From 1962 to 1965, federal spending on non-defense-related education and training rose from $9.6 billion to $19.5 billion, while from 2001 to 2004, it rose from $178.4 billion to $217.5 billion. Given that the Consumer Price Index ( in January) was 30.0 in 1962, 31.2 in 1965, 175.1 in 2001, and 185.2 in 2004, which was the larger increase in education and training expenses?

Question

I know from 62-65 there was a 9.9b increase and a cpi increase of 1.2

from 01-04 there is 39.1b increase and cpi is 10.1 increase

this is where im confused do i multiply the 2 sets together and the bigger one is the larger increase?

thanks

Answer 1

You could work this problem in one of two ways. You could convert all of the nominal dollar values your are given and convert them into 1984 dollars (CPI in 1984 = 100). Or you express the 1965 nominal dollar in real 1962 dollars by dividing by the change in CPI from 62 to 65. Same same for the 2001 to 2005 values.

So, method one:
$9.6 in 1984 dollars = 9.6/.30=$32
19.5 in 1984 dollars = 19.5/.312=62.5
% change is (62.5/32)-1 = 95.3%
That is, real education spending grew by 95.3%
repeat for 2001 to 2004

Method two.
19.5 in 1962 dollars is 19.5/(.312/.3) = 18.75
% change is (18.75/9.6)-1 = 95.3%

Again, repeat for 2001 to 2004