Government Finance in a Model of Currency Substitution

Our model is a variant of the cash-in-advance model. Goods must be purchased in the seller's currency, but currency may be traded before shopping at a cost. This cost is a measure of substitutability. The model is applied to seignorage taxation. We show that optimal money growth is positive and increasing in substitutability if and only if first- and second-period consumption are gross substitutes. If governments act independently, money growth is suboptimally low if currencies are sufficiently substitutable and too high otherwise.