So we can see how Bitcoin is useful, but how does that solve the initial problem statement?
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This is the United States Consumer Price Index since 1775. It is the price marked in US Dollars of a basket of goods purchased by households and is often used to track inflation. The common pattern in US history is that war causes massive inflation as the war has to be funded. As Benjamin Franklin conceded, depreciation of currency acts as a tax to pay for war.
Fortunately, after a war, gold and silver act as a stabilizing force. For instance, after the Revolutionary War, the populace rejected the hyper-inflated dollars and preferred gold and silver and the government was forced to adjust monetary policy until the dollar regained its comparative value.
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This pattern of inflation followed by deflation happened for every subsequent war, and for over a hundred years the dollar managed to retain its long term value. The Great Depression followed by World War II is when this all changed. In 1933, Franklin D. Roosevelt required all Americans to give up any gold they owned. Soon after that, contractual obligations of the United States government such as bonds payable in gold were nullified. This meant that when the money inflated rapidly for World War II, there was no incentive to deflate afterwards. The stabilizing force of peoples gold was swept from under them and thatcombined with a radical shift in monetary policyhas led to the last 40 years: a consistent devaluation of the US dollar coupled with rapid cycles of economic booms and busts worldwide.
With this instability, we see an increasing wealth inequality across the globe and monetary policy that is making it worse, not better. We see the middle class declining as their taxes are used to bail out the banks almost as an acknowledgement that this is indeed how the system is supposed to work.
Dr. John Nash in his work on Ideal Money says that we should not revert to the gold standard, but we need something that will stabilize our money. He gives an example by imagining an Industrial Consumer Price Index (ICPI), an optimally chosen basket of international prices which would provide an international basis for value comparison. According to Nash, the problem with this is that it would be difficult to make it politically neutral, which is a fundamental property of Ideal Money. The incentives are such that if the nations can choose between influencing the ICPI somehow or fixing their own monetary policy, they will do the former. Choosing gold as an ICPI also fails because it does not have a stable or predictable value. Mining gold depends entirely on the technology whose evolution is often unexpected and significant, vastly altering the predicted supply growth.
Enter Bitcoin, a system that is politically neutral with a predictable inflation rate (see figure above). We can estimate precisely how much energy was used to compute every block on the Bitcoin blockchain. Over time, as it is shown to be resistant to coercion and as its monetary policy remains fixed, people around the world will slowly include Bitcoin into their investment portfolio, for example, as a way to hedge against the next recessions. In parallel, nations will be forced to stabilize their moneys value because there will be a stable non-political store of value against which their money is compared.
But dont take my word for it, Christine Lagarde, head of the International Monetary Fund, is thinking the same:
For instance, think of countries with weak institutions and unstable national currencies. Instead of adopting the currency of another countrysuch as the U.S. dollarsome of these economies might see a growing use of virtual currencies. Call it dollarization 2.0.
 So in many ways, virtual currencies might just give existing currencies and monetary policy a run for their money. The best response by central bankers is to continue running effective monetary policy, while being open to fresh ideas and new demands, as economies evolve.