About 10-15 (or more?) years ago the Bureau of Transport and Research Economics (I think that was their name), produced a study which said that making public transport free Australia wide would result in savings of $2 billion annually. Due to factors such as reduced accidents, reduced wear on road infrastructure, increased population fitness (more exercise), reduced pollution, no need for expensive ticketing systems, no need to pay for fare enforcement officers, etc.

I've since looked for the paper in the past but haven't had any success. I think it may be paper number 71 on this list from 1985 http://www.btre.gov.au/op_index.aspx but it's only available as hard copy, so don't count on it. There might be some other info on that site that's useful though.