He asks his father what he should do. Ward tells him "Lets put our heads together and see what we can figure out." There is silence as Ward tries to let him try solve his own issue. Finally Beaver says "I was kind of waiting for you to go first." Ward recommends a solution. I wonder if in some small way, Ward was trying to use the Patrol Method (allowing the Beaver to find a solution for his own issue) in some small way. Granted there wasn't a patrol but the patrol method doesn't have to be used just in a small group.
I appreciate parents who try to let their kids learn things themselves. Rescuing your kid, in most situations, isn't helpful for them to become responsible adults.
In the end, Beaver gave up 50% of his allowance each week until the bill was paid. Painful but effective.