Tell Me the Growth Rate
Suppose half of the sectors of the economy grow forever at 4%, while the rest completely stagnate. I’m strongly tempted to say that this economy’s growth rate equals 2% forever. Anyone tempted to disagree? If so, why?
Before you answer: Would it matter if the 4%-growth sectors were all in “virtual reality” – and the stagnant sectors were for actual food, shelter, cars, etc.? If it matters, why does it matter?
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If half of the sectors are growing and half are not, the "better" half will become a larger and larger fraction of the economy. So the growth rate of the overall economy will asymptotically approach 4%.
I know nothing about macro but that sounds unlikely, but that's still how I interpret your question.
The growth rate will gradually approach 4% as that sector more and more dominates. And no, it doesn’t matter, economically, if the growth sector is virtual (however defined).