There's some important things to consider when trying to make the link between economic production and overall influence/power.
First off, there's a difference between income (i.e GDP) and overall wealth. National "wealth" gets built up over several years of high GDP, and is one of the key reason Western Europe/Russia are able to punch above their economic weight in influence, and will continue to do so for a while.
By wealth I do not just mean something as simple as financial assets sitting in some account - though that is highly useful. Rather, there are far more tangible things; infrastructure is a major one. Britain still uses quite a lot of Victorian infrastructure - railways, bridges, buildings, tunnels, sewers, plumbing - to great effect. Modernization and upkeep are necessary to be sure, but those are far cheaper than building something brand new. This also holds true for productive facilities like factories or shipyards - even if they were built 50 years ago, they can still work fairly effectively. It is also very important in terms of the "knowledge economy" - social infrastructure that can ensure human resources that are highly skilled - be it in finance, military, governance or anything else.
That allows a developed economy to channel a far greater portion of their economic production to "power" activities such as expanding their influence abroad and developing a high-tech military vis-a-vis a developing economy that would see a greater portion of activity focused either on the basic life needs of the population or on social development (building infrastructure, housing, schooling, etc) as well as a higher level of productivity for carrying out those "power" activities
A similar phenomenon happens with population; rapid growth has led to a lot of states (like Brazil) with a high population today; but the relative population weight of Russia or France was much higher over the last century, and that shines through in the various assets that have been inherited from the past.
The underlying point here is that Brazil becoming a Great Power by 1940 is not merely a matter of getting rid of the various historic setbacks, nor is it becoming a Great Power by today merely a matter of greater focus on military spending over the past decades. A state needs a high level of relative economic production over quite a long time in order to "catch up" in terms of the various military, diplomatic, economic and resource assets that translate to power. The only exceptions are when a state can project enough power by virtue of sheer size (i.e India and China having 20-25 times the population of middle powers) or when it has a high level of power across a "narrow" focus such as critical natural resources.
In 1900 Brazil had only 17m people and a GDP perhaps a thirtieth of that of the major European states. In 1820 that population was only 5m. That is a much lower base than what every other historic Great Power contender had at the time; and to this we must add the extra difficulties of lower literacy/social institutions and a large, undeveloped frontier. The fact that Brazil has come within sight of being significant power within our lifetimes is a quite significant statement of it having both outperformed many contenders and it being free of external interference.
But still, that was nowhere near enough to make it one of the greats in 1940. To do that, you'll need to ramp up immigration, industrialization and resource extraction from an early point, perhaps even during the colonial era. Perhaps a Napoleonic PoD that results in Portugal being more permanently shed of its royal court, meaning that the eventual Brazilian Empire has a much greater focus on Brazil proper and greater stability/development during the country's first century. If that results in tackling the slavery issue early it can also help with encouraging immigration (needing cheap labour) as well as provide the grandiose, centralized and long-term mindset that is needed to significantly improve infrastructure in the country. I.e, have the whole process start about 50 years earlier, make it more intensive, and prevent it from being cut short by coups and instability.
First off, there's a difference between income (i.e GDP) and overall wealth. National "wealth" gets built up over several years of high GDP, and is one of the key reason Western Europe/Russia are able to punch above their economic weight in influence, and will continue to do so for a while.
By wealth I do not just mean something as simple as financial assets sitting in some account - though that is highly useful. Rather, there are far more tangible things; infrastructure is a major one. Britain still uses quite a lot of Victorian infrastructure - railways, bridges, buildings, tunnels, sewers, plumbing - to great effect. Modernization and upkeep are necessary to be sure, but those are far cheaper than building something brand new. This also holds true for productive facilities like factories or shipyards - even if they were built 50 years ago, they can still work fairly effectively. It is also very important in terms of the "knowledge economy" - social infrastructure that can ensure human resources that are highly skilled - be it in finance, military, governance or anything else.
That allows a developed economy to channel a far greater portion of their economic production to "power" activities such as expanding their influence abroad and developing a high-tech military vis-a-vis a developing economy that would see a greater portion of activity focused either on the basic life needs of the population or on social development (building infrastructure, housing, schooling, etc) as well as a higher level of productivity for carrying out those "power" activities
A similar phenomenon happens with population; rapid growth has led to a lot of states (like Brazil) with a high population today; but the relative population weight of Russia or France was much higher over the last century, and that shines through in the various assets that have been inherited from the past.
The underlying point here is that Brazil becoming a Great Power by 1940 is not merely a matter of getting rid of the various historic setbacks, nor is it becoming a Great Power by today merely a matter of greater focus on military spending over the past decades. A state needs a high level of relative economic production over quite a long time in order to "catch up" in terms of the various military, diplomatic, economic and resource assets that translate to power. The only exceptions are when a state can project enough power by virtue of sheer size (i.e India and China having 20-25 times the population of middle powers) or when it has a high level of power across a "narrow" focus such as critical natural resources.
In 1900 Brazil had only 17m people and a GDP perhaps a thirtieth of that of the major European states. In 1820 that population was only 5m. That is a much lower base than what every other historic Great Power contender had at the time; and to this we must add the extra difficulties of lower literacy/social institutions and a large, undeveloped frontier. The fact that Brazil has come within sight of being significant power within our lifetimes is a quite significant statement of it having both outperformed many contenders and it being free of external interference.
But still, that was nowhere near enough to make it one of the greats in 1940. To do that, you'll need to ramp up immigration, industrialization and resource extraction from an early point, perhaps even during the colonial era. Perhaps a Napoleonic PoD that results in Portugal being more permanently shed of its royal court, meaning that the eventual Brazilian Empire has a much greater focus on Brazil proper and greater stability/development during the country's first century. If that results in tackling the slavery issue early it can also help with encouraging immigration (needing cheap labour) as well as provide the grandiose, centralized and long-term mindset that is needed to significantly improve infrastructure in the country. I.e, have the whole process start about 50 years earlier, make it more intensive, and prevent it from being cut short by coups and instability.