NEW YORK — Two New York taxi medallions — aluminum plates that grant the right to operate a yellow cab — changed hands this week for $1 million apiece, the highest recorded sale since the city’s modern livery system began.

The sale was the culmination of decades of astonishing growth for the humble medallion, which is nailed to the hood of every yellow cab in the city. When New York issued its first batch of medallions in 1937, the going price was $10 even, or $157.50 in today’s dollars.

Some perspective: The Dow Jones industrial average has risen 1,100 percent in the past 30 years. In the same period, the value of a medallion is up 1,900 percent. That return beats gold, oil and the American house.

“It’s a lot of money, and it is an investment that someone would not make without being confident in the industry and the future of the city,” said David Yassky, chairman of the city’s Taxi and Limousine Commission.

The million-dollar sale was hatched this year, when a taxi financing specialist named Nat Goldbetter received a visit from an old acquaintance looking to sell two medallions bought for $80,000 apiece in the 1980s. There was an offer that valued each medallion at $975,000, but the seller was hoping for more.

With many owners reluctant to sell these days, hoping for the value to keep rising, Goldbetter figured he could find a willing buyer. The papers were signed Wednesday morning.