I think it depends on how we come about the energy cost decreasing, if we have nuclear fission and it drives energy costs down it just encourages more people to participate in the network and increases security as more people are mining at cheaper costs
The price would then have to find a equilibrium between the cost to create and the need to cover those costs
If it's only bitcoin that now takes up no energy, I don't see it surviving as what does it tether itself too as a real world expense to create? The whole point of hard money is that it takes a cost to produce, a cost we could choose to produce bitcoin or produce something with a higher stock to flow than bitcoin
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If it did not cost energy there would still be limited supply of asics. So yes, the current hashrate would not change much and not suddenly.
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-FOLLOW UP QUESTION-
If it suddenly required no energy to mine bitcoin, then wouldn't it incentivize millions of people to turn on their computers at home and mine? And wouldn't the price be able to stay high because bitcoin would still be valuable in terms of its utility and finite amount?