Currency Price, the Nominal Exchange Rate, and Security Prices in a Two Country Dynamic Monetary Equilibrium

This paper examines a continuous-time two-country dynamic monetary equilibrium in which countries with possibly heterogeneous tastes and endowments hold their own money for the purpose of transaction services formulated via money in the utility function. Given a price system, no-arbitrage pricing results are provided for the price of each money and the nominal exchange rate. Characterizations are provided for equilibrium prices for general time-additive preferences and non-Markovian exogenous processes. Under a Markovian structure of model primitives, the currency prices are shown to solve a bivariate system of partial differential equations. Assuming that each country is endowed with heterogeneous separable power utility and the exogenous quantities all follow geometric Brownian motions, an equilibrium is shown to exist and additional characterization is provided. A further example of non-separable Cobb-Douglass preferences is investigated. The additional features over customary environment of homogeneous logarithmic preferences are emphasized