Despite overwhelming empirical evidence of the failure of factor price equalization, most teaching of international trade theory (even at the graduate level) assumes that economies are incompletely specialized and that factor price equalization holds. The behavior of trading economies in the absence of factor price equalization is not well understood, and some major textbook treatments err. The authors map regions of specialization and diversification for standard competitive economies and show how outputs, goods, and factor prices change as economies move within and across different regions of diversification and specialization. Two examples of how the analysis can enrich graduate-level trade teaching are given: the substitutability of goods trade and factor movements, and debates over the trade and inequality. (Contains 8 figures and 7 notes.)