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?
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
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
To determine which period had the larger increase in education and training expenses, you need to compare the adjusted values of the expenditures based on the Consumer Price Index (CPI).
First, calculate the CPI change for each period:
- From 1962 to 1965: CPI change = 31.2 - 30.0 = 1.2
- From 2001 to 2004: CPI change = 185.2 - 175.1 = 10.1
Next, adjust the initial spending values for each period based on the CPI changes:
- For the 1962-1965 period:
Adjusted spending in 1962 = $9.6 billion x (CPI in 1965 / CPI in 1962) = $9.6 billion x (31.2 / 30.0)
Adjusted spending in 1962 = $9.6 billion x 1.04 ≈ $9.98 billion
- For the 2001-2004 period:
Adjusted spending in 2001 = $178.4 billion x (CPI in 2004 / CPI in 2001) = $178.4 billion x (185.2 / 175.1)
Adjusted spending in 2001 ≈ $188.72 billion
Now, compare the increases in adjusted spending:
- From 1962 to 1965, the increase is approximately:
Increase = Adjusted spending in 1965 - Adjusted spending in 1962
Increase = $19.5 billion - $9.98 billion
- From 2001 to 2004, the increase is approximately:
Increase = Adjusted spending in 2004 - Adjusted spending in 2001
Increase = $217.5 billion - $188.72 billion
Compare the two calculated increases to determine which one is larger.
To determine which period had the larger increase in education and training expenses, you need to adjust the dollar amounts for inflation using the Consumer Price Index (CPI).
First, calculate the CPI increase for each period:
- From 1962 to 1965: CPI increase = 31.2 - 30.0 = 1.2
- From 2001 to 2004: CPI increase = 185.2 - 175.1 = 10.1
Next, adjust the dollar amounts for inflation using the CPI increase for each period:
- For the period from 1962 to 1965:
- Adjusted spending in 1962 = $9.6 billion * CPI in 1965 / CPI in 1962 = $9.6 billion * 31.2 / 30.0
- Adjusted spending in 1965 = $19.5 billion
- Increase in spending = Adjusted spending in 1965 - Adjusted spending in 1962
- For the period from 2001 to 2004:
- Adjusted spending in 2001 = $178.4 billion * CPI in 2004 / CPI in 2001 = $178.4 billion * 185.2 / 175.1
- Adjusted spending in 2004 = $217.5 billion
- Increase in spending = Adjusted spending in 2004 - Adjusted spending in 2001
Finally, compare the two increases in spending to determine which period had the larger increase.
It's important to note that comparing the dollar amounts without adjusting for inflation may not accurately reflect the real increase in spending, as the value of money changes over time due to inflation.