Can you show me how difficulty affects price?

Supply and demand.  Difficulty limits supply, if it drops it actually means your supply (mining income) is going up, relative to the number of miners involved.  Each miner gets more BTC, if they sell their excess it's a glut in supply.

Currently, difficulty increasing each adjustment means supply is decreasing, which causes prices to rise.


I realize it's a lot more complex than I have made it out to be, but independent of other variables it seems that a difficulty decrease would just be the first warning sign that value may be dropping.

Difficulty simply regulates the rate of supply. The hardcoded limit is static and will not change.

I understand what you are saying.  The overall supply is the same.  But supply of 50 bitcoins going to 10 miners is very different from 50 bitcoins going to 1000 miners.  If difficulty goes down it means there are fewer miners, as such supply of bitcoins going to each miner goes up.  The supply per miner is directly affected by difficulty, and it's really more important than global supply in this case.
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Why does it matter if it goes to 10 miners or 1000 miners?  Why is that more important?

The overall dispersion of bitcoins doesn't matter unless you are positing that localized concentrations mean immediate trading pressures. For some of these bitcoins, they will be spent, saved, etc.. Doesn't guarantee they will be put into the market and traded.

Could go either way, I'll admit.  But part of me thinks that miners make up a certain percentage of the bitcoin community.  If say, 25% of the miners quit, resulting in a difficulty drop, that could be an indicator that 25% of the bitcoin community as a whole lost interest, which also means fewer buyrs and speculators.

The other aspect is personal needs, expectations, and diminishing returns.  If you are mining 10 BTC a week and making a profit, and suddenly difficulty drops such that you are now mining 20 BTC a week, you have a few possibilities.  You can try to keep selling at the same value and make double your profit, but you know all you competitors (other miners) also have a sudden doubling of bitcoin income, so you might want to reduce your price a bit, since if you made a profit before you could now sell for half the price and make that same profit.  Where you might not be willing to sell so cheap in the previous week.

Part of the problem with difficulty growth at the moment is a lack of availability on the top end AMD GPUs. I'm not sure if miners bought the majority of those high end cards or if they were just the straw that broke the camels back. Either way the lack of any for purchase is slowing network power growth.

Oh no!  Don't tell me people are hoarding graphics cards now...that'll send the graphics card economy into a deflationary death spiral straight to hell. 

I think difficulty is at least somewhat of an indicator of demand for bitcoins (because miners do not sell everything they mine).  However, there are plenty of other factors affecting difficulty (ie. graphics card supply as mentioned) that would confound such a simple analysis as "difficulty going down is an indication of demand for bitcoin is going down."  I would also suspect that infrastructure available to people for mining could also be constraining growth (I live on the hairy edge of tripped circuit breakers myself).  It's summer on the northern hemisphere (where most miners are located), so cooling becomes a bigger problem.  And, it's entirely possible that people could conclude that they are better off investing in bitcoins directly or that investing in bitcoin related business is more profitable than mining, but their interest in bitcoin is unaffected.  

All of this means that while I think difficulty partially reflects bitcoin demand, making predictions about the future value of bitcoins based on mining difficulty is problematic.  It's more likely that the temporary leveling off in price at around $8-$9 caused a slight moderation in difficulty growth with a bit of time lag...I wouldn't be surprised if this recent run up to $18 triggers another wave of difficulty growth (assuming people can obtain graphics cards).  

Why would they decide to sell them all?  Why not just keep the extra ones?  If you need to sell 2 to recover costs, and can save the rests, having fewer miners would have *fewer* on the general market since now instead of 80% being held, 90% are.