Professor expects me to attend a conference. I can't afford to go,even with 50% funding I am a first year Ph.D. student. During my master's (which was in a different university), a professor (call him M) and I worked on a paper on banking regulations. Apart from the single idea, all of the paper and results were done by me. We worked on it for a couple of months and tried to submit our work at many journals.  All of them rejected it.  Finally, it has been accepted recently at a conference. This conference is not major league but niche. 

Prof. M wants me to attend, but I do not have funding. Initially, he expected me to spend from my own pocket for travel and registration (around USD 2,000). Being a graduate student and living in one of the expensive cities, I am living hand-to-mouth. So, I informed him politely that I am not keen to attend due to my inability to fund myself.  He asked me to apply to funding agencies, or else he is willing to fund 50% of my expenses. 

The fact of the matter is that I cannot afford even 50% of the travel expenses.  Out of nowhere, this conference comes up and it further cripples my shoestring budget. 

How should I proceed?  I am really hesitant to discuss my financial shortcomings with Prof. M, but if I don't, he'll assume that I can afford the travel.
I am really hesitant to discuss my financial shortcomings with Prof.
  M, or else he assumes that I can afford the travel.


I think you need to get past this. You do not have financial shortcomings, you just don't have money. Working on a PhD without family financial support, with existing student debt, and with limited school support is not easy. I respect you for doing it. Take pride in making the hard choices that involves.

With that attitude, explain to Prof. M that you cannot afford any travel expense, and will only be able to go to the conference if your expenses are fully covered. Check any funding sources he suggested, and ask advisors at your current university if they know of any sources.

From comments: Also check with the conference organizers. They may have scholarships or be able to discount the conference fee, and find free or inexpensive accommodations. You may need to work several angles to align the total cost with the available funding.

If you can't get the full funding you need, tell Prof. M. that you regret you cannot attend the conference. At the worst, you will have to withdraw the paper. However, there are alternatives the conference may permit.


Remote video presentation
If anyone from your current university is attending, ask them to present the paper
Prof M. may be able to get a current student or a collaborator who is attending the conference to present it.