In theory yes, but in practice it’s a bit more complicated than this.
1) There is 3 sectors of the economy. Primary is natural resources, Secondary is production and Tertiary is services. The first two are limited by resources so indeed you are right that continual growth is impossible. But for the tertiary sector the limiting factor is human resources. In that case, more humans mean more people to receive and provide services. It’s not 100% true because even services will need some natural resources and manufactured goods, but to a lesser extend. Developed economy are in majority made up of the tertiary sector (70%+).
2) Resources are indeed finite, but there is a LOOOOT of resources. Far more than we would realistic need. We currently extract about 90 billions of tons of material from the earth, but the earth is freaking massive. At our current pace we would need 16 quadrillion years to run out of Uranium, 2 quadrillion years to run out of copper and 234 quadrillion years to run out of silicon.
Now obviously, we can’t extract all of what exist on earth. Some material will just never be accessible no matter what, but it give you a scale of what we are talking about. We find more source of material, we develop new technology to reach new sources of material, we find alternative material, alternative method of extraction can become financially feasible as price of certain material increase, we find new way to recycle material or decrease the need of specific material. So the question to you question depend only on weather or not our technology progress can keep up with the increase in demand. And if it can’t, can we find alternative.
And then you need to take into account our solar system. The asteroid belt for example is just a fraction of the mass of the earth, but most of it’s material is far more accessible than on earth. You have the moon, other planets and satellite. We might not be able extracting those resources right now, but do we really believe that it will be impossible to ever do so? The moment certain material would be profitable to extract from asteroid, we will do it. And if we don’t have the tech, we will develop it. Might take a long time, but I have no doubt that it will eventually happen.
Now will there be moment of lag better the moment we start running out of specific material and the moment we can develop new technology that would resolve that scarcity? Probably. Could our constant hunger for more resources might create more harm in other sector? Probably. And could there ever be a moment in the future were limiting our constant growth might be the better alternative? Maybe.
It’s a complicated issue. But what is sure is that we have at our reach more than enough resources for the entirety of the human future. What is important is our technological capability to get to those resources and what is the cost of doing so.
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