Well, the first part of the graph from 1904 to 1954 is a historical accident. Basically the subway was built by contracting it out to private companies, namely the BMT and IRT. But the city couldn't afford the full price up front, so part of the payment was that these companies got to also run the service and collect fares. Part of the contracts made certain stipulations to prevent these companies from screwing the public, among them being fares were capped at 5 cents. Flash forward 50 years, inflation happens but fares are still capped. Populist view both companies as "greedy corporations" and have been trying to murder them since the 20s, and so they finally get their wish. Neither company could stay solvent at that price cap, and no elected official wanted to amend the contract and let them raise it. The city buys up the bankrupt private operators which is how we get to where we are today. Then for the first time fares get to rise to match (and apparently surpass) inflation.