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Unformatted text preview: 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 r Background on index numbers r Simple index numbers c Price relatives r Unweighted Aggregate Price Indexes c Simple relative price index c Ratio of unweighted aggregate price index r Weighted Aggregate Price Index Numbers c Laspeyres Price Index c Paasche Price Index c Fisher Price Index r Consumer price index (CPI) as an deflator 3 Background on Index Numbers r 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 r Index numbers allow relative comparisons over time r Index numbers are reported relative to a Base Period Index r Base period index = 100 by definition r Used for c an individual item or c changes in several variables (composite indexes) r We will focus on price index numbers for intertemporal comparisons (i.e. over time comparison). 4 Simple Index Numbers r 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 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 ( x x I i i = 5 Price Relatives r The ratio of prices at two different points in time is known as a price relative r It is a common practice to use price relatives to measure changes in the price of a single commodity over time. r 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: 2 7 h Prices in 1996 were 90% of base year prices, i.e. the prices in 1996 were a 10% lower of the prices in 2000. h Prices in 2000 were 100% of base year prices (by definition, since 2000 is the base year) h 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 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 . 107 100 00 . 48 36 . 51 100 3 2003 = × = × = p p I The value of this index in 2003 is 107.0 indicating the price in is 107....
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This note was uploaded on 10/21/2009 for the course ECON 1320 taught by Professor John during the Three '08 term at Queensland.
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