Currency prices, the nominal exchange rate, and security prices in a two-country dynamic monetary equilibrium

This paper examines a continuous-time two-country dynamic monetary equilibr ium in which countries with possibly heterogeneous tastes and endowments ho ld their own money for the purpose of transaction services formulated via m oney in the utility function. Given a price system, no-arbitrage pricing re sults are provided for the price of each money and the nominal exchange rat e. Characterizations are provided for equilibrium prices for general time-a dditive preferences and non-Markovian exogenous processes. Under a Markovia n structure of model primitives, the currency prices are shown to solve a b ivariate system of partial differential equations. Assuming that each count ry is endowed with heterogeneous separable power utility and the exogenous quantities all follow geometric Brownian motions, an equilibrium is shown t o exist and additional characterization is provided. A further example of n onseparable Cobb-Douglas preferences is investigated. The additional featur es over the customary environment of homogeneous logarithmic preferences ar e emphasized.