For decades, the New York City yellow cab has powered the consummate immigrant story — a tale of a new arrival who becomes a driver, a driver dogged enough to eventually become his own boss.

The proof of that feat has been the taxi medallion, which grants the right to operate a yellow cab. The aluminum plate is pinned to the hood, the emblem of a dream achieved for those who work hard enough to afford it.

But in an age of soaring prices across the city, the taxi industry has emerged as a striking example of how exclusive some corners of New York have become.

On Thursday, at the city’s first medallion auction in over five years, the largest bid for a “mini-fleet” of two medallions exceeded $2.5 million, by far the highest ever recorded. At the last auction, in 2008, the high bid on a similar package was a little over $1.3 million. In 2004, the offer fetched less than $350,000.