InstaEDU Written Lesson
Tutor: Cody B.
Date: 3/28/14
Question:
The following information is available for an economy for years 2012 and
2013. Nominal GDP for 2012 and 2013 are respectively, $800 billion and $1,400
billion. The Laspeyres price index for 2013 (base 2012) is 120 and the Paasche price
index for 2013(base 2012) is 140. Calculate the chain weighted real GDP for 2013.
Real GDP vs. Nominal GDP
Real GDP is the value of final goods and services produced in a given year when
valued at the prices of a reference base year. By comparing the value of production in
the two years at the same prices, we reveal the change in production
Nominal GDP is the value of final goods and services produced in a given year when
valued at the prices of that year.
Application to the question at hand: We know the nominal GDP values but we do not
know if the nominal GDP increased due to an increase in the productivity of the
economy, an increase in the price level, or both.
Lasperyres vs. Paasche price indices
Above are the formal equations for the Lasperyres and Paasche price indices, not
very helpful I know.
Here are the definitions and the differences between the two indices in simpler
terms:
The Laspeyres index measures the quantities of the base year valued at the prices of
next year. Ex. the quantities of 2012 valued at the prices of 2013.
The Paasche index measures the quantities of the new year at the prices of the base
year. Ex. the quantities of 2013 valued at the prices of 2012.
Chain weighted real GDP calculation
In order to complete our chain weighted GDP calculation, we need to find the
percentage change in production at the 2012 prices, and the 2013 prices, then find
the average of the two percentage changes. This will give us the average percentage
change in 2013, which we can use to find our chain weighted real GDP for 2013.
2013 production at 2012 prices
- Calculated by dividing the 2013 nominal GDP by the Paasche index and
multiplying by 100
($1400bn/140)*100 = $1000bn
2012 production at 2013 prices
- Calculated by multiplying the 2012 nominal GDP by the Laspeyres index and
dividing by 100
($800bn*120)/100 = $960bn
Value of Production
Billions of Dollars
(a) At 2012 prices
Nominal GDP in 2012
800
2013 production at 2012 prices
1000
Percentage change in production at 2012 prices
25%
(b) At 2013 prices
2012 production at 2013 prices
960
Nominal GDP in 2013
1400
Percentage change in production at 2013 prices
45.8%
(c) Average percentage change in 2013
35.4%
Since 2012 is our base year, we simply multiply the average percentage change
value we just calculated by the nominal GDP in 2012 to calculate the chain weighted
real GDP in 2013.
$800bn * 1.354 = $1,083bn
Chain-weighted real GDP in 2013 is $1083bn