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If a country was to turn to a steady-state economy (or circular economy) where there is neither economic nor population growth with time, and there is no natural resources being added to the system while still being provided with the energy (say dependence on solar energy), would this economy still have the same GDP as it did when it was not a steady-state economy?

I ask this question because I read that in a steady-state economy, that "the rate of profit would tend to fall and investment opportunities would diminish" and this therefore will result in lower wages and more competition. So would this result in the reduction of the value of goods and services that this country is having compared to the time when it was a normal growing economy?

EDIT: I just thought that my question can be rephrased in a simpler way: If the economy was/became a zero-sum game, would people still work as much as they do and generate the same GDP?

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Smith pointed out that as wealth was growing in any nation, the rate of profit would tend to fall and investment opportunities would diminish.

Source

The first half of the sentence makes it clear that this is not about steady state economies, as wealth is still growing.

my question can be rephrased in a simpler way: If the economy was/became a zero-sum game

No, this is not a rephrasing of your question. Steady-state economies are not zero-sum games. It is possible that every day I milk my goat, you harvest some corn, and we trade half of our goods for the others. There is no growth here, total production is always the same, yet the trade was win-win.

would this economy still have the same GDP as it did when it was not a steady-state economy

Possibly? Without additional information, this is an impossible comparison. If you are saying that all industries were just as active plus there was also mineral extraction, then of course the added value of mineral extraction increases GDP, but this is by definition.

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