To be honest, I do not see the connection of the title with the question body because you ask about inflation, rather than the impact on trade (you mention trade, but in the context of price stability).
Paul Krugman's The Return of Depression Economics and the Crisis of 2008 has, in my opinion, the best layman's explanation for the impacts of a single currency. I highly recommend this book if you are extremely interested in this problem (or (monetary) economics in general).
Krugman explains this with a fictional currency called globo. A quick summary:
- Businessmen in particular like this system because they could buy and sell anywhere with a minimum of hassle
- Careful management of the currency could prevent a boom-bust cycle for the
world as a whole, but not for each country (also applies to regions within countries, but usually to a lesser extent because of the same language, free movement of labour etc).
The other article I recommend reading is optimum currency area. Since shocks would be very different in different countries (some may grow, others shrink), prices and wages and /or factor (labor) mobility must be very flexible for a country to regain competitiveness. A country (region) can either decrease prices relative to other countries, or workers leave the country where the unemployment rate is high to take jobs elsewhere. That way, the unemployment rate in that country decreases back to normal. In summery, even under a fixed exchange rate, countries can adjust their real exchange rate in the medium run but these adjustments may take longer and be more painful compared to flexible exchange rates with independent monetary policy.
Either way, I am not sure how you define price stability? If you mean low inflation, that is rather unrelated to trade but mainly a subject of economic activity relative to money in circulation.