Sorry, but no. It's an equilibrium that sits on those three things (cost for a GH/s of mining power, price of btc in $, difficulty). What we have seen recently is price driving difficulty, but difficulty rising above a certain threshold (determined by a ratio of price and cost of GH/s) can cause rising price to cause an alignment to the ratio (because nothing in the market is making cost of GH/s lower in that ratio). This has happened clear twice as far as I've seen, and is probably happening again with the 50% increase soon.
Explain to me the mechanism behind difficulty having an effect on price. Because I cannot come up with any explanation for it since the same amount of BTC are produced regardless of difficulty. The supply is completely independent of the expense of mining. Just because it's more expensive to mine now doesn't mean that you can get more $ for BTC...
I'm just going to quote from another post of mine where I was talking about the exchange price at $200/btc and $5/btc.
"Something to note is that there is a bit of a difference in demand in these two scenarios. People don't have a demand for btc, they have a demand for the transaction. Let's say they want to use btc to buy a spot troy oz of silver ($36.25). In the first case they need .18 btc, in the second case they need 7.25 btc. Even though the real demand is the same, the nominal demand for btc is higher when the price is lower."
People keep confusing nominal demand for real demand, and I don't get why.
And another thing, an increase in difficulty represents a relative increase in cost to the miner (in both operational and opportunity costs). An increase in costs to the supplier translates into a rightward shifting supply curve. Remember supply is btc as a function of dollars, so higher doller costs means lower btc supply.
You don't seem to understand where prices come from in the aggregate market.
I have to first tackle the last part of your post, or what follows won't make sense. BTC supply is not affected by anything - it is fixed at ~6.7 million BTC in the short term and the rate of increase is fixed at ~2000 blocks per 2 weeks (given steady network hash power). The only thing that changes is the QUANTITY supplied, which is a function of price. The supply curve itself does not move (well, moves to the right at 2000 blocks per 2 weeks).
The demand for BTC is derived from the demand of doing transactions with it and from speculating (it's not really investing at this point, too risky). There most certainly is a demand for BTC. Any good or service (currency included) has a demand and a supply. Even if people only value the transaction, BTC is needed for the transaction, and thus there is a derivative demand for BTC.
Like I said before, price is determined by the intersection of supply and demand. The equilibrium price is the one that clears the market - everyone who wants to buy for more than that $ amount has been satisfied, and everyone who is willing to sell for less is also satisfied. For the price to reach $200/BTC, there has to be a LOT of demand because he supply is fixed.
To give an analogy, let's say there is an island that has 100 rocks, which the islanders use as currency. If there are 100 islanders, each one can have a rock on average. If there are 200 islanders, each one can only have 1/2 of a rock. The real value of a rock has increased DUE TO increased demand. This is the exact mechanism behind BTC dollar price in the long run (short run there's all kinds of speculation etc).
In your example, the real demand for BTC cannot be the same on an aggregate level. There can be only one price that clears the market (law of one price) for any given levels of supply and demand. Since the supply is fixed, demand must be different in your example.
Here's my visual for this, courtesy of MS paint:
Notice that the quantity of BTC traded for dollars depends on the demand for BTC. A move from low demand (D1) to high demand (D2) increases both the quantity sold of BTC and the dollar price of BTC. Difficulty or whatever else variable you want to throw in does not have any bearing on the dollar value of a bitcoin. Everything depends on how much people want to have bitcoins vs. how much people want to have dollars.