When the cost of land is too high, cities tend to expand upwards instead of outwards, as is the case, for instance, in Manhattan Island. However, most US cities expand outwards as there is usually plenty of land available.
Another factor that determines the manner in which a city expands is the geological characteristics of the territory that would require cheaper or more expensive construction materials. In areas which are very complicated in terms of geology, constructing tall buildings would require costly technology and materials and hence this type of expansion is very unprofitable if compared with expading outwards.
