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A city is a relatively large and permanent settlement. Although there is no agreement on how a city is distinguished from a town within general English language meanings, many cities have a particular administrative, legal, or historical status based on local law.

For example, in the American state of Massachusetts an article of incorporation approved by the local state legislature distinguishes a city government from a town. In the United Kingdom and parts of the Commonwealth of Nations, a city is usually a settlement with a royal charter. Historically, in Europe, a city was understood to be an urban settlement with a cathedral. This distinction also applies in England (but not to the entire United Kingdom), where the presence of a cathedral church distinguishes a 'city' from a 'town' (which has a parish church).

Cities generally have complex systems for sanitation, utilities, land usage, housing, and transportation. The concentration of development greatly facilitates interaction between people and businesses, benefiting both parties in the process. A big city or metropolis usually has associated suburbs and exurbs. Such cities are usually associated with metropolitan areas and urban areas, creating numerous business commuters traveling to urban centers for employment. Once a city expands far enough to reach another city, this region can be deemed a conurbation or megalopolis.

According to Vere Gordon Childe, for a settlement to qualify as a city, it must have enough surplus of raw materials to support trade and a relatively large population. Bairoch points out that, due to sparse population densities that would have persisted in pre-Neolithic, hunter-gatherer societies, the amount of land that would be required to produce enough food for subsistence and trade for a large population would make it impossible to control the flow of trade. To illustrate this point, Bairoch offers an example: "Western Europe during the pre-Neolithic, [where] the density must have been less than 0.1 person per square kilometer". Using this population density as a base for calculation, and allotting 10% of food towards surplus for trade and assuming that city dwellers do no farming, he calculates that "in order to maintain a city with a population of 1,000, and without taking the cost of transportation into account, an area of 100,000 square kilometers would have been required. When the cost of transportation is taken into account, the figure rises to 200,000 square kilometers...". Bairoch noted that this is roughly the size of Great Britain.

:(1) O = s^2, where O is the output (area protected) and s stands for the length of a side. This equation shows that output is proportional to the square of the length of a side.

The inputs depend on the length of the perimeter:

:(2) I = 4s, where I stands for the quantity of inputs. This equation shows that the perimeter is proportional to the length of a side.

So there are increasing returns to scale:

:(3) O = I^2/16. This equation (solving for s in (1) and substituting in (2)) shows that with twice the inputs, you produce quadruple the output.

Also, economies of scale:

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