Why Capitalism always grow wealth ?

An idea has been bugging me for some time, so I decided to articulate it in a more formal way, here goes ....
Why Capitalism can never be a zero-sum game and why this is a law as strong as the law of supply and demand or the law of gravity. We will see why there is no option, but to expand both in material and non-material world.
To be able to explore the topic in a single article we will have to constrain the problem i.e. make some natural assumptions to simplify the problem. The major one is that we will use the purely economic definition of CAPITALISM and will distance ourselves from any political ramification. Many people assume Capitalism has something to do with governance or redistribution, we will eschew that. I'm interested in what it IS, not what it OUGHT to be.

So here is our working definition :
Capitalism is voluntary exchange with established property rights. Nothing more, nothing less.

Only in this scenario incentives align in correct manner.
Our other soft assumptions in order :

Our next task is to explore the process, the main actor of which is the entrepreneur/capitalist.
(BTW if are to be more correct Capitalist is the one providing the capital and Entrepreneur is the one implementing the idea. But here we are going to use both words interchangeably).
We start with economy which contains numerous but finite number of products.
The Entrepreneur once he decides to ACT have two options on his hands pursuing profit :

First option consequences are pretty straightforward to follow. The entrepreneur have to produce the product for cheaper price and/or better quality and below cost to make profit (dependent on time and location of the business). That is enough for now for option one.
Second option is slightly more complicated. First the entrepreneur must have the knowhow to invent a new product, without it there is no expansion process. (If we go for Ethics we may say that the entrepreneur must have the freedom to think and act, but we will proceed without that assumption for now).
Let's split the process in "stages" to frame the problem. Those stages are not so clear cut in reality, but this simplification allows us to make our reasoning more concise. The logic will still work if we blur the lines.
So he invents totally new product. Initially the number of items will be small and cost more. In most cases the Entrepreneur will reinvest the proceeds. Thus Stage 1 will characterize the establishment of market footprint.
In the second stage there will be stable production with high margin and good profit, the product is still not widespread, so there is no competition to talk about.
Because the money supply&velocity in our example are stable and based on the principle of opportunity cost any consumer who buys this new product will not buy any of the other products on the market, from which it follows that the price of all other products in the economy has to go down to compensate, same amount of money chasing more products. This has positive wealth effect for the consumer and squeezing of the margins for businesses. If a business goes bankrupt because of this squeeze then it makes a room for the benefit of the other businesses in the same niche that will now get better margins again. The market over time self regulate by pruning uncompetitive businesses to keep healthy margins but still cheaper prices.
Now he has to decide :

Sorry to spoil the party, but those were imaginary options ;). What I mean by that ? The entrepreneur has no option but to expand. Why ? Because if he have healthy margins, sooner than later competitors will enter his market.
That is why society practicing Capitalism has no choice, but to GROW Wealth ?
The pressure to grow comes from competition and new-products (keep in mind money are static), until margins are squeezed to the optimal amount.
Here by growing I don't mean Luddite meaning of the word i.e. exhausting the resources of the world, because the depletion process as we know is counteracted by the increase of the price of the product due to increase of price of resources if they become more scarce. So as long as the system is voluntary and transparent there is no worry of depletion. On top of that there is also product substitution (oil replaced whale oil, electricity replaced oil : in lighting ).
By growing I mean inventing new products and services, increasing the wealth-pie and as we will see in a second tirelessly pushing prices on known products down to bare-knuckle-cost.
So to repeat myself there is no choice, but to expand production to stage 3. This is where competition enters the scene. Stage 3 is also no-choice scenario, this time the Entrepreneur has to lower his margins no matter what. He can coast for awhile, but the moment the competition arrives he has to start slashing prices, otherwise over time inventories will be left unsold and the profit can turn into loss.
So we circled back where we started. The New-product market is now mature market, which will sustain multiple businesses and will ebb and flow to accommodate the changes on the competitive grounds.
Then finally we get to Stage 4 were the product is in mature market, where the price will be grind-ed down to oblivion. Probably over decades the product will either be almost at cost or disappear as a product at all because of superior replacement.
To rephrase my point, once an Entrepreneur enters the market the choices are taken out of him, he has to grow the Wealth-pie, it doesn't matter if his business grew or died. Once the idea of the new-product is introduced it is always there in the 'ether' to be picked by the next guy.
That is why Capitalist system can never be zero-sum. Human desires are infinite, so there is always a place for new unknown product to be invented, which then goes trough the four stages we mentioned to become mainstream. What we end up is constantly lower prices for known products driven by competition and the 'opportunity-cost' of the new products. At the same time every new product or service no matter material or immaterial by its mere existence has increased the overall wealth of every person on the planet and beyond.
If you think to object that there is limit on product creation, think again. How many new products were invented in last century, may be tens of thousands. If you skeptic and think this can't continue, may be you are the guy who will not invent new one, which prove my point i.e. you lack the imagination to create one :)
When in doubt always keep in mind the assumptions we introduced.
If we relax our assumptions about Money supply and velocity the dynamics will change, but at the core of our conclusions still hold true. All of today economies have government issued money, the prices react on the "siphoning'-principle i.e. government and its cronies are the first to benefit from the new money which from there flows in the economy. In market issued money the effect is more asynchronous where money in small amounts are generated here and there across the economy.
We can only speculate how margins spreads throughout, what we can be sure of is the tendency for lower margins in inflation corrected prices.
The only regime under which our conclusions probably don't hold is during high inflation or hyper-inflation, but this also so far has been a country-wide phenomena, the rest of the world can continue with the program.

Now for some projections. What is the consequence of our discovery of the idea of CAPITALISM ?

If left on its own devices in a matter of a century or so the process (and it is a process not instantaneous action) will give us myriad but super cheap products and services, which will require more people than we currently have to fulfill all the jobs required to provide those products.

Infinite desires ==means==> Infinite products ==means==> infinite work ==means==> infinite jobs.

At the same time the number of people involved in any particular industry will have to shrink drastically. The need to lower margins forces the need to increase productivity, which forces automation, which means less people doing the same or more work. That have been the trend so far.
In a sense the only thing that guarantee healthy balance is the ability of individuals to generate new ideas. The creation of new products pulls the job market toward itself and competition pushes jobs out of competitive markets toward new-born industries.
Last century we saw agriculture occupation follow the way of the Dodo, what is it, something like 1-2% of the population are involved in it. Next in line for the chopping block in this century is Manufacturing ...

But let me stop you dreaming ... there is an "OUGHT" to deal with.
And that is the tricky one, because it has to do with Politics and Capitalism just "IS", it does not offer us a solution to this problem. It is tirelessly churning under the hood, making our life better as long as we allow it to do its job, leaving us the harder task to solve the "OUGHT" problem, which by its nature is categorically different problem and has nothing to do with Capitalism.
On the other hand Socialism by its definition is Politico-economic idea i.e. mixes IS with OUGHT, therefore is booby-trapped with assumptions and their different interpretation. "This was not true Socialism", ... anyone :)