Assume a two-country two-good two-input model. Let the countries in the model be the United States and the Rest of the World and the goods be steel and wheat. The two factors of production are capital and land. Further, the United States is capital-abundant and steel production is capital-intensive. Suppose, in the absence of trade, the United States operates at a point on its production-possibility curve where it produces and consumes 20 units of wheat and 20 units of steel. Once it engages in free trade, the international price of one unit of steel is two units of wheat. In response to the opening of trade, the United States moves along its production-possibility curve to a new point where it produces 30 units of steel and 10 units of wheat. Is the United States better-off following the opening of trade? Provide a logical proof of your answer.