The type of conflict which is implied in the above passage is Person vs. Self.
In the short story “The Gift of Magi,” the American writer O. Henry speaks about the feeling of love and the emotions related to it. The couple Della and Jim are so much in love with each other that they would sacrifice anything for their partner to be happy. Since they are poor, they both fall short in arranging money for the Christmas gift. Della wanted to buy a platinum chain for Jim’s watch, but her savings were not enough for the gift. Della decided to sell off her long hair and buy a platinum chain for Jim's watch while Jim sold off her watch to buy a beautiful comb for Della's beautiful hair. The last scene of the story reflects on their love for each other which is beyond the materialistic nature of the world. Their sacrifice for each other made them the wisest people like Magi.
Now they can't wait to try out the brother-in-law's new toy, a miniature unicycle.
Now they were back still talking at the fork of the trail
