Non-trivial relationship between scaling behavior and the GDP microstructure in Indonesian cities

Urban scaling analysis has shown that various aggregated urban quantities obey power-law relationships with the population size. Despite the rapid progress, direct empirical evidence that shows how the power-law exponents $\beta$ depend on the cities microstructure has been lacking. Moreover, urban scaling studies are hardly reproduced in developing countries due to inadequate official statistics. We tackle these issues by performing urban scaling analysis on Indonesian cities using globally harmonized functional cities delineations and global-scale gridded Gross Domestic Product (GDP) datasets. First, we observe that the GDP and area of Indonesian cities scale linearly with the population size. For GDP in particular, the deviations from the scaling law follow a geographical pattern. Second, we determine the economic hotspots in each city and observe that the area of the hotspots scales mildly sublinear with the population size. Interestingly, the GDP of hotspots scales sublinearly with the population size, indicating a physical growth of hotspots that is not followed by the increasing returns due to scaling. Third, by classifying the cities based on the GDP microstructure in two dimensions (heterogeneity and spatial dispersion) and examining the scaling exponents of each class, we discover a non-trivial relation between scaling behavior and the GDP microstructure. Spatial dispersion strongly affects the scaling behavior in heterogeneous cities, while such effect is weakened for homogeneous cities. Finally, we find that the scaling effect in terms of economies of scale (sublinearity of area) and increasing returns (superlinearity of GDP) is stronger for cities with spatially compact GDP distribution.