Why are you so convinced they undercut on pricing? Simply because they are cheaper than taxis?
Uber is privately held, which makes it hard to do any sort of deep dive analysis because we don't have a lot of insight into their financials. We don’t know what their overhead costs are, what their long-term forecasts are, what their marketing budget looks like, what their legal costs are, and so forth.
We do know that the old Silicion Valley edict is to raise as much capital as you can, grow as fast and as big as you can, and worry about turning a profit later.
Anybody who has been involved in a business start-up knows that start-up costs are significant. From legal and licensing issues, to recruitment and hiring, to marketing, there are a lot of up-front costs. The legal uncertainty Uber has faced in many jurisdictions has certainly been expensive. Take Alberta as an example – they effectively shut Uber down a few months ago. That cost to Uber has got to be expensive. Multiply that across many jurisdictions in North America and Europe and factor in who knows how many $1,000/hour lawyers and you can get to hundreds of millions pretty quick. Maybe even billions.