Answer: it emphasizes the difference between the financial situation of the dentist and the mayor.
It is less vivid; "raced after" emits a feeling of either action, suspense, or energy. It allows the reader to connect and fully understand what is going on. "ran after" is vague and emits little high energy.
I would have to go with the first and last option, because they are the only ones that make sense to me.
The prostitutes name is Sunny