Between 1990 and 2000 the surfaces of each of the 120 cities he and his team studied grew on average more than twice as fast as their populations. These rates, he says, are unlikely to change. That means that the amount of urban land will double in only 19 years, whereas the urban population will double in 43 years.Note the "on average". What was the variance?
Aside from that, there should be no surprise that metropolitan areas grow outward, denoting declining average urban densities. Findings like that can still bring on fainting spells in some circles.
But the size/growth story is incomplete. The reality is much richer and much more interesting. Cities grow because they can -- when they can. They compete because most labor and capital are mobile. How do mobile factors choose where to settle? Where do they sense they can most benefit from local supply chains -- chains that involve transacting as well as chains that do not, including social ties that help incubate ideas? This means interacting with many others already there -- which involves a look at location patterns as well as interaction opportunities. There is a cost side. Land and accessibility and other costs must be noted and weighed agains the benefit assessment.
Its a cinch that most expected net benefit packages are found in peripheral areas -- as the cited passage corroborates. The fact of growth and the placement of growth cannot be separated. I have noted many times in these posts that there is no single "best" density for anything. Local conditions vary considerably and offer unique packages and solutions. It is all about the fine details of spatial arrangements, not simply overall city size.
Consider the simplest cases of land use planning. How do mall developers create site and leasing plans? Is there one "best solution?" Not likely. The profit-maximizing mall developer chooses a desired site plan from a very large combinatorial space. The favored choices vary a lot; we see very little successful cookie-cutter design. And these are just the simplest of spatial arrangement problems.