If you have a strong dollar, you can lower rates. But the dollar is at an all-time low, so then to have a 75bps drop hit it, the result is essentially pushing it towards hyperinflation.
That's the theory anyway. There's been alot of criticism on it, but macroeconomists in reserve banks around the world tend to subscribe to this theory when using interest rates to control growth and inflation.
The relationship between interest rates and the dollar is via the interest rate parity condition (http://en.wikipedia.org/wiki/Interest_rate_parity), which is a feature of open markets (to take into account arbitrage opportunities). Lowering the value of the dollar doesn't cause inflation directly. I suppose it does so indirectly by stimulating exports and raising output growth, which leads to lower unemployment and so on.
Lowering interest rates will likely increase inflation, but hyperinflation is a bit rich. Current US inflation is 4%, which is high, but a long way from hyperinflation (see zimbabwe - 1000%+).
> Actually in classical macro theory, lower interest rates (which amounts to the Fed increasing the money supply) ... hence price inflation.
If the money supply is increased (more dollar bills are printed), you'll need more to pay for the same thing: and that is directly price inflation. You can ignore the expected effects in the middle. (In fact, there's no direct correlation to cheaper credit and greater investment.)
4% is stated core inflation. The true inflation number is much higher, but it's hard to know because there's a lot of effort put into diminishing it, for obvious reasons. Sure we're not in hyperinflation yet, but the idea is that it could get there quickly. While it seems impossible from the comfort of growing up in the second half of the 20th century, America is in much more trouble than it realizes.
I guess that given the huge drops in housing values, combined with the layoffs that will (and have) occurred in the banking and housing industries, I am more worried about deflation than inflation. $100 oil and a lower dollar don't matter as much as banks going under and people walking away from their houses.
Deflation is also bad. Bernanke thinks that the effects of the Great Depression could have been mitigated if monetary inflation would have offset the deflation that was occurring. And I think that what he's doing here. Unfortunately, he's about to find out why that doesn't work.