Now suppose that Person A increases production of Good X by Xa units and decreases production of Good Y by Yb units, while Person B follows the opposite course. The two parties then exchange the goods, so that they realize the same total stocks as before. Under this arrangement, Person A's new total cost is as follows:

Since x_a + y_a was A's total cost prior to the agreement, A benefits by this exchange. Person B's new total cost is as follows:

Since x_b + y_b was B's cost prior to the agreement, B also benefits.