The share of taxi rides in Manhattan has decreased by almost the same amount Lyft and Uber rides have increased [1]. The overall number of rides has increased in the other boroughs due to Lyft and Uber ridership.
Maybe, it is very likely that NYC rides need to be propped up with incentives by ridesharing companies. We won't know the economics until somebody tries to IPO or shutters their company.
Actually, the normal Yellow Cab rates are so high in NYC that Uber can still charge rates twice that of Chicago Uber and come out ahead (NYC $1.75 per mile, Chicago $0.90 -- twice the amount).
1. http://toddwschneider.com/posts/analyzing-1-1-billion-nyc-ta...