Coexistence of Physical and Crypto Assets in a Stochastic Endogenous Growth Model

We study a stochastic dynamic model with risky real investment and a positive long-term growth rate. With growing wealth, the economy gets clogged with increasing complexity costs (the classical "Leviathanian" inefficiencies in the form of implicit taxation and abuse of power, red tape, outlays on conflict resolution between special interest groups, etc.). To escape the Leviathan, agents can, in addition to the usual investment in physical capital, access the universe of crypto assets outside the reach of the mainstream state-supported economy. Crypto assets enjoy no legal protection, so converting them back into the real life consumption good is risky (due to digital criminality, hacking, regulatory crackdowns, etc.). A global ergodic solution is found for this model, demonstrating that crypto and conventional assets are capable of long-term coexistence, although the use of crypto assets, far from being universal, tends to be the choice of the wealthier part of the population.