6.4 The Size and Distribution of Cities

The rank-size rule says the nth-largest city in a country has about 1/n the population of the largest. So the second city has about half the largest city's population, the third about a third, and so on. A country that roughly follows it has a balanced network of cities of many sizes, and economic activity is spread fairly widely.

A primate city is a country's largest city when it's more than twice as large as the next largest and dominates the country's economy, politics and culture. Geographer Mark Jefferson described the pattern in 1939. Examples include Bangkok in Thailand, Paris in France, Lima in Peru and Mexico City in Mexico.

Primate cities are common in countries with a highly centralized government and in former colonies, where colonial powers built one main port and capital to collect and ship resources. A primate city attracts most investment and migrants, which can leave the rest of the country behind.

Walter Christaller developed central place theory in 1933, studying towns in southern Germany. A central place is a settlement that provides goods and services to the surrounding area, called its market area or hinterland. Two key terms:

• Range: the maximum distance people will travel to get a good or service. It's short for low-order goods like gas and groceries and long for high-order goods like a pro sports game or a specialized hospital.
• Threshold: the minimum number of customers needed to support a business. A convenience store needs only a few thousand nearby; an IKEA or a children's hospital needs a whole metro area.

Christaller predicted a hierarchy: many small places (hamlets and villages) offering low-order goods, fewer towns, and very few cities offering high-order goods. Market areas fit together as hexagons, because hexagons cover a flat surface with no gaps or overlaps.

The model assumes a flat, uniform plain, evenly spread population with equal incomes, travel possible in every direction at equal cost, and shoppers who always go to the nearest place. Real places have rivers, mountains, highways and uneven wealth, and people combine trips or shop online. Still, the basic idea explains why small towns have a gas station but not a stadium.

The rank-size rule and central place theory both describe a hierarchy of cities, but they explain different things: rank-size describes population sizes, while central place theory explains how settlements are spaced by the services they offer.

The gravity model predicts that interaction between two places, such as trade, migration, phone calls or travel, increases with their populations and decreases with the distance between them. A common form is: interaction = (population of A × population of B) ÷ distance². Big places that are close together interact the most. It's a useful starting point but ignores borders, language, cost and culture, which can block interaction between close places or create strong links between distant ones.