If a bitcoin can be split like a dollar is split into 4 quarters than there is no problem. A mature market will correctly value bitcoins if the splitting makes more bitcoins. If there were a desert island that operated on dollars and had no outside trade, basically a fixed quantity of money, and you were to give everyone on that island twice the money they had before, it wouldn't be long until everything doubled in price. The production is fixed, the money adds no real value besides as a means of valuing goods so the value of goods changes with the supply of money. The market would do this to bitcoins if there was a flood of them.

If bitcoins became a easily convertible and widely accepted currency, and say the American dollar were to shit the bed, then people would move out of dollars and buy up bitcoins. If your dollars were buying you less and less (deflation) and bitcoins were holding thier value because they were an acceptable world wide currency, lots of people would move into bitcoins. This would drive the value of bitcoins up, the limited supply of bitcoins become more valuable as people demanded more. This is one of the main forces driving up the price of silver and gold over the past few years. Fears of the safety of fiat currency makes people desire to hold a more stable currency. Of course the rich would get more of the bitcoins than the rest of us. They have more money to throw around and can use that money to hire people who understand the economy giving them an information advantage. Money managers tell the rich to buy up bitcoins, they jump in first, the rest of us get on board a little bit later, the rich see their investment in bitcoins grow at a much greater rate than the rest of us poorer late adopters. The money managers then tell the rich that bit coins are overvalued, they sell off to the rest of us, make a heap of money, the value of bitcoins plummets and we wonder why we bought this funny internet money.

Gold and silver suck to hold as they are both heavy, and not so easy to convert into goods, but they hold value well. precious metals have plenty of real world uses that help preserve their value, and a long history of use, makes em a pretty safe bet. They make a terrible basis for a widely circulated currency. The growth of the money supply becomes dependent on how many shiny things you dig out of the ground. It makes the quantity of money dependent on the discovery of mineral deposits of changes in technology. Economies in this position can rapidly inflate/deflate as money enter the system of gets pulled out due to the rich hording in time of panic.