The demographic patterns of two ethnic groups, a minority, and a majority are examined in this study with respect to population welfare. The assimilation rate and the minority proportion are shown to have a negative correlation. Assimilation may bring fewer benefits as the minority percentage grows. Incentives that are designed to temporarily boost the minority birth rate keep the minority population stable for a long time, and sometimes convert minority groups to the majority. Future generations had tremendous gains from their ancestors’ choice of assimilation. Without a birth rate boost, pure minority groups eventually go extinct.