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The brechtsche law (after Arnold break; it called it law of the progressive parallelism mentioned by expenditures and population massing) that with rising population density the public expenditures for pro head rise. The law stands thereby in close relationship for the term of the improved number of inhabitants.
This law justifies in the financial adjustment that larger municipalities receive superproportionally much money in relation to the population (gradated population key). Such keys form mostly basis of lengthy negotiations with the financial adjustment.
A possible explanation for the brechtsche law is that the Leistungsniveau of large cities is larger than in small. In addition there high costs come by a negative urbanization (e.g. Criminality).
At club goods the danger of an overstocking rises with increasing population density swimming pool). Straight one in densely populated areas is however expensive the development land for an extension of the plant.
There are however also factors those the brechtschen law works against, about that also in densely populated regions certain fixed costs exist for infrastructure. This lowers the expenditures for pro head with rising population in the region.
A larger municipality has higher expenditures for the infrastructure. One thinks of the underground in large cities, the public suburban traffic is superproportionally expensive in centers of dense development.
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