Lecture 9 - Topics Econ1320 Lecture 9 Index Numbers...

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1 Econ1320 Lecture 9 Index Numbers Sections 16.4, 16.6 of Text Book Extra readings: Chapter 12 of Harrison and Tamaschke on BB 2 Topics ring4 Background on index numbers ring4 Simple index numbers circle6 Price relatives ring4 Unweighted Aggregate Price Indexes circle6 Simple relative price index circle6 Ratio of unweighted aggregate price index ring4 Weighted Aggregate Price Index Numbers circle6 Laspeyres Price Index circle6 Paasche Price Index circle6 Fisher Price Index ring4 Consumer price index (CPI) as an deflator 3 Background on Index Numbers ring4 A ratio of a measure taken during one time frame to that same measure taken during another time frame, usually denoted as the base period ring4 Index numbers allow relative comparisons over time ring4 Index numbers are reported relative to a Base Period Index ring4 Base period index = 100 by definition ring4 Used for circle6 an individual item or circle6 changes in several variables (composite indexes) ring4 We will focus on price index numbers for intertemporal comparisons (i.e. over time comparison). 4 Simple Index Numbers ring4 A number, expressed as a percentage, determined by computing the ratio of a price, (quantity or cost) for a particular year of interest to the price (quantity or cost) of a base year Where: x 0 is the price (quantity or cost) in the base year x i is the price (quantity or cost) in the year of interest I i is the index number of the year of interest ) 100 ( 0 x x I i i = 5 Price Relatives ring4 The ratio of prices at two different points in time is known as a price relative ring4 It is a common practice to use price relatives to measure changes in the price of a single commodity over time. ring4 Simple Price Index p s is the price for the base year p t is the price for year t I st is the price index number for year t with base year s 100 × = s t st p p I 6 Price Relatives: Example 1 Airplane ticket prices from 1996 to 2004: 90 ) 100 ( 320 288 100 2000 1996 1996 = = × = p p I 124.1 397 2004 120.0 384 2003 114.4 366 2002 108.8 348 2001 100.0 320 2000 100.6 322 1999 97.2 311 1998 92.2 295 1997 90.0 288 1996 Index ( base year = 2000) Price Year 100 ) 100 ( 320 320 100 2000 2000 2000 = = × = p p I 120 ) 100 ( 320 384 100 2000 2003 2003 = = × = p p I Base Year:
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2 7 head2right Prices in 1996 were 90% of base year prices, i.e. the prices in 1996 were a 10% lower of the prices in 2000. head2right Prices in 2000 were 100% of base year prices (by definition, since 2000 is the base year) head2right Prices in 2003 were 120% of base year prices i.e. there was a 20% increase in the price from 2000 to 2003 Price Relatives: Interpretation 90 ) 100 ( 320 288 100 2000 1996 1996 = = × = p p I 100 ) 100 ( 320 320 100 2000 2000 2000 = = × = p p I 120 ) 100 ( 320 384 100 2000 2003 2003 = = × = p p I 8 Price Relatives: Example 2 Suppose we observe the price of a 60 litre tank of petrol 4 3 2 1 0 t 113.5 54.48 2004 107.0 51.36 2003 106.3 51.00 2002 103.8 49.80 2001 100.0 48.00 2000 Index ( base year = 2000) Price Year 0 . 107 100 00 . 48 36 . 51 100 0 3 2003 = × = × = p p I The value of this index in 2003 is 107.0 indicating the price in 2003 was 7% higher than 2000.
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