| Quote #1
Besides, he was rich; unlike most boys his age, he had never even begun collecting baseball cards. (1.2)
Jamie is the first character in the book described as rich—and it's because he has a lot of allowance money saved up. That might not count for much in the adult world, but it sure does to Claudia, who can't even save up for a sundae sometimes.
| Quote #2
"Well, you see, Claude," Jamie whispered, "I have quite a lot of money."
Claudia thought that old Jamie would end up being a business tycoon someday. Or at least a tax attorney like their grandfather. (1.44-45)
In the book, it's obvious that some people have a better awareness of money, and others don't. Even though Claudia is older, she wisely realizes that Jamie is the one who has a knack for making and keeping track of money. And she… well she would probably blow it all on ice cream.
| Quote #3
Claudia appointed him treasurer; he would not only hold all the money, he would also keep track of it and pass judgment on all expenditures. (1.60)
He who holds the money also holds the power—or something like that. Claudia may be the bossy older sister who plans the whole trip, but she lets Jamie have a say, too. He gets to stop her from making stupid purchases.