A search‐theoretic model is constructed, where money and Bitcoin can be used as mediums of exchange. We investigate how each currency facilitates transactions and how they compete with each other. Quantitative analysis shows that welfare in an economy with both money and Bitcoin is lower than in a money‐only economy due to congestions in the confirmation of Bitcoin transactions and that the welfare gap between the two economies expands as inflation rises. Moreover, an increase in transaction fees for Bitcoin can increase welfare by reducing inefficient Bitcoin transactions.
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