This paper presents the way in which can be determined the exchange rates that simultaneously balance the trade balances of all countries that trade with each other within a common market. A mathematical synthesis between the theory of comparative advantages of Ricardo and Mill and the New Theory on International Trade of Paul Krugman is also presented in this paper. This mathematical synthesis shows that these theories are complementary. Also presented in this paper is a proposal to organize a common market of the American hemisphere. This economic alliance would allow to establish a political alliance for the common defense of the entire American hemisphere. The formula we developed in this paper to determine the exchange rates of the countries solves the problem that Mexico, Canada, Europe, Japan and China currently experience with the United States in relation to the deficits and surpluses in the trade balance of the countries and their consequent impediment so that stable growth of international trade can be achieved.