Academic geographers use remote sensing techniques to measure the "footprint" of growing cities. From outer space, you can identify how much land area a metropolitan area such as Cairo or Boston takes up and how this changes over time. Researchers such as Yale's Karen Seto track these footprints.
Today's NY Times has an article focused on urban growth in the Amazon Brazil's new cities. In this case, there is a significant global environmental externality associated with urban growth. Why? Don't forget the concept of opportunity cost. The land that is urbanized used to be tropical forests and these forests sequester significant amounts of carbon dioxide and this reduces global GHG emissions. As these cities grow, a type of increasing returns to scale takes place and such growth may stimulate even more growth. This is likely if the growing cities have increased political clout and can attract national subsidies for new infrastructure such as roads.
Given that there is a global negative externality associated with Amazon urban growth, what is good public policy? Should the United Nations collect global funds and pay the Brazilian government to encourage urbanization away from the Amazon? Should the UN help the Amazon cities to grow vertically so that their land footprint doesn't grow? Cities such as Singapore and Hong Kong have shown how millions can be stacked in relatively small land areas. Have urban planners in LDC nations been thinking about how to build vertical cities so that the city can achieve the win-win of urban growth without embodying a large land footprint?
The incentive problem here is the property rights and protection for the Amazon's forests. These are global public goods. If these were private property, the owner would internalize the $ benefits the world enjoys from carbon sequestration and he would be paid for these benefits. Right now, the world is free riding on Brazil and the self interested urbanites in these growing cities have no incentive to internalize the externality their urban growth causes. Public property gets trampled. Even hippies now understand why we need fences.