Reviewing transformation functions, production possibility curves, and factor contract curves, we present explicit formulas of the Transformation Functions for Pareto efficient factor allocations. These production possibility frontiers (Envelopes) are explicitly stated for any Cobb-Douglas (CD) sector technology parameters and any factor endowments of labor and capital. Exact Variable Elasticity of Transformation (VET) curves of non-joint productions are derived. Core Theorems of international trade are unified, extended, and economically stated explicitly with structural parameter formulas. Multiple output Revenue functions are obtained in closed forms. The output formulas of the Transformation and Revenue functions are compared with the autarky general equilibrium expressions. Explicit autarky formulas of comparative advantage (price, cost) for prediction of trade pattern are derived and demonstrated for bilateral trading economies with any CD sector technologies, CD consumer preferences, and any country endowment ratios (proportions) of labor and capital.