I think you guys have it backwards. The cause is the price, the effect is the difficulty.
Difficulty has almost no influence on price, because the supply of coins is independent of difficulty.
The price is the incentive of mining, and hence, of difficulty. As long as the *cost* of difficulty is below the price,
there is an incentive to mine more, which will result in higher difficulty.
When the cost of difficulty is higher than the price, mining is not profitable any more.
A miner can choose to continue and go broke, or stop the losses. Difficulty will hence decrease until
mining becomes profitable again.
The cost of difficulty as a function of difficulty is given by technological advances.
But I don't see at all how difficulty can have any influence on price.
Difficulty should follow price (with some lag), corrected for technological advances.
I don't agree. The only circumstance where difficulty would have no influence on price is one where someone could pay for the expense of mining with bitcoin. This is most likely not the case, and miners must sell the btc they mine to pay for things like electricity, which would reflect the downward pressure on BTC price. However, with a decrease in difficulty, miners are effectively producing more at the same expense, which may alleviate some of that selling pressure. How much, I'm not sure.