How to determine exchange rates under risk neutrality: A note

The goal of this paper is to determine the exchange rates consistent with an equilibrium in the international assets and goods markets. We present a wealth model of a two-country economy where financial assets and goods are traded. We consider the case where the agents are risk neutral, a very common assumption in finance in order to have explicit solutions for prices, and, in particular, in international finance for exchange rates using the non-null Pareto optima. We show that the Pareto optima in the international assets and goods markets are found to coincide with the net trade allocations. More notably, under a no-arbitrage condition in the assets markets, we can define an exchange rates system for which PPP holds. We provide conditions to have a non-null Pareto optimum to compute the exchange rates. We give an example with a non-null Pareto optimum associated with the determination of the exchange rate.