The climax of "The Gift of the Magi" is an excellent illustration of the use of a paradox to make a point. A paradox is "a statement that is apparently self-contradictory or absurd but really contains a possible truth."
The whole purpose of the plot development in "The Gift of the Magi" is to illustrate how foolishly Jim and Della acted. They were poor, living with reduced income and very few resources upon which they could draw for life's necessities. The only things they owned that had any real value were Jim's family heirloom watch and Della's fabulous hair. Any prudent couple would have saved these treasures until they were forced to sell them so the proceeds could be used to pay for rent, utilities, or food - requirements for continued survival.
Jim and Della, however, wasted the profits from the sales of their treasures in the purchase of Christmas gifts for the other that would not help them live, and that turned out to not be usable at all in the immediate future.
The paradox is that Jim and Della, in demonstrating the depth of their love and commitment for each other, showed their true wisdom. Gifts are to be given out of love, not for material reasons as did the original magi and their "gifts to the Babe in the manger." Jim and Della "were the wisest. Of all who give and receive gifts, such as they are wisest. Everywhere they are wisest. They are the magi."