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The classic case is Germany in the 1920s, Germany had hyper inflation do to the fact it had to pay the allies off for "causing" WWI. The pay offs had to be in Gold, Fracs or Pounds NOT German Marks.
In countries where their debts are in their own currency, inflation can get to double digits, but sooner or later the inflation eliminates the debts and with that elimination the push to cause inflation dies (no more debt to inflate away). In countries with debts in currency other then their own, inflation can NOT eliminate the debt, the country can inflate its own currency and any debts listed in its own currency, but can NOT eliminate the foreign debts via inflation. Thus the traditional way to eliminate National debt, to inflate it away (Adam Smith in his "Wealth of Nations" point out that no country had ever paid off its debts, they sometimes go through the motion of paying off the debt, but generally only after inflating it to next to nothing first, through sometime this can be delayed for Centuries, the Classic Case was the City of Florence, which ran deficits for over 800 years, till Napoleon took over the city during the Wars of the French Revolution and made it part of his Kingdom of Italy).
Back to hyper inflation. Hyper inflation occurs when a country can NOT inflate away its debts for the debts are NOT in its own currency. No matter how much inflation you have, the debts stays about the same in real terms for the debt is in a currency NOT under the control of the Country with the debt. Countries with huge debts NOT in their currency end up with Hyper inflation, for no matter how high the inflation gets, the debt can NOT be inflated away. Such countries try the traditional way to "pay" off the debt, i.e. inflating it away, but finds all they do is inflate whatever domestic savings their have away, and then continuing on with even higher inflation in attempts to "pay" off the debt, but since the debt is NOT in their Currency, the debt stays the same in real terms and the push for inflation continues till you get into a situation where money becomes worthless and even the people holding the non domestic denominated debts realized that they can NOT trade theses debts or ever hope to get them paid off and either invade the country OR accept the fact the debts will NOT be paid off on face value and accept a much lower value (or even a non-value) and with that decision the Hype Inflation ends (This is basically how Germany stopped its hyper inflation, the US arranged for lesser payments to be made, and then even deferred them to a later date, for example the debts from WWI, did NOT become due till after Germany was re-united in 1991, and then paid off on the debts face value (ignoring inflation since the 1920s) last year (2010). Yes, Germany paid off is WWI debts but on their face value NOT on what those debts would have been had the debts kept up with inflation.
The problem with the US debts is it is in US DOLLARS, which is under the complete control of the US Government. If the Government decide to inflate away the debt, the Government can do do at double digits inflation rates, and before such rates even get close to triple digits, the debt is already inflated away and with the debt inflated away the push in inflate the currency disappears. Thus long before countries whose debts are in their own currency get to hyper inflation, the debt that is causing the inflation become worthless, and as it becomes worthless any inflationary push of the debt disappears.
Thus Hype Inflation can NOT happen in the US, given that US debts are in US Dollars. Until the majority of US Debts are in some other Currency the US can NOT have hyper inflation(And while China has One Trillion of US debts, it is US debts in terms of US Dollars NOT Chinese Yuans, thus the value of that One Trillion Dollars of Debts is in the control of the US Government NOT the Chinese Government).
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