Money mining: technology diffusion and transactions validation
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We develop a continuous-time Lagos-Wright model to study private and decentralised money production with a time-consuming mining technology and with a diffusion process for this technology. There exists a unique equilibrium where the value of money reaches a monetary steady state and a continuum of perfect-foresight equilibria indexed by the starting value of the currency where the price of money vanishes gradually even without appreciation periods. In opposition to previous results in the literature, private money is used for transactions along the equilibrium path. These results still hold when agents choose a portfolio with a competing government fiat money. We additionally demonstrate that the monetary policy can prevent mining activity. Finally we entangle transactions and their validation and create a continuum of boom and bust equilibria via inflationary taxation on mined money holders.