Railroads in an actual railroad monopoly only have this property at small sizes, not at the limit, because the value of new stops is decreasing as you exploit less and less economically active areas. The fact that the network that’s able to reach route N+1 includes route N doesn’t make up for the fact that no one was going to N anyway. Plus there are costs to the network of new lines, like new switches needing to be installed, the complexity of managing routes, etc. If you were a railroad exec and you had unlimited resources (so it wasn’t merely a question of the costs increasing faster than the benefits), you still wouldn’t snap your fingers and cover the surface of the earth with railroad tracks. True examples in the realm of commerce and physical items are pretty much impossible, unless you are a paperclipper.
Other things that have network effects but don’t have increasing marginal utility are markets (the marginal stock trader provides no liquidity and makes no trades), Facebook (the marginal account has no friends), telephone networks (the marginal customer makes and receives no calls), etc. Decreasing marginal utility is very universal. Even trust, which is a very good example, is probably more like one of these tipping point things rather than true in an absolute sense. The marginal value of a trust increment may always be positive, but it decreases past the tipping point.
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.
Railroads in an actual railroad monopoly only have this property at small sizes, not at the limit, because the value of new stops is decreasing as you exploit less and less economically active areas. The fact that the network that’s able to reach route N+1 includes route N doesn’t make up for the fact that no one was going to N anyway. Plus there are costs to the network of new lines, like new switches needing to be installed, the complexity of managing routes, etc. If you were a railroad exec and you had unlimited resources (so it wasn’t merely a question of the costs increasing faster than the benefits), you still wouldn’t snap your fingers and cover the surface of the earth with railroad tracks. True examples in the realm of commerce and physical items are pretty much impossible, unless you are a paperclipper.
Other things that have network effects but don’t have increasing marginal utility are markets (the marginal stock trader provides no liquidity and makes no trades), Facebook (the marginal account has no friends), telephone networks (the marginal customer makes and receives no calls), etc. Decreasing marginal utility is very universal. Even trust, which is a very good example, is probably more like one of these tipping point things rather than true in an absolute sense. The marginal value of a trust increment may always be positive, but it decreases past the tipping point.
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.