More food grown efficiently leads to more people being able to be supported (as opposed to hunting and gathering which is a more per person method).
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The development of agriculture lead to government because people were no longer nomadic and they stayed in one place. This resulted in the need for government and services for the population of people living in the region. Religion,art, and means of protection were also the result of agricultural advances.
Since farming produces food for more people than the actual farm family, this lead to other people free to pursue other careers other than growing food. These careers not only involved building things and teaching others, but also politics and government. Farming essentially creates society, and society needs some solid base of rules and regulations that has to come from somewhere, and so the government is that body that states and votes on the rules and regulations for society.
Largely to determine population amounts by state, and population shifts. This can lead to adjustment in a states allotted number of House seats in Congress, among other things
By writing a book that proposed human suffering and death from starvation because the population of humans went up exponentially but the supply of food goes up arithmetically. Darwin took this idea as an insight. He figured that populations of organisms produced far more progeny then the environment could supply with resources. So a selective process would be put in place. The fitter organisms would survive and reproduce while this much less fit would lose the struggle for existence.