Liquidity Premium and International Seigniorage Payments

Why do people hold dollar denominated assets when higher rate of return alternatives are available? Can a country collect seigniorage payments from other countries in the long run? Does the supplier of the international currency benefit from doing so? I provide qualitative answers to these related questions in terms of a model with price dispersion, heterogeneous agents and two government-backed assets (interest-bearing monies). In the steady state one of the assets is used primarily in low price transactions and earns a relatively low (measured) real rate of return. The stable demand country that issues the relatively liquid asset gets seigniorage but its welfare may be less than under autarky because trade increases the uncertainty about demand in the relevant markets and uncertainty sometimes leads to ex-post pricing mistakes and waste.