Index numbers99
- 2. Definition of Index Number A summary measure that states a relative comparison between groups of related items Price Relative or Percentage Relative A Number used to measure how much somthing has changed from one time period to another
- 3. Simple Price Relative Index An index which describes a single item or commodity in a given period versus the base period
- 5. 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 1997. What are the price indicies of the three figures, with 1990 as the base (written, 1990 = 100)?
- 6. 1990 1995 1997 ( ) $2. $2. 00 00 100 100 = ( ) $3. $2. 22 00 100 161 = ( ) $6. $2. 04 00 100 302 = PRICE INDICES YEAR (1990 = 100) $2.00 $3.22 $6.04 $2.00 $3.22 $6.04 I p p = n o
- 8. Value Index I PQ PQ = ×100n n oo V
- 9. Unweighted Aggregate Price Index (Summarizes a groups of items or commodities) I P P = × ∑ ∑ 100 n o
- 10. Price Commodity 1995(po) 1997(pn) Milk (pint) 19.6 21.4 Round Steak(lb) 188.5 189.5 Flour,wheat (lb) 19.9 16.9 Eggs, GradeA large (dozen) 77.0 81.5 305.0 309.3 Unweighted Aggregate Price Index: Unweighted Aggregate Price Index: I p p = × ∑ ∑ 100n o 101 0.305 3.309 100 0.779.195.1886.19 5.819.165.1894.21 ==× +++ +++ =I
- 11. Price Commodity 1995(po) 1997(pn) Milk (pint) 19.6 21.4 Round Steak(lb) 188.5 189.5 Flour,wheat (lb) 19.9 16.9 Eggs, GradeA large (dozen) 77.0 81.5 305.0 309.3 156.8 171.2quart 442.2 459.1 Unweighted Aggregate Price Index: Unweighted Aggregate Price Index: I p p = × ∑ ∑ 100n o 16.134100 0.779.195.888.156 5.819.165.1892.171 =× +++ +++ =I 101=134.16 .
- 12. Dow Jones Industrial Average (DJIA) Divisor P DJIA n n∑= = 30 1 Where: Pn = the price of stock n Divisor = the special DJIA divisor
- 13. Unweighted Average of Price Relatives Index I P P k = ×∑ 100 n o
- 14. Price Commodity 1995(po) 1997(pn) pn/po Milk (quart) 156.8 171.2 1.09 Round Steak(lb) 188.5 189.5 1.01 Flour,wheat (lb) 19.9 16.9 0.85 Eggs, GradeA large (dozen) 77.0 81.5 1.06 305.0 309.3 4.01 I P P k = ×∑ 100n o I = + + + × = = ( . . . . ) . ( ) . 109 101 085 106 100 4 4 01 100 4 100 25
- 15. Weighted Aggregate Price Index Takes prices and quantities (weights) into consideration Laspeyres Index Paasche Index Fixed-Weight AggregatePrice Index
- 16. Laspeyres Index Quantities are from the base period Reflects changes in prices alone Tends to overestimate price Ignores changes in consumption Easiest to calculate Consumer Price Index-modified
- 17. Laspeyres Index I P Q P Q = × × × ∑ ∑ 100 n o o o
- 18. 1990 1996 p90 q90 p96 q96 Refrigerator 335 2 444 12 Range 425 3 588 18 Toaster 18 22 25 58 TV 390 12 440 29 Laspeyres Index= I P Q P Q = × × × ∑ ∑ 10096 90 9090 p96q90 888 1764 550 5280 8482 p90q90 670 1275 396 4680 7021 8.120100 7021 8482 =×=I
- 19. Paasche Index Quantities are from the given period Reflects changes in production or consumption Tend to underestimate price change Weights have to be revised each time period Can be costly and time consuming
- 20. Paasche Index I P Q P Q = × × × ∑ ∑ 100 n n o n
- 21. 1990 1996 p90 q90 p96 q96 Refrigerator 335 2 444 12 Range 425 3 588 18 Toaster 18 22 25 58 TV 390 12 440 29 I P Q P Q = × × × ∑ ∑ 100Paasche Index= 96 96 9690 p96q96 5328 10584 1450 12760 30122 p90q96 4020 7650 1044 11310 24024 I = × = 30122 24024 100 125 4.
- 22. Fixed-Weight Aggregate Price Index Weights are from one or more representative periods Bureau of Labor Statistics revises weights every 10 years Producer Price Index Government agencies indicies are publishes in series (impractical to use Paasche)
- 23. Fixed-Weight Aggregate Price Index I P Q P Q = × × × ∑ ∑ 100n a ao
- 24. Weighted Arithmetic Mean of Price Relatives Index Where w = paqa ∑ ∑ ×× = w P P w I 100))(( n o
- 25. Standard and Poor’s (S&P) 500 Index 10 .. & 500 1 = ∑= VO PN PS i ii Where: O.V. = original valuation in 1941- 43 Ni = number of shares outstanding for Firm I Pi = price of shares for Firm i
- 26. Consumer Price Index Fixed-weight aggregate price index (modified Laspeyres)
- 27. Consumer Price Index 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 Published monthly by Bureau of Labor Statistics 400 goods and services
- 28. Uses of CPI Economic Indicator Escalator Deflator for real wages Process called deflating money wages Price index - deflator Deflated dollar value = constant dollar
- 29. Real Wages CPI1987 = 100 Real Wages98 = Current Wage98 Consumer Price Index98 X 100 100 6.113 853,30$ 33.159,27$ ∗=
- 30. Purchasing Power of Dollar $.82 = 1 122 X 100 $ = 1 CPI X 100 $0.18 decrease in purchasing power of $
- 31. % age Increase or Decrease Current Wage - Past Wage Past Wage X 100 30000 - 20000 20000 X 100 = 50%
- 32. Median Family Income CPI1987=100 Real Income 1990 1998 $20,000 $30,000 105.5 130.5 $18,957.35 $22,988.51 50% increase 23.7% increase 21.3% increase