Exchange-rate exposure in a “Rule of Three” Model

We examine exchange-rate exposure in an international Bertrand model of differentiated goods using a “Rule of Three” (RoT) market structure that allows both within and between countries competition. We construct two versions of our model, a static and a dynamic one. In the latter, we explore how the intertemporal effects of exchange rates on the optimal prices of a firm’s domestic and international rivals will affect a firm’s long-run exposure in relation to its short-run exposure. We find that in the static version, the addition of a domestic competitor increases the firm’s exposure, while the effect on its foreign competitor is ambiguous. In the dynamic case, we find that the gap in exposure between the RoT model and the international duopoly case is larger in the long run than in the short run for the company facing a domestic rival, while the exposure for that firm can be either smaller or larger in the long run relative to the short run. Finally, the firm that remains a monopolist in its domestic market has a smaller exposure in the long run as compared to the short run.