Starting in the late 20th century, the Brazilian federal government created several programs to increase the access to water and sanitation. However, although these programs made improvements in water access, sanitation was generally overlooked. While water supply, and waste collection are available in the majority of the Brazilian municipalities, the sewage system is still spatially concentrated in the Southeast region and in the most urbanized areas. The Southeast region has roughly 42% of Brazilian population and includes the cities such as Rio de Janeiro and São Paulo.
In order to explain this spatially concentrated pattern it is frequently assumed that the size of cities does really matter for sanitation services provision, specially for sewage collection. As a matter of fact, as cities grow in size, one should expect economies of scale in sanitation infrastructure volume. Economies of scale in sanitation infrastructure means a decrease in basic sanitation costs, proportional to the city size, leading also to a (expected) power law relationship between the expenditure on sanitation and city size. Using population, N(t), as the measure of city size at time t, power law scaling for infrastructure takes the form where , Y denotes infrastructure volume and is a constant.
Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have (increasing returns), whereas those accounting for infrastructure display (economies of scale).[1][2][3]
We verified this relationship using data from Brazilian Federal Government databases, denominated Integrated Planning and Budgeting System, and referred to hereinafter as SIOP. Preliminary results show decrease, proportional to the city size, in federal grants-in-aid to municipalities to help finance public sanitation projects. For the initial budget allocation, was found to be roughly 0.62 for municipalities over twenty thousand inhabitants; to be roughly 0.9 for municipalities over twenty thousand inhabitants; and to be roughly 1.15 for municipalities over fifty thousand inhabitants. For the expenditure commitments, was found to be 0.43 for municipalities over two thousand inhabitants; to be roughly 0.58 for municipalities over twenty thousand inhabitants; and to be roughly 0.6 for municipalities over fifty thousand inhabitants.[4]
References
[1] Bettencourt, Luís MA. The origins of scaling in cities. Science, v. 340, n. 6139, p. 1438-1441, 2013.
[2] Batty, Michael. Cities as Complex Systems: Scaling, Interaction, Networks, Dynamics and Urban Morphologies, 2009.
[3] Bettencourt Luis MA. Urban growth and the emergent statistics of cities. Science advances, v. 6, n. 34, p. eaat8812, 2020.
[4] SIOP. https://www1.siop.planejamento.gov.br/painelorcamento/