Lets say that Ethereum is running at 95-100% of max tps, wich means gas price will rise. And then lets say we update the blockhain and dobble the tps. Would that lead to a halving of gas price?
The question is 3ys old. But here is my take since it is an economic question. The Ethereum network is auctioning "space in the blockchain" which is limited. In an auctioning system there is a little the tendency that prices only rises over the absolute minimum (which would be for a normal transaction 1 Gwei*21000) IF there is NOT enough "room" for everybody. Lets say a block takes about 135 tx every 13,5 seconds. If there only are 135 transactions, why would someone bid more then the minimum?
So to answer your question: If a capacity increase leads to the point that most of the time every transaction comes immediatley in the next block, prices will not half but fall to minimum.
If the capacity increase leads to a block size that not all transactions get included, then what still happens is: the number of people "left outside" is still shrinking dramatically (given that the increase in TPS is meaninfull), which are the "bidders that bid up prices". Since "the price driving force" shrunk overproprtionally, the price fall will be overproportional to capacity increase. So in your expample doubling the tps would lead to maybe 70-99% price reduction.
That is in theory. In practise many users will just take the suggestions that the wallet gives them, which in tendency seem a bit to high. In economy this difference from actual behavior to theoretical modelled behavior is called "rigidity". The lower the rigidity the more thoughtfull and flexible people adjust to the real world. In essence your question is: how high (or low) is the rigidity of the people that use Ethereum txs. Well i don't know that. But i would still assume that prices would drop more than 50%.