well I am not convinced yet. Though we may be agreeing, but not realising it...
the CPI was 3.1 for december 2008
so price of x was 3.1% higher in dec 2008 than dec 2007
the CPI was 3.0 for January 2009
so price of x was 3.0% higher in Jan 2009 than Jan 2008
The prices didn't fall, they just didn't rise as fast.
If the price rise was uniform over the year (so the monthly rate is CPI/12)
Then
X= 100 in dec 2007
X= 100.258 in Jan 2008 (100 + 0.258%)
X= 103.10 in dec 2008 (100 + 3.1%)
X= 103.27 in Jan 2009 (100.258 + 3.0%)
(I think...)
So, in this case where the inflation has dropped by .1% the price has still actually risen
In your example of 12% and 6% inflation
X= 100 in dec 2007
X= 101 in Jan 2008 (100 + 1%)
X= 112 in dec 2008 (100 + 12%)
X= 107.06 in Jan 2009 (101 + 6%)
So, yes, in this case, in order to see such a large drop in CPU, the price has actually fallen from dec 2008 to jan 2009
See page 13 of
http://www.statistics.gov.uk/pdfdir/cpi0209.pdf where it shows the index over the last 3 years.