Abstract: This paper constructs a searching model to study the impact of monetary
policy, fiscal policy, transaction costs of private cryptocurrency and regulatory uncertainty
on the competitive equilibrium between Central Bank Digital Currency and private
cryptocurrency. The results show: (1) Central Bank Digital Currency and private cryptocurrency can conditionally coexist. (2) The level of economic welfare is related to monetary
policy and fiscal policy but independent from the issuance and transaction of private
cryptocurrency. (3) Under complete competition of private cryptocurrency mining, the
mining cost becomes deadweight loss for whole society.

Key words:  Central Bank Digital Currency, Private cryptocurrency, Regulatory uncertainty