>When campaigning for a second term in office, U.S. President Richard Nixon announced that the rate of increase of inflation was decreasing, which has been noted as "the first time a sitting president used the third derivative to advance his case for reelection."[2] Since inflation is itself a derivative—the rate at which the purchasing power of money decreases—then the rate of increase of inflation is the derivative of inflation, opposite in sign to the second time derivative of the purchasing power of money. Stating that a function is decreasing is equivalent to stating that its derivative is negative, so Nixon's statement is that the second derivative of inflation is negative, and so the third derivative of purchasing power is positive.
p = price
t = time
dp = change in price
dp/dt = change in price over time = inflation
d^2p/dt^2 = change in change in price over time over time = change in inflation over time = what we are talking about
Second derivative I think. Inflation is change in prices. Change in inflation is a second order derivative? I wish more Americans knew at least a little conceptually about derivatives. Personally, I need to review them. Anecdotally, the number of accountants that I've met that haven't progressed beyond middle school level math is depressing as well.
No, acceleration is going down. Not a lower rate of acceleration. The second implies acceleration is still increasing, but at a slower rate. What is actually happening is we're decelerating (so we're still going fast, meaning inflation is high, but inflation is going down...)
Without trying to be mean, I would also argue your framing is also poor as some inflation is not bad.
To put it in context, if current trends hold we'll expect 3-5% inflation yoy. That is not awful. Higher than last decade or so but we have had super low inflation for a long time. Averaging out, inflation over the last decades, even including the recent high inflation, will still be pretty low, around 3%.
There's no cliff (at least for this to be the third, or even second, derivative with regard to.) Its not like there is a magic bad nominal price level.
Right, the cliff is when people lose confidence in the dollar, which probably has a lot to do with the inflation rate, changes in the inflation rate, and the duration over which we've seen what sort of behavior (... and probably a lot of other things) but not much to do with the actual price level itself.
If we average 2%yoy every single decade for the next 300 years, people will probably have a lot of trust in the dollar in the decade following. If we hit that same price level tomorrow, people will rightly flip. $1700 milk either way, but in one case we'd expect $1700 milk the following day and in the other we'd expect the dollar to plummet further from the shock of it.
Since inflation is a 1st derivative of price, 4th derivative of inflation would actually be a 5th derivative of price. It'd be like: "The increase of the acceleration of the rate of price increase is slowing."
Definitely not a statement that I would be able to visualize :)
