Actually, it was jets in general that allowed the masses to fly cheaper, especially 707 and, the DC8.
The 747 did increase the ability of the airlines to decrease air fares.
people.hofstra.edu/geotrans/eng/ … 3c4en.html
War again encouraged the rapid growth of air transportation. Indeed, it was only after World War II that air transportation became the dominant mode of long-haul passenger travel in developed country markets. In 1956, more people traveled on intercity routes by air than by Pullman car (sleeper) and coach class trains combined in the US. In 1958, airlines carried more passengers than ocean liners across the Atlantic for the first time. Even more momentous, in October 1958, the Boeing 707 took its maiden commercial flight. The 707 was not first jetliner, but it was the first successful one. The 707 and other early jets, especially the Douglas DC-8, doubled the speed of air transportation and radically increased the productivity of airlines (Davies, 1964) which enabled fares to fall. Just a few years after the 707s debut, jet service had been extended to most major world markets [Figure: Pan Am Jet Service].