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Index number


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Index number

  3. 3. INTRODUCTION•An index number measure the relativechange in price, quantity, value, or someother item of interest from one time period toanother.•A simple index number measure the relativechange in one or more than one variable
  4. 4. WHAT IS AN INDEX NUMBER•An index number measure how much a variablechanges over time.•We calculate the index number by finding theratio of the current value to a base value.
  5. 5. DEFINITION“Index numbers are quantitative measures ofgrowth of prices, production, inventory andother quantities of economic interest.”
  6. 6. CHARACTERISTICS OF INDEX NUMBERS• Index numbers are specialized averages.• Index numbers measure the change in the level of a phenomenon.• Index number measure the effect of changes over a period of time.
  7. 7. USES OF INDEX NUMBERS• To framing suitable policies.• They reveal trends and tendencies.• Index numbers are very useful in deflating.
  8. 8. PROBLEMS RELATED TO INDEX NUMBERS• Choice of the base period.• Choice of an average.• Choice of index.• Selection of commodities.• Data collection.
  10. 10. METHODS OF CONSTRUCTING INDEX NUMBERS Simple Aggregative UNWEIGHTED Simple Average of Price RelativeINDEX NUMBER Weighted Aggregated WEIGHTED Weighted Average of Price Relatives
  11. 11. SIMPLE AGGREGATIVE METHODIT consists in expressing the aggregate price of allcommodities in the current year as a percentage of theyear.
  12. 12. EXAMPLEFrom the data given below construct the index number for the year 2007 on the base year 2008 in Rajasthan state. COMMODITIES UNITS PRICE (Rs) PRICE (Rs) 2007 2008 SUGAR QUINTAL 2200 3200 MILK QUINTAL 18 20 OIL LITRE 68 71 WHEAT QUINTAL 900 1000 CLOTHING METER 50 60
  13. 13. SOLUTION COMMODITIES UNITS PRICE (Rs) PRICE (Rs) 2007 2008 SUGAR QUINTAL 2200 3200 MILK QUINTAL 18 20 OIL LITRE 68 71 WHEAT QUINTAL 900 1000 CLOTHING METER 50 60 TOTAL p0=3236 p1=4351Index number for 2008- p01 1 × 100 = 4351 × 100 = 134.45 0 3236It means the prize in 2008 were34.45% higher than the previous year.
  14. 14. SIMPLE AVERAGE OF RELATIVE METHOD The current year price is expressed as a price relative of the base year price. These price relatives are then averaged to get the index number . The average used could be arithmetic mean, geometric mean. Where n is number of itemWhen geometric mean is used
  15. 15. EXAMPLEFrom the data given below construct the index number for the year 2008 taking 2007 as by using arithmetic meanCOMMODITIES PRICE (Rs) PRICE (Rs) 2007 2008 P 6 10 Q 2 2 R 4 6 S 10 12 T 8 12
  16. 16. SOLUTION Index number using arithmetic meanCOMMODITIES PRICE (Rs) PRICE (Rs) PRICE RELATIVE 2007 2008 pn ×100 P0 Pn P0 P 6 10 166.7 Q 2 2 16.67 R 4 6 150.0 S 10 12 120.0 T 8 12 150.0 TOTAL 603.37 603.37=120.63 5
  17. 17. WEIGHTED INDEX NUMBERS• These are those index number in which rational weights are assigned to various chains in an explicit fashion .• Weighted aggregative index numbers. These index numbers are the simple aggrigative type with the fundamental diffrence that weights are assigned to the various items included in the index. Laspeyres method Paasche method Fisher’s method Marshall-edgeworth method Kelly’s method
  18. 18. LASPEYRES METHOD This method was devised by Laspeyres in 1871. In this method the weights are determined by quantities in the base. × 100PAASCHE METHOD This method was devised by a German statistician Paasche in 1874. The weights of current year are used as a base year in constructing the Paasche’s Index number. × 100
  19. 19. FISHER’S METHOD Fisher’s method Index number is Geometric mean of the laspeyre’s and paasche’s Index numbers. × 100MARSHALL-EDGEWORTH METHOD In the index the numerator consists of an aggregate of the current years price multiplied by the weights of both the base year as well as the current year. × 100
  20. 20. Kelly’s methodKelly thinks that a ratio of aggregates with selected weights givesthe base index number q qq refers to the quantities of the which is selected as the base. It maybe any year, either base, year or current year
  21. 21. EXAMPLEGiven below are the price quantity data , with price quoted in Rs. Per kg and production in qtls. Find - Laspeyres method , Paasche method , Fisher’s methodITEMS PRICE PRODUTION PRICE PRODUTIONBEEF 15 500 20 600MUTTON 18 590 23 640CHICKEN 22 450 24 500
  22. 22. SOLUTION:-ITEMS PRICE PRODU PRICE PRODU p1q0 p0q0 p1q1 p0q1 TION TION p0 p1 q0 q1BEEF 15 500 20 600 10000 7500 12000 9000MUTTO 18 590 23 640 13570 10620 14720 11520NCHICKE 22 450 24 500 10800 9900 12000 11000NTOTAL 34370 28020 38720 31520
  23. 23. Laspeyres method × 100 34370 × 100 = 122.66 28020Paasche method × 100 38720 × 100 = 122.84 31520Fisher’s method × 100 = 122.69
  24. 24. TEST FOR PERFECTION1. Time reversal test:- P01 * P10 = 12. Factor reversal test:- P10*Q01= ∑p1q1 ∑p0q01. Circular test:- P01*P12*P20=1
  25. 25. CHAIN BASE INDEX NUMBERS• Chain base index numbers are those numbers in which the year immediately preceding the one is taken as base year.
  26. 26. • Link Relatives= Current Year’s Price * 100 Previous Year Price• Chain Base Index=Link Relative Of Current Year * Chain Index Of Prev. Year 100
  27. 27. Conversion Of Chain Index To Fixed Base Index• Current Year FBI= Current Year’s CBI * Previous Year’s FBI 100
  28. 28. BASE SHIFTING• One of the frequent operation necessary in the use of index number in changing the base of an index. It is needed in 2 reasons:-1. When present base year has become rather old.2. When some series are to be compared with other whose base years are different.
  29. 29. SPLICING• Splicing is a process by which new series of indices is tied with old index series or old series of indices is tied with new index series.
  30. 30. DEFLATING• It refers to the correction for price changes in money wages or money income series.• REAL WAGE= Money Wage * 100 Price Index• Real Wage Index No.= Index Of Money Wage Price Index
  31. 31. CONSUMER PRICE INDEX• It is those numbers which measure the effects on living conditions of different classes of consumer for any change in the level of prices over a period of time.
  32. 32. METHODS FOR CONSTRUCTING CONSUMER PRICE INDEX1. Aggregate Expenditure Method2. Family Budget Method
  33. 33. Aggregate expenditure method• In this wages are assign to items on the base of base year quantities.• Consumer Price Index (P01) = ∑p1q0 * 100 ∑p0q0
  34. 34. Family budget method• In this method weights are assign on the basis of percentage expenditure on item.• Consumer price index = ∑ PW ∑W*W = p0q0
  35. 35. THANK YOU