Preliminaries | Exercise No. 2 Consumer Price Index

Exercise No. 2

The following table shows the average retail price of butter and the Consumer Price Index from 1980 to 2010, scaled so that the CPI = 100 in 1980.

	1980	1990	2000	2010
CPI	100	158.56	208.98	218.06
Retail price of butter (salted, grade AA, per lb.)	$1.88	$1.99	$2.52	$2.88

a.       Calculate the real price of butter in 1980 dollars. Has the real price increased/decreased/ stayed the same from 1980 to 2000? From 1980 to 2010?

b.      What is the percentage change in the real price (1980 dollars) from 1980 to 2000? From 1980 to 2010?

c.       Convert the CPI into 1990 = 100 and determine the real price of butter in 1990 dollars.

d.      What is the percentage change in the real price (1990 dollars) from 1980 to 2000? Compare this with your answer in (b). What do you notice? Explain.

a.       Calculate the real price of butter in 1980 dollars. Has the real price increased/decreased/ stayed the same from 1980 to 2000? From 1980 to 2010?

Real price of butter in year t = CPI 1980 / CPI t x nominal price of butter in year t.

	1980	1990	2000	2010
Real price of butter (1980 $)	$1.88	$1.26	$1.21	$1.32

The real price of butter decreased from $1.88 in 1980 to $1.21 in 2000, and it increased from $1.88 in 1980 to $1.32 in 2010, although it did increase between 2000 and 2010.

b.      What is the percentage change in the real price (1980 dollars) from 1980 to 2000? From 1980 to 2010?

Real price decreased by $0.67 (1.88 - 1.21 = 0.67) between 1980 and 2000. The percentage change in real price from 1980 to 2000 was therefore (-0.67/1.88) x 100% = -35.6%. The decrease was $0.56 between 1980 and 2000 which, in percentage terms, is (-0.56/1.88) x 100% = -29.8%.

c.       Convert the CPI into 1990 = 100 and determine the real price of butter in 1990 dollars.

To convert the CPI into 1990 = 100, divide the CPI for each year by the CPI for 1990 and multiply that result by 100. Use the formula from part a and the new CPI numbers below to find the real price of milk in 1990 dollars.

	1980	1990	2000	2010
New CPI	63.07	100	131.80	137.53
Real price of butter (1990 $)	$2.98	$1.99	$1.91	$2.09

d.      What is the percentage change in the real price (1990 dollars) from 1980 to 2000? Compare this with your answer in (b). What do you notice? Explain.

Real price decreased by $1.07 (2.98 - 1.91 = 1.07). The percentage change in real price from 1980 to 2000 was therefore (1.07/2.98) x 100% = -35.9%. This answer is the same (except for rounding error) as in part b. It does not matter which year is chosen as the base year when calculating percentage changes in real prices.