Extensionless URLs are a good idea because it helps with unavoidable future platform transitions. If you switch server technologies, you might end pages in .jsp or .html or something else.
Search engines generally consider every character when determining separate URLs. This goes for adding .html and even capital letters. Therefore, these two URLs are different in the eyes of search engines:
But to really answer your question, adding an extension should have little to no effect on page authority. Search engines are more concerned with your page's content, relevancy, popularity, authority, etc.