and B, who each gain 1 unit.

Bubble Wealth Numerical Example

 Period A holdings B holdings C holdings Social Wealth Perceived Social Wealth 0 10 10 10 30 30 1 10+Coin 10 10 30 30 2 11 9+Coin 10 30 31 3 11 11 8+Coin 30 32 4 11 11 8 30 30

The example could be extended by adding more individuals and more trading periods, but the basic point remains unchanged. As long as Coin is trading, it creates bubble wealth defined as the difference between actual social wealth related to future consumption and perceived social wealth. This gap between the perceived and actual social wealth persists until there is a crash and the value of Coin drops to its fundamental value of zero. At that point, it is becomes clear that the invention of Coin did not create wealth, but only promoted its transfer – in the case of the example from C to A and B.

One problem with the simple example is that there is no reason for trading in Coin to start in the first place. In the real world, however, there may be a number of catalysts. Trading Coin could be a way for criminals to move funds around or could serve as a mechanism for avoiding tax. In the example, Coin provides absolutely no services, but in reality Coin could be a substitute means of exchange providing a convenience yield. Whatever the reason that trading starts, if the price begins to rise then in a world of incomplete information and heterogenous beliefs, the price increase could become self-fulling in a manner such as that originally described by Harrison and Kreps (1978).

Although a pure example of Coin might not exist in the real world, some actual securities such as cryptocurrencies like Bitcoin or stocks such as Nikola, AMC and GameStop can be thought of as portfolios consisting of a combination of a security that has rights to future consumption and Coin. The Coin part of the portfolio would function just like pure Coin did in the example and have all the same effects.

The fact that Coin does not create social wealth does not mean its crash cannot destroy wealth in a more realistic context than the simple example. If market frictions and politics are involved, wealth transfers caused by the crash of Coin could have important real effects. Furthermore, if individuals make spending decisions based on their perceived wealth there could be macroeconomic effects.

Finally, just as initial trading in Coin requires a catalyst, so does the crash. If investors currently holding Coin want to convert their holdings into consumption, they will have to sell. Because Coin provides no rights to future consumption, there are no fundamental investors willing to buy Coin. The only buyers are other speculators. If the price has risen to the point where no speculator is willing pay more than the last transaction price, the seller will have to accept a discount. As soon as the price falls, the speculative reason for holding Coin disappears and the price collapses.

References

Harrison, Michael J., and David M. Kreps, 1978, Speculative investor behavior in a stock market with heterogenous beliefs, Quarterly Journal of Economics, 92 (2), 323-336.