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Urban economies are composed of diverse activities, embodied in labor occupations, which depend on one another to produce goods and services. Yet little is known about how the nature and intensity of these interdependences change as cities increase in population size and economic complexity. Understanding the relationship between occupational interdependencies and the number of occupations defining an urban economy is relevant because interdependence within a networked system has implications for system resilience and for how easily can the structure of the network be modified. Here, we represent the interdependencies among occupations in a city as a non-spatial information network, where the strengths of interdependence between pairs of occupations determine the strengths of the links in the network. Using those quantified link strengths we calculate a single metric of interdependence–or connectedness–which is equivalent to the density of a city’s weighted occupational network. We then examine urban systems in six industrialized countries, analyzing how the density of urban occupational networks changes with network size, measured as the number of unique occupations present in an urban workforce. We find that in all six countries, density, or economic interdependence, increases superlinearly with the number of distinct occupations. Because connections among occupations represent flows of information, we provide evidence that connectivity scales superlinearly with network size in information networks. [ABSTRACT FROM AUTHOR]

Medieval European urbanization presents a line of continuity between earlier cities and modern European urban systems. Yet, many of the spatial, political and economic features of medieval European cities were particular to the Middle Ages, and subsequently changed over the Early Modern Period and Industrial Revolution. There is a long tradition of demographic studies estimating the population sizes of medieval European cities, and comparative analyses of these data have shed much light on the long-term evolution of urban systems. However, the next step—to systematically relate the population size of these cities to their spatial and socioeconomic characteristics—has seldom been taken. This raises a series of interesting questions, as both modern and ancient cities have been observed to obey area-population relationships predicted by settlement scaling theory. To address these questions, we analyze a new dataset for the settled area and population of 173 European cities from the early fourteenth century to determine the relationship between population and settled area. To interpret this data, we develop two related models that lead to differing predictions regarding the quantitative form of the population-area relationship, depending on the level of social mixing present in these cities. Our empirical estimates of model parameters show a strong densification of cities with city population size, consistent with patterns in contemporary cities. Although social life in medieval Europe was orchestrated by hierarchical institutions (e.g., guilds, church, municipal organizations), our results show no statistically significant influence of these institutions on agglomeration effects. The similarities between the empirical patterns of settlement relating area to population observed here support the hypothesis that cities throughout history share common principles of organization that self-consistently relate their socioeconomic networks to structured urban spaces. [ABSTRACT FROM AUTHOR]

The factors that account for the differences in the economic productivity of urban areas have remained difficult to measure and identify unambiguously. Here we show that a microscopic derivation of urban scaling relations for economic quantities vs. population, obtained from the consideration of social and infrastructural properties common to all cities, implies an effective model of economic output in the form of a Cobb-Douglas type production function. As a result we derive a new expression for the Total Factor Productivity (TFP) of urban areas, which is the standard measure of economic productivity per unit of aggregate production factors (labor and capital). Using these results we empirically demonstrate that there is a systematic dependence of urban productivity on city population size, resulting from the mismatch between the size dependence of wages and labor, so that in contemporary US cities productivity increases by about 11% with each doubling of their population. Moreover, deviations from the average scale dependence of economic output, capturing the effect of local factors, including history and other local contingencies, also manifest surprising regularities. Although, productivity is maximized by the combination of high wages and low labor input, high productivity cities show invariably high wages and high levels of employment relative to their size expectation. Conversely, low productivity cities show both low wages and employment. These results shed new light on the microscopic processes that underlie urban economic productivity, explain the emergence of effective aggregate urban economic output models in terms of labor and capital inputs and may inform the development of economic theory related to growth. [ABSTRACT FROM AUTHOR]