The Impact of Migration and Innovations on the Life Cycles and Size Distribution of Cities

We present a comprehensive agent-based model of a closed system of cities. The model includes two types of agents - employees and firms. Firms compete for workers and make decisions concerning what to produce and whether to adopt innovations. Individual employees make migration decisions. Some migrants become intrapreneurs when their employers adopt production process innovations that they propose. Some migrants become entrepreneurs when the product innovations that they propose are implemented by their employers in new subsidiary firms. These firms tend to be technological leaders. The decisions of individuals and of firms generate innovation-migration dynamics that generate a variety of city sizes. A city that is home to firms that are currently relatively attractive to migrating innovators experience moderate or fast growth. Because of particular decision patterns by individuals and firms this growth may decline and stop and the city may stagnate and loose workers as its relative attractiveness decreases. Cities that remain unattractive or long periods can stop growing and shrink. We model explicitly the extent to which cities attract immigrants and innovators and demonstrate that the size distribution of cities is defined by the ability of its resident firms to adopt the innovations and to let the product innovators establish technologically advanced enterprises. These decisions result in high market value of the most productive firms, of the entire industrial system the city where the firm is located and of the entire urban system.