Money that is saved can be A). Used by the person retaining the wealth for investment in his own means of production. B) saved in a bank account, where it allows the bank to make business and private loans to other people coming up who need the capital for their own investments.

As there's more investment in the economy, demand for materials, education, resources, and labour increases. the higher demand on these economic resources drives the price of the resources up.

It's not actually putting the horse in from of the cart. You lift the horse and cart at the same time. Investment does correlate growth in every economic model that's used.

Here's the biggest problem with it for a society's perspective. As technology has increased automation has taken over many of the roles that would be done by workers. Without the increased demand for labour that increased investment and production brings wages could actually fall instead of rise. Then the horse isn't rising with the cart as you say.

Now eventually as automation moves up the wealth generated goes to a very few select individuals who own the means of production. It's the primary reason for the huge wealth gap in many nations right now.

Say we get to a point where we can produce so much and with say only 10 million workers are needed in a world with 8 billion people. That's the direction we are very quickly heading to.

There's a form of economic system being discussed amount academic economists that is trying to answer these questions.

Please please give this article a read: Its how in the future our level of production will be so high and done by so few workers that there has to be a shift from capitalism. It's the best written article for basic income theory I've ever found.

https://medium.com/@RickWebb/the-economics-of-star-trek-29bab88d50