spur of the moment stupid  plan  thought up by Emilia as Tobias is, consciously, and unconsciously comparing her to Dahlia, and feeling insecure in all the ways she's found wanting. It was supposed to kind of make him feel a little bad about Dahlia, and because Emilia doesn't actually realize the state of Tobias' finances, she expected him to go out and buy a replacement brooch instead of going to ask Dahlia for a brooch that didn't actually exist. She believed he'd be too proud to do that.