Brazil's only capital rich land lies to the south, near the border with Uruguay. All other lands are more capital poor because of temperature and challenging geography. The United States is a massive power because it controls the mississippi river system, which is the largest interconnected river system in the world. Rivers are like veins for countries. They make it easier and cheaper to move goods and products around, which makes it more profitable to do so. Not only this, but overlaying the mississippi is the second largest piece of arable farmland on the planet. The combinations of an excess of capital rich lands, a large river network, and an absence of enemies allowed the US to grow into the strongest industrial power. Once it gained access to the pacific ocean, it was able to project power both east and west, making it a global superpower. Brazil has none of these advantages. Brazil is large in physical size, but has little else. Even the lands of the interior that are not jungle require extensive fertilization and clearing to be profitable, and maintenance must be continued regularly to keep them profitable. The US is successful simply because it holds the best lands with the fewest constraints. Brazil isn't because it holds only a small region of capital rich land and faces many constraints.

But geography isn't the end of the road. Argentina by all accounts SHOULD be a great power having the best lands in South America...but it isn't.

I am just going to address differences in the two "variables" you listed.

1. European settler nations

With the exception some of the British colonies, European nations were incredibly exploitative of their colonies. This resulted in them never developing the nation past what was necessary to extract natural resources/control the colonies' ports. Mercantilism was centered around the belief that countries should extract as much wealth from colonies (in terms of selling manufactured goods for resources then using the money to subsidize domestic manufacturing.) Thus the longer a country was a colony the more the development of that country would be delayed. This gives an advantage to the US.

2. Economies with slave basis (I am going to also talk about plantation based economies in this response, as they often go hand and hand with slavery and stagnant growth within plantation economies is worsened by slavery.)

Generally, non subsistence based agriculture can cause economies to suffer from the paradox of plenty. Businessmen/states can easily extract wealth/power by controlling natural resources, this prevents them from investing in improving capital (including human capital.) This is worsened by slavery as it artificially lowers labor prices. The two main impacts of low labor prices are that labor intensive agricultural processes are subsidized and that incentive to improve efficiency is reduced.

To examine how damaging slavery and plantation heavy economies are too long term growth I think one just has to compare the northern and southern states before the US Civil War. The Southern economy was built around cotton. The profitability of cotton diverted capital from manufactoring towards plantations. Additionally, plantations generally require a lower level of infrastructure and human capital than manufacturing (think paradox of plenty.) Although in the short run cotton made the South wealthy, there was almost no growth from it. In contrast, the investments in human capital, infrastructure, and manufacturing that the North made caused the economy of the North to eventually surpass that of the South.

Brasil, economically, was similar to the Southern States, which didnt really rise economically until the fall of cotton.

If you're interested in this area I would recommend "The Political Economy of the Cotton South: Households, Markets, and Wealth in the Nineteenth Century."

Thank you for the answers, this was very interesting to learn about.

From a thread a while back:

A nitpick: you can observe from Maddison's figures that when Brazil obtained independence the 1820s, it was already dramatically poorer than the United States, with Maddison estimating it to have half the population and (atop that) half the GDP per capita (this is including estimates for native populations and other colonies in the modern borders of Brazil and the US).

At $646 this is basically in the ballpark of Maddison's estimates for China (600), Japan (669), and Indonesia (612) per capita GDP in 1990$ in 1820 (for context: US 1257, France 1230, UK 1707). The US was already well into industrial takeoff. Brazil would roughly take another century to reach the level of per capita output that the US had in 1820.

(The World Economy, A Millenial Perspective. Don't take the exact numbers too seriously, they are estimates warped by additional purchasing power estimates)

So, they were not quantitatively similar. I can also recommend /u/tiredstars answer on that thread.

It's not only the quality of your land, it's what you want of it: Brazil and United States have a extremely different approach to the use of their land. It all comes down to the treaty of Tordesillas.

• USA, since the beginning, has been looking to expand to the west. It was eventually completed and the land inbetween both coasts would be valorized and integrated thanks to its extraordinary qualities that other redditors detailed.

• Brazil, from the beginning, was shaped by the treaty of Tordesillas: the idea that there is an imaginary line, somewhere to the west, that can't be crossed, because after, it's spanish land. Brazil never try to occupy its interior land, and it still doesn't. They kept stuck to the coasts.
  The portuguese were a nation of sailors and merchants. They were interested in making coastal cities in Brazil to trade with them (first slaves in, sugar out, and then mining, then coffee). The coastal lands were perfect for growing sugar and coffee, so why go further in the land? It took the discover of gold in Minas Gerais, in 1690, to make brazilians make a little step inside their country and start to really populate a non-coastal land. Minas Gerais would prosper but that was it.

Brazilians didn't really try to go further in, so much that the government would take measures and create planified capitals from scratch to finally move the gravity center to the west. So they made Teresina (1832), Belo Horizonte (1897) and even the nation capital, Brasilia (1960). Even after those efforts, most of the population lives on the coast (study from IBGE) .

So even if Brazil was granted with a huge piece of fertile land, there was never a will to fully use it.

I'm reading "Why Nations Fail" at the moment. The book's main premis is that countries with extractive institutions don't do as well as countries with inclusive institutions. Brazil started as a slave colony with a small elite controlling all economic and political institutions. The US lacked any enslavable natives and its settlers forced the development of inclusive institutions. The US continued along a virtuous cycle of more and more inclusive institutions. Brazil never developed this until very recently. The elites there were doing everything they could to hold on to power. They feared any changes to make things more inclusive would threaten their grip on power.