In the following article, Historian Thomas Woods correctly points out that the "Robber Barons" of the late 19th centrury controlled huge market shares of certain industries. However, contrary to the tales that these people were monopolists, they gained their market shares by lowering prices and expanding output. Basically they out competed their competitors by providing the lowest price and best quality. Dr. Woods points out a few examples:
"Andrew Carnegie, for instance, almost single-handedly reduced the price of steel rails from $160 per ton in 1875 to $17 per ton nearly a quarter century later. John D. Rockefeller pushed the price of refined petroleum down from more than 30¢ per gallon to 5.9¢ in 1897. Cornelius Vanderbilt, operating earlier in the century, reduced fares on steamboat transit by 90, 95, and even 100 percent. (On trips for which a fare was not charged, Vanderbilt earned his money by selling concessions on board.)"
Dr. Woods continues to write, “During the 1880s, when real GDP rose 24 percent, output in the industries alleged to have been monopolized for which data were available rose 175 percent in real terms. Prices in those industries, meanwhile, were generally falling, and much faster than the 7 percent decline for the economy as a whole. We’ve already discussed steel rails, which fell from $68 to $32 per ton during the 1880s; we might also note the price of zinc, which fell from $5.51 to $4.40 per pound (a 20 percent decline) and refined sugar, which fell from 9¢ to 7¢ per pound (22 percent). In fact, this pattern held true for all 17 supposedly monopolized industries, with the trivial exceptions of castor oil and matches.”
So while the history books present the Robber Barons as monopolists, there doesn’t seem to be much evidence that they were charging monopoly prices or reducing output. In the end, most economists recognize that a certain company can control a huge market share of a given industry without being a monopolist.