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Just over 10 years ago, he had a popular blog post asking can economic growth can last? A couple of days ago, he published his main arguments in a Nature Physics comment titled Limits to Growth , the full text of which you can also access here. He makes two main arguments. One relates to waste heat, and the other to physical resource limits.
At the moment this is negligible. However, if energy usage grows at 2. It is simply an illustration of a real limit. His other argument relates to physical resources. There must be some limit to our use of physical resources. You could imagine a scenario where we reach a stage where economic growth decouples from the use of physical resources. The problem that Tom Murphy highlights is that this means that economic activity associated with these physical resources will become an ever decreasing fraction of total economic activity.
However, these would be activities that are crucial to our survival, such as food and energy. He suggests that this would be ludicrous. For example, if they become effectively free, how do you stop someone from buying it all and raising the price?
What I would be very interested to hear are mainstream rebuttals to the above argument. Another could be, as the paper suggests, that the finite physical resources will always be associated with a non-negligible fraction of total economic activity. Hence, they essentially act to limit how much overall economic growth is possible. Alternatively, maybe there are ways to have continued economic growth even if those sectors associated with physical resources become a vanishingly small part of the global economy.
Economic activity could be just reselling the same physical object over and over again. For example you buy a painting, and after some time sell it.