Is it appropriate to ask a professor for a discount on his expensive book?
Authors usually don't and cannot sell directly copies of their books, and the price is decided by the publisher. 

Of course, an author has their draft copy in electronic format, but they might not even have the final electronic version as published. Authors typically receive a few courtesy copies of their books, but they have no access to other copies for free.

My suggestion however is to borrow the book from your university library: that's what library are for, after all.

If the library doesn't have a copy, depending on your position, you can:


Suggest the library to buy a copy. Many university libraries buy books according to the suggestions of their faculties: if you cannot do this directly, probably your adviser can.
Ask your library if they can loan it from another library. In many countries there is a system of interlibrary loans, and sometimes it works even across different countries.