If 1 BTC = 1 USD in 2010, and 1 BTC = 500 USD in 2013, the proposed solution would be to "rebase" bitcoin, by creating inflation of bitcoin at x500, so 500 times more bitcoin are in circulation in 2013, and therefore 1 BTC still is equal to 1 USD, and the price of bitcoin is stable.
The problem I have with this is that, in the case were the Bitcoin supply is fixed like that of Gold, the end users, the holders of bitcoin, the common man, the poor, the middle class, received an increase of value of their bitcoin by 500x, because in three years there Bitcoin is now 500 times more valuable, and their purchasing power therefore has increased by that much.
On the other hand, by "rebasing" the supply, you transfer wealth and value from the end users, the holders of bitcoin, the common man, the poor and the middle class, directly into the hands of whoever gets the newly created bitcoin, via the tax of inflation. The bitcoin user then would have seen a 500x decrease in the value of their bitcoin in 3 years because their bitcoin would have been 500 times less valuable, and 500 times less purchasing power.
I view bitcoin as the "Gold Standard" of crypto currencies, so that all other crypto currencies are valued based on their value in Bitcoin. We need a "Gold STandard" of crypto currencies, and thus we need Bitcoin to remain scarce. It is this scarcity that makes bitcoin such a good store of value, just like the scarcity of gold makes it such a good store of value. To enable inflation in order to achieve price stability would come at the cost of Bitcoin's capabilities as a store of value.
The solution to the problem then is not to fundamentally change the Bitcoin protocol to allow for inflation and more than 21 million bitcoins, but rather to create an alt coin that is pegged to the price of Bitcoin in the same way as proposed, thus avoiding drastically altering the mission statement and vision of Satoshi for Bitcoin to mimic the qualities of Gold. The alt coin would produce more coins or reduce coins according to the price of Bitcoin, creating inflation and deflation to create price stability in that coin, which would be a unit of account because the resulting price stability, but not a very good store of value.
The limited supply, and fixed supply of bitcoin is fundamental to it's Store of Value property which serves as the cornerstone of all alt coins. all alt coins rest upon the value that is stored in Bitcoin. As soon as you remove the limit, and increase the supply, you compromise the store of Value property of bitcoin.
We can have price stability in an alt coin, and in fact, this need of price stability is a huge opportunity for someone looking to create a useful alt coin, simply peg the value to the price of bitcoin and inflate or deflate accordingly. But the cost of getting rid of the 21 million limit on bitcoin is far too much to justify going through it. The scarcity is a necessary part of being the "Gold Standard" of crypto currencies that Bitcoin is.
For that btcwill need to find his own value,that value will be represented by btc coins and priced in fiat money
It will deflation and inflation but gap will be small,with his own value btc will be independent from fiat money