What sort of file size is currently reasonable for a webpage? Considering a responsive design being served to both a desktop with a high-bandwidth connection and a slow connection mobile device.
It depends. You can try to find some relevant statistics in order to get some basis:
Please also consider different types of devises: tablets, smart phones, etc. I would say the rule of thumb is still the same: try to decrease your webpage size as much as you can.
Who knows, maybe some internet-enabled fridge will say "Thank you" one day.
The answer is that it should be as small as is reasonable.
Smaller webpages are generally faster; have a better conversion; a better UX; and are cheaper to serve. The only downside to a smaller file size is that you have to have less in it. You have to balance the two for your audience and your application.
For one application and audience, 2MB may be fine, but for another 50kb is too big.
As others have said there's no right answer, it depends. It's best to take an overall approach to optimization with tools like Google's Page Insights and Pingdom tools. It's easy to test often during the dev stage to constantly have an idea of what's going on and develop your own mental optimization heuristics.