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Western University

Economics

Economics 2152A/B

Simona Cociuba

Fall

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Measurement: Quantity and Price Indices
2220 A: Lecture 4
Simona Cociuba
Fall 2012 Assignment 1 is on WebCT
Due date is Wednesday, September 26 in class Recap: Nominal and Real GDP
Nominal GDP: uses current year prices to value current output.
Real GDP: uses base year prices to value current output.
old rule or ﬁxed-weight real GDP (fairly simple)
I
use base year prices instead of current period prices for all years
new rule or chained-weight real GDP (a bit more complicated)
1. Get the Fisher index. This means, compute a ratio of real GDP in two
consecutive years by taking a geometric average of the Laspeyres
and Paasche indices. This ratio is also called a growth factor.
2. Get the level of real GDP. Start with base year: real GDP equals
nominal. Then, use the geometric averages from above to infer
chained-weight real GDP for other years.
s
▯ ▯ ▯ ▯
cwRGDP = cwRGDP ▯ ∑ p ▯1 ▯qt ▯ ∑ pt▯qt
t t▯1 ∑ p ▯q ∑ pt▯q
| t▯1 t▯{z t▯1 }
Fisher Int▯1, t Why Do We Call It the"Chain-Weight" Real GDP?
Suppose the base year is period t = 0.
cwRGDP t = cwRGDP t▯1 ▯Fisher Index ▯ 1, t
= cwRGDP t▯2 ▯Fisher Index ▯ 2,▯1 ▯Fisher Index ▯ 1, t
= ...
= cwRGDP 0 ▯Fisher Index 0, 1..▯Fisher Index t▯1, t
Chained-weight real GDP in year t is linked to chained-weight real
GDP in base year 0 through the entire chain of Fisher indices
computed for two adjacent years (0,1), (,2 ) (,3 )...( ▯ 1,t)
) level of real GDP in year t is expressed in the prices of base year. Example from Last Class
Year 1 Year 2 Year 3 Year 4
Prices
good 1 20 21 22 23
good 2 60 59 58 57
Quantities
good 1 75 76 77 78
good 2 25 30 35 40
1. Nominal GDP 3,000 3,366 3,724 4,074
2. Fixed-weight Real GDP 3,100 3,412 3,724 4,036
(base=year 3)
3. Chained-weight Real GDP ??? ??? 3,724 ???
(base=year 3)
s ▯ ▯ ▯ ▯
∑ p3▯q4 ∑ p4▯ q4
cwRGDP 4= cwRGDP 3▯ ▯ = ...
∑ p3▯q3 ∑ p4▯ q3 Measurement: Price Indices
We talked about how to measure real GDP. Real GDP is an index of the
quantity of production in a given year relative to the base year
A quantity index=weighted average of quantities of stuff
produced. The weights are prices.
Next, we’ll talk about price indices.
A price index=a weighted average of the prices of goods and
services produced in an economy. The weights are quantities.
I
if all goods and services are i)cgeneral price level
I if only goods and services consumed by co)suCPI Measurement: Price Indices
Two commonly used prices indices:
Implicit GDP price deﬂator= Nominal GDP ▯100
Real GDP
Cost of base year quantity at current prices
Current year CPI= Cost of base year quantity at base year prices
CPI is a ﬁxed-weight price index (use base year quantity as weight)
Assumes that consumers don’t change buying habits
So, changes in relative prices over time affect measurement
I goods that become more expensive will get a higher weight than
they should in the CPI
I hence measured inﬂation will be higher than actual
I this upward bias is about 0.5 percentage points for Canada. 2009 CPI Basket in Canada
Includes the following categories:
Food: weight about 16%
Shelter: ~27.5%
Household operations and furnishings: ~11.8%
Clothing and footware: ~5.6%
Transportation: ~19.3%
Health and personal care: ~5%
Recreation, education and reading: ~11.8%
Alcoholic beverages and tobacco: ~3%
Weights of b

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