AP MACROECONOMICS---Ippolito 2014
Name:
KEY
How to Calculate a Price Index
A price index is used to measuring the rate of price increases (i.e. inflation). The two most common price indices used in
AP Economics are the consumer price index (CPI) and the GDP Deflator.
There is more than one method for constructing a price index. The easiest method is the weighted-average method which
uses a fixed quantity market basket of goods priced in different years.
Step #1:
Compute the total cost of the market basket for each year
Step #2:
Pick a Base Year (The base year index will always = 100)
Step#3:
Compare the total cost of each year to the cost of the base year to calculate each price index:
Index Number
=
Current-year cost
Base-year cost
X 100
1) Please fill in all blanks ($______) in the table below to help you construct a price index.
Market Basket Items
# of Units
Year 1 (2000)
$ per unit Total Cost
Year 2 (2003)
$ per unit Total Cost
Year 3 (2006)
$ per unit Total Cost
Cheese
2 lbs
$1.75
$3.50
$1.50
$3.00
$1.50
$3.0
Blue Jeans
2 pairs
$12.00
$ 24.0
$15.50
$31.0
$20.00
$40.0
10 gallons
$1.25
$12.50
$1.60
$16.0
$2.70
$27.0
-----------
-------
_$_40.0
-------
$50.0
-------
$70.0
Gasoline
Total Cost of Basket
2) Using year 1 as our base year, using the formula above to calculate the index for each year:
Year 1 Index =
($40/$40) x 100 = 100 index
Year 2 Index =
($50/$40) x 100 = 125 index
Year 3 Index =
($70/$40) x 100 = 175 index
(base year)
3) Calculate the inflation rate on a percentage basis for the following:
a. Hint: formula = [(Ending index – Beginning index) / Beginning Index] X 100
b. For example: if a stock price rose from $6 to $8 share the % gain is [(8-6)/6] X 100 = +33%
Year 1 to Year 2:
(125 – 100)/100 = +25.0%
Year 1 to Year 3:
(175 – 100)/100 = +75.0%
Year 2 to Year 3:
(175 – 125)/125 = +40.0%
Part B
Changing the Base Year
We need not have chosen Year 1 to be our base year. To determine if our choice of base year influenced the results, let’s
use Year 2 as our base year and recompute both the index numbers and the percentage changes between the years. The
first percentage change in prices has been done for you.
Change the Base Year of a Price Index:
Index Numbers
Year
Percentage Change in Prices
Year 1
(Year 2 = Base) (calculated by using changes in index numbers)
($40/$50) x 100 = 80
Between Yr. 1 and Yr. 2
([100 – 80]/80 x 100= + 25%
Year 2
($50/$50) x 100 = 100
Between Yr. 2 and Yr. 3
(140 – 100)/100 = +40.0%
($70/$50) x 100 = 140
Between Yr. 1 and Yr. 3
(140 – 80)/80 = +75.0%
(base year)
Year 3
5) Do the index numbers change when the base year is changed from Year 1 to Year 2?
YES!
6) Does the percentage change in prices between the years change when the based is changed from Year 1 to Year 2?
NO!
explain why: PICKING A BASE ONLY CHANGES THE INDEX #’S =>
INFLATION NEVER CHANGES BETWEEN YEARS BASED ON BASE
YEAR
7) Would the priced index numbers change if you chose a different set of expenditures patterns were selected for weighting for
the market basket?
(i.e. if you changed the make-up of the market basket)
YES!
explain why: MARKET BASKET COMPOSITION & WEIGHTING
MATTER. If you increase the % of computers in a basket => inflation is
different….
8) Would your inflation calculations be accurate if the quality of goods in your market basket changed over the years?
(assume no adjustment for quality))
NO! explain why: If price is unchanged for a good but quality rises, the real
price of the good has fallen! Inflation would be OVERSTATED
9) What is a COLA:
cost of living adjustment……
10) Would a COLA based on a price index be accurate for you if you spent money differently than the market basket weightings?
a. If not, would it be too high or too low?
No, it could be too high or too low depending on what you bought and the relative
inflation