01/05/22
- Journals
We study the valorization of cryptocurrency in an overlapping generations model where agents
have the choice between crypto- and central bank currency. We pay attention to three features of
cryptocurrency: it is a risky asset (because of frauds and hacks), which one acquires by bearing
transaction costs, and its supply reaches its upper limit in a finite time (e.g., Bitcoin). We consider
both the standard case with linear–quadratic utility functions and the more general case where utility
functions are not specified. We find that the effect of an increase in cryptocurrency on the currency
prices depends on the transaction costs that individuals bear to get cryptocurrency. In particular, when
these costs are convex non-increasing in the quantity of cryptocurrency, the cryptocurrency price may
increase with this quantity. Otherwise, when the transaction costs are either increasing or concave
non-increasing, the cryptocurrency price decreases with the quantity of cryptocurrency. We also show
that the cryptocurrency and the central bank currency prices always move in opposite directions.
