In the case of a monopoly on something (railroads aren’t really the greatest thing to have a monopoly on, because taking the train has so many substitutes—the ideal would be more like water and air), the number of sources that you wish to own is “all of them.” If you lose even one source of that something, that’s quite bad, worse than losing the second.
In general, there are two ways of avoiding the un-realism of increasing marginal utility—either have there be some upper limit on the valuable stuff that prevents it from getting out of hand, or have the marginal utility only be increasing within some common domain but decreasing eventually. A monopoly is more like the first of these than the second.
But a monopoly wanting all of something isn’t the same as increasing marginal utility, it just means that marginal utility is always positive. For increasing marginal utility it has to be the case that each unit increases the value of the monopoly more than the last unit. Once a network has become large enough, you can ignore the existing network for the purposes of comparing the marginal utility of additional nodes in it. For monopolies that aren’t based on network effects but pricing power, you get most of the pricing power at market shares significantly less than 100%. So there is some market share increment where you get the benefits of monopoly pricing with your normal cost structure, and the next market share increments don’t allow you to increase your prices but still have your cost structure in place, ergo they have a marginal utility less than the monopolizing increment.
In the case of a monopoly on something (railroads aren’t really the greatest thing to have a monopoly on, because taking the train has so many substitutes—the ideal would be more like water and air), the number of sources that you wish to own is “all of them.” If you lose even one source of that something, that’s quite bad, worse than losing the second.
In general, there are two ways of avoiding the un-realism of increasing marginal utility—either have there be some upper limit on the valuable stuff that prevents it from getting out of hand, or have the marginal utility only be increasing within some common domain but decreasing eventually. A monopoly is more like the first of these than the second.
But a monopoly wanting all of something isn’t the same as increasing marginal utility, it just means that marginal utility is always positive. For increasing marginal utility it has to be the case that each unit increases the value of the monopoly more than the last unit. Once a network has become large enough, you can ignore the existing network for the purposes of comparing the marginal utility of additional nodes in it. For monopolies that aren’t based on network effects but pricing power, you get most of the pricing power at market shares significantly less than 100%. So there is some market share increment where you get the benefits of monopoly pricing with your normal cost structure, and the next market share increments don’t allow you to increase your prices but still have your cost structure in place, ergo they have a marginal utility less than the monopolizing increment.