But I'd guess there will be huge inital drop when the few batches of ASICs from both AVALON and BFL will hit the public after mid of this month.
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That's not how Bitcoin works. Increasing the hashing power on the network does not significantly increase the amount of bitcoins that "appear". It only affects who gets the bitcoins that were already going to "appear". Every 2016 blocks the protocol automatically adjusts the target difficulty to attempt to keep the total number of blocks found by the entire network around 144 blocks per day.
Lets take a look at some numbers:
The next difficulty change is due to occur at block 231840
At that time there will be 11,046,000 bitcoins in existence
If no new hashing power comes online for 2 weeks after that, there should be 2016 blocks solved and a total of 50,400 bitcoins will "appear".
This is an increase of 0.4563%
If enough ASIC instantaneously come online to double the entire network hashing power the exact moment after the 231804'th block is solved, then the difficulty won't have adjusted enough and the next 2016 blocks will occur twice as fast as normal. At the end of one week 2016 will have been solved, and the protocol would then double the difficulty. Therefore during the remaining week 1008 blocks would be solved for a total of 3024 blocks and a total of 75,600 bitcoins will "appear".
This is an increase of 0.6844%
At that time, due to the increase in difficulty, the network would return to 2016 blocks per week.
In this highly unlikely scenario of a complete instantaneous doubling of the entire network hashing power in a precise single moment immediately after the next difficulty change, there is only an extra 25,200 bitcoins that have come early. Only a 0.2271% increase over the expected supply of 11,096,400.
It is far more likely that ASIC will come online spread out over several weeks giving the protocol time to keep up with the increase in hashing power by continuously adjusting the difficulty target. As a result the number of extra bitcoins is likely to be significantly less than 25,200 resulting in a significantly smaller than 0.2271% increase in supply.
Furthermore, the community knows that ASIC are coming online, and understands that this is likely to lead to a very slight short-term increase in supply. As such, any price that the market settles on likely already takes into consideration this likelihood, and the increase in supply shouldn't have a significant effect on the exchange rate.