People trying to justify the recent Republican tax plan often talk about the importance of long run economic growth. And you can see how, if that were true, it could be a really important argument. The difference between 2% and 3% annual growth over a hundred years would be a factor of two and a half. If that sort of change were really possible it would justify quite a bit. Even if all that extra growth went to rich people then even at the new, lower, tax rates that would be much more tax money available for social programs.
Sadly there's no way cutting taxes could have such a large effect in the US.
The theory behind the cuts is that people become more productive when they've got more or better machines. Machines cost money, so leaving businesses more money to buy machines will make them more productive. More machines leads to more money leads to more machines in a virtuous cycle. Except that in a developed economy it's often very hard to figure out how to usefully add more machines.
At work I mostly use a computer. Giving me a second computer might increase how much I get done by a bit, but it wouldn't increase it very much. Diminishing returns is a fact of life and finding ways to usefully spend money increasing productivity is hard. Some people are working at companies where they have to make due with 20 year old computers and it's quite possible that they would work faster if they could upgrade. But that's not typical in the US. It does exist and there are cases where extra money can result in research that yields better computers for everyone. This is why we try to slant the tax code to favor investment over consumption. But again expecting lower taxes to increase growth by a large sustained amount is wrong.
There are cases, not in the modern US, where it can play out like that. If you happen to live in a country that's pretty poor and where most businesses don't have the latest technology then you could quite plausibly have huge growth rates based on money to machine to money virtuous cycles. That's what's happening in China right now. It also happened in Japan 50 years ago. If there's some other country that's figured out how build awesome machines you don't have yet then you might very well find yourself limited by how many of them you can buy - though you might also have other problems that are more pressing.
In this case what you really want to do, as a government interested in growth, is to increase the rate savings rate, how much people invest relative to how much they consume.
One strategy for this, pursued by prewar Japan, is to just tax poor people and give out the money as business loans. Even today richer people save more of their income and that was more true when you have a population of peasants without access to banks.
The early 19th century US didn't have quite the bureaucratic sophistication of late 19th century Japan but managed to do something similar. By introducing tariffs that raised the price of imported cloth and other goods they indirectly increased the profits of factory owners, allowing them to invest more by buying pirated copies of machines already in use in Britain. It's much easier to apply taxes at single ports of entry on obvious things like ship arrivals than it is to do something like an income tax.
The early 20th century Soviet Union took this approach to new extremes. Most new machinery in the early days was paid for by selling grain abroad. The need to more efficiently expropriate grain was part of the reason for the drive to collectivize agriculture. Big centralized farms are again much easier for the state to manage than lots of little spread out farms. Sometimes there was mass starvation but the country industrialized rapidly.
You might have noticed that China's economy has been growing rapidly recently but there hasn't been a lot of mass starvation. As far as I can tell the main difference was that they jump-started things with foreign investment These days the trillions in domestic savings drown out the $100 billion or so in foreign capital but when the current boom was starting money from Taiwan, Japan, etc was crucial. This seems like a far more human way of jump-starting growth than the other methods above.
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