The case against eliminating large denomination bills

When large denomination bills are preferred in illegal activities, what is the optimal policy response? We construct a dual currency model where illegal activity can be reduced by modifying the payment environment. In our model, legal (goods) traders are indifferent between small and large bills, but illegal (goods) traders face a lower transaction cost of using large bills in comparison to small bills because it is easier to conceal. We show that eliminating large bills can reduce illegal trade and its associated social cost. However, this pooling equilibrium is sub-optimal because the government can collect more seigniorage by allowing illegal traders to use large bills with a lower rate of return. When the transaction cost of using small bills for illegal traders is sufficiently large, a separating equilibrium, where legal traders use small bills and illegal traders use large bills, can maximize welfare by making an implicit transfer from the illegal traders to the legal traders.