ECON2913 (Spring 2012)
28.2 & 2.3.2012 (Tutorial 3)
Consumer price index (CPI) and cost-of-living adjustment (COLA)

Cost-of-Living Index: ratio of the present cost of a typical bundle of consumer goods and
services compared with the cost during a base period.
Example:
Two sisters, A and B whose preferences are identical. Person A and B began their university
education in 1990 and 2000 respectively.
Person A in 1990
 Her parents gave $500 for to A to spend on food and books
 Price of food = $2, and Price of book is $20
 A’s consumption: 100 food and 15 books
 I1  $2  100  $20  15  $500
Person B in 2000
 Price of food = $2.2, and price of book is $100
 Her parents decided to give B the amount which is equivalent in buying power to the
budget given to A. How much would be the budget?
 B’s consumption: 300 food and 6 books (same utility level as A’s bundle and B
consumes more food and less books after the price change)
 I 2  $2.2  300  $100  6  $1260

The ideal cost of living index: the cost of attaining a given level of utility at current
prices relative to the cost of attaining the same utility at base prices

In this example, ideal cost of living index: $1260/$500 = 2.52 (152% in the cost of
living)
Books
25
I4
A
15
12.6
B
U1
6
I1
100
I3
I2
250 300
Food
572
1
Laspeyres price index (keep the bundle fixed as the base year bundle)

Amount of money at current year prices that an individual requires to purchase a bundle
of goods/services chosen in a base year divided by the cost of purchasing the same
bundle at base-year prices. Example: CPI (Consumer price index)
P Q  P2t Q2b
 LI  1t 1b
P1b Q1b  P2b Q2b

The Laspeyres price index assumes that consumers do not alter their consumption
patterns as prices change

The Laspeyres price index tends to overstate the true cost of living index. (Why?)
$2.2  100  $100  15 $1720
 In this example, LI =

 3.44
$2  100  $20  15
$500
Paasche index (keep the bundle fixed as the current year bundle)

Amount of money at current year prices that an individual requires to purchase a current
bundle of goods/services divided by the cost of purchasing the same bundle in a base
year
P Q  P2t Q2t
 PI  1t 1t
P1b Q1t  P2b Q2t

It assumes that individuals will buy current year bundle in the base period, however,
facing the base year prices, consumers would be able the achieve the same utility at
lower cost with another bundle

The Paasche price index tends to understate the true cost of living index. (Why?)
$2.2  300  $100  6 $1260

In this example, PI =

 1.75
$2  300  $20  6
$720
Comparison of indexes

Comparison between LI and PI

Both LI and PI are fixed weight indexes. Quantities of various goods and services in
each index remain unchanged (Verify!)
 Chain-Weighted Indexes: Cost-of-living index that accounts for changes in quantities of
goods and services
 Introduced to overcome problems that arose when long-term comparisons were make
using fixed weight price indexes
COLA
If salary is indexed to inflation, COLA recipients are always better off. Would individuals be
better off or worse off in the time of deflation if there is COLA in their salaries?
Price
I1
A
U2
U1
I4
I3
I2
Quantity
2