Heckscher-Ohlin via Factor-Intensive Production Function

We develop further the Heckscher-Ohlin international-trade theory, by analyzing the two-sector, two-input model of production. The domestic-product primal maximizes the output value, subject to the technology and input constraints. Because the theory focuses on factor endowments and the capital/labor ratio in production, it is natural to set up the primal via factor-intensive production functions. The domestic-income dual then involves the factor-price frontier, the conjugate of the factor-intensive production function. The dual chooses input prices to minimize the value of the resource endowments, subject to the constraint that the prices lie on or above the factor-price frontiers. The necessary and sufficient conditions for solution to the primal and the dual provide the basis for a traditional comparative-statics analysis. The theorems of the Heckscher-Ohlin theory—factor-price equalization, Rybczynski, Heckscher-Ohlin direction of trade, and Stolper-Samuelson—revolve around factor prices and factor intensity. Differentiating the necessary and sufficient conditions obtains simple formulas that prove these theorems. The envelope condition explains key results.