As the difficulty increases, more potential investors will invest into bitcoins directly instead of mining, thus increasing the price.
Also as the difficulty increases, miners will begin to sell their mining equipment, usually in exchange for bitcoins. This increase in demand for bitcoins helps drive the price up further.
This would be true if people were trying to get a certain amount of bitcoins. If I wanted to get 50 bitcoins, I could mine or buy them. But I'm not aware of anyone who actually thinks this way. Anything that is priced in Bitcoins tends to fluctuate in BTC price based on the trade rate.
I cannot speak for those who don't do their homework. There are a lot of miners who don't like risking money, but have the equipment, so they will go after free money. There are a few people who calculate between buying mining equipment and buying coins.
What matters more is the difficulty/price ratio. If the price is very high compared to the difficulty, people will mine rather than buy. If the ratio is the other way, less will mine and more might invest.
What happens when the difficulty rises? It does what you describe and makes mining less profitable and might make someone invest in coins. Anyone investing in coins for this reason is making a pure speculation play, since they anticipate the price of coins to rise.
Therefore, difficulty drives price, though not with as much influence as much as price drives difficulty.
I believe the rush about a month ago from $1.XX to $8.00 was a slight bubble, driven by speculation. The following decline in value was due to more investors investing in mining equipment than bitcoins directly, compared with historical values. Now, as the difficulty level is catching up, and investors realize that profitability in mining may not remain for much longer, they have switched back to investing in bitcoins directly, driving the price back up.
Who cares?
Any investor should care. If difficulty drives price, even to a small extent, then price can be predicted, on average, to go up as difficulty goes up.
Thoughts? Comments?
It's a decent theory, although we need to look at the ratio of price to difficulty. When I did the calculation, difficulty was at 60k and price was $3.50. At that point, the difficulty was considerably less than the expected price. I wish I still had my spreadsheet, but it was quite a bit off (I think the expected price would have been $1.80).
I think you are right in another regard- difficulty increases tend to correspond greatly with increased interest in BTC. So while not cause and affect, but if there is more interest, either that interest is going to increase the difficulty or increase the price, or both. If a lot goes toward increasing difficulty, the next wave may decide going for the coins themselves is a better approach. So we see that increased interest and investment leads to one of the two or some combination of both increasing. If one goes up too fast, you see a swing to the other one in the next batch of investment.
The supply affects demand, but the total daily new supply tries to remain constant (it doesn't in reality- in a growing hashing power, the beginning of difficulty periods are slower than the end by a lot).