INDEX NUMBERS

Definition of Index Number l A summary measure that states a relative comparison between groups of related items l Price Relative or Percentage Relative l A Number used to measure how much somthing has changed from one time period to another

Simple Price Relative Index An index which describes a single item or commodity in a given period versus the base period

Simple Price Index 100 n o. I P =

Example of Simple Price Index Suppose the price of one pound of a certain brand of coffee was $2.00 in 1990, $3.22 in 1995 and $6.04 in What are the price indicies of the three figures, with 1990 as the base (written, 1990 = 100)?

PRICE INDICES YEAR (1990 = 100) $2.00 $3.22 $6.04 $2.00 $3.22 $6.04 I p p  n o

Quantity Index Q n o

Value Index nn oo V

Unweighted Aggregate Price Index (Summarizes a groups of items or commodities) I P P    100 n o

Unweighted Aggregate Price Index: n o

quart Unweighted Aggregate Price Index: n o 101=

Dow Jones Industrial Average (DJIA) Where: P n = the price of stock n Divisor = the special DJIA divisor

Unweighted Average of Price Relatives Index I P P k    100 n o

n o

Weighted Aggregate Price Index l Takes prices and quantities (weights) into consideration l Laspeyres Index l Paasche Index l Fixed-Weight AggregatePrice Index

Laspeyres Index l Quantities are from the base period l Reflects changes in prices alone l Tends to overestimate price l Ignores changes in consumption l Easiest to calculate l Consumer Price Index-modified

Laspeyres Index no oo

Laspeyres Index= 96 90

Paasche Index l Quantities are from the given period l Reflects changes in production or consumption l Tend to underestimate price change l Weights have to be revised each time period l Can be costly and time consuming

Paasche Index nn on

Paasche Index= I 

Fixed-Weight Aggregate Price Index l Weights are from one or more representative periods l Bureau of Labor Statistics revises weights every 10 years l Producer Price Index l Government agencies indicies are publishes in series (impractical to use Paasche)

Fixed-Weight Aggregate Price Index na a o

Weighted Arithmetic Mean of Price Relatives Index Where w = p a q a     w P P w I 100))(( n o

WEIGHTED ARITHMETIC MEAN OF RELATIVES INDEX

Standard and Poor’s (S&P) 500 Index Where: O.V. = original valuation in N i = number of shares outstanding for Firm I P i = price of shares for Firm i

Consumer Price Index Fixed-weight aggregate price index (modified Laspeyres)

Consumer Price Index l Measures average changes in prices of a fixed “market basket”of goods and services usually bought by urban wage earners and clerical workers from one time period to another l Published monthly by Bureau of Labor Statistics l 400 goods and services

Uses of CPI l Economic Indicator l Escalator l Deflator for real wages n Process called deflating money wages n Price index - deflator n Deflated dollar value = constant dollar

Real Wages CPI 1987 = 100 Real Wages 98 = Current Wage 98 Consumer Price Index 98 X 100

Purchasing Power of Dollar $.82 = X 100 $ = 1 CPI X 100 $0.18 decrease in purchasing power of $

% age Increase or Decrease Current Wage - Past Wage Past Wage X X 100 = 50%

Median Family Income CPI 1987=100 Real Income $20,000 $30, $18, $22, % increase 23.7% increase 21.3% increase

Median Family Income $20,000 $30,000 50% increase CPI 1987= % increase Real Income $20,000 $24, % increase Shift Base CPI 1990= % increase