Hyperinflation

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Zimbabwe has been in the news these past few days (having just held a presidential election).  In reading the latest reports on the vote counting, nearly every article gave as background material two statistics describing the economic hardships in Zimbabwe:  the unemployment rate is between 80% and 90%, and the annual rate of inflation is 100,000%.

Both of those facts are stunning, but I felt I could understand the first one — I can conceive of life in a society with an 80% unemployment rate.   But the inflation rate is so extreme, I found it difficult to continue reading, and felt a need to put that information into a context I could grasp.

To convert the interest rate to a daily rate, we imagine a daily inflation  rate of r, which in turn causes consumer prices to rise on average by a factor of $1+r$ per day.  Each subsequent day involves a further multiplication by the factor $1+r$.  Over the course of a year, we have prices increasing by a factor of 1000, and hence $(1+r)^{365} = 1000$, and $r = \sqrt[365]{1000} - 1 \approx 0.019$.

Thus the daily inflation rate is just under 2%.  A product costing $100 on a given day, would cost$101.91 the second day, $103.86 the third,$105.84 the fourth, $107.86 the fifth, and so on. In late March 2008, President Mugabe ordered food prices to be lowered to their levels of February 12, the day that pay raises took effect for public employees. By how much would prices have risen in a 45 day period, if the annual inflation rate is 100,000%? After 45 days, a$100 item would cost   $\ 100\cdot(1000)^{45/365}\approx \ 234.35$.  When Mugabe ordered food prices rolled back to their levels from one and a half months earlier, he was cutting prices by nearly 60%.

The Times Online (London) has a recent article detailing the brutal reality of these economic hardships, the consequences when prices for some goods and services can triple in just three days, the challenges of purchasing soap, cooking oil, and other necessities.