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# Types Of Index Numbers

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Based On the types of Index Numbers.
Prepared By Siddhant Kumar Behera.
Ravenshaw University Student Of IMBA-FM.

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### Types Of Index Numbers

1. 1. 20-2
2. 2.  A price index measures the changes in prices from a selected base period to another period.  EXAMPLE: Price index is widely applied in various economic and business policy formation and decision making.It is used to measure cost of living of teachers,farmers and weavers.It is also used to construct price index of securities in securities markets.
3. 3.  A quantity index measures the changes in quantity consumed from the base period to another period.  EXAMPLE: Federal Reserve Board indexes of quantity output.
4. 4.  A special-purpose index combines and weights a heterogeneous group of series to arrive at an overall index showing the change in business activity from the base period to the present.  EXAMPLE: Profits or sales or production,Price index of stock markets or productivity index
5. 5.  A value index measures the change in the value of one or more items from the base period to the given period. The values for the base period and the given periods are found by PxQ. Where p = price and q = quantity  EXAMPLE: the index of department store sales,agricultural production,export,industrial production.
6. 6.  A value index measures changes in both the price and quantities involved.  A value index, such as the index of department store sales, needs the original base-year prices, the original base year quantities, the presentyear prices, and the present year quantities for its construction.  Its formula is: V = ∑p q ∑p q t t 0 0 (100) = \$10,600 (100) = 117.8 \$9,000
7. 7.   The consumer price index (CPI) / cost of living index is a measure of the overall cost of the goods and services bought by a typical consumer. It is used to monitor changes in the cost of living over time.
8. 8. The inflation rate is calculated as follows: Inflation Rate in Year2 = CPI in Year 2 - CPI in Year 1 × 100 CPI in Year 1
9. 9. 5% 6% 6% 5% 5% Housing Food/Beverages Transportation 40% 17% 16% Medical Care Apparel Recreation Other Education and communication
10. 10.  An aggregate index is used to measure the rate of change from a base period for a group of items Aggregate Price Indexes Unweighted/ Simple aggregate price index Weighted aggregate price indexes Paasche Index Laspeyres Index
11. 11.  A simple price index tracks the price of a single commodity  The formal definition is: Simple aggregate index = ∑p ∑p n × 100 o Where Σpn = the sum of the prices in the current period Σpo = the sum of the prices in the base period 20-12
12. 12. Automobile Expenses: Monthly Amounts (\$): Index Year Lease payment Fuel Repair Total (2001=100) 2001 260 45 40 345 100.0 2002 280 60 40 380 110.1 2003 305 55 45 405 117.4 2004 310 50 50 410 118.8 I2004  ∑P = ∑P 410 × 100 = (100) = 118.8 345 2001 2004 Unweighted total expenses were 18.8% higher in 2004 than in 2001
13. 13.  Airplane ticket prices from 1995 to 2003: Index Year Price (base year = 2000) 1995 272 85.0 1996 288 90.0 1997 295 92.2 1998 311 97.2 1999 322 100.6 2000 320 100.0 2001 348 108.8 2002 366 114.4 2003 384 120.0 I1996 P1996 288 = × 100 = (100 ) = 90 P2000 320 Base Year: P2000 320 I2000 = × 100 = (100 ) = 100 P2000 320 I2003 P2003 384 = × 100 = (100 ) = 120 P2000 320
14. 14. I2000  Prices in 1996 were 90% of base year prices P2000 320 = × 100 = (100 ) = 100 P2000 320  Prices in 2000 were 100% of base year prices (by definition, since 2000 is the base year)  I1996 P1996 288 = × 100 = (100 ) = 90 P2000 320 Prices in 2003 were 120% of base year prices I2003 = P2003 384 × 100 = (100 ) = 120 P2000 320
15. 15. Unweighted aggregate price index formula:  n ( IUt ) = Pi( t ) ∑ i=1 n ∑P i=1 ( IUt ) n × 100 t = time period n = total number of items = unweighted price index at time t ∑P i=1 (0) i i = item (t) i = sum of the prices for the group of items at time t n Pi( 0 ) ∑ i=1 = sum of the prices for the group of items in time period 0
16. 16. Weighted index no. Consists of –  Laspeyres index   20-17 The Laspeyres index is also known as the average of weighted relative prices In this case, the weights used are the quantities of each item bought in the base period
17. 17.  The formula is: ∑p q Laspeyres index = ∑p q n o × 100 o o Where: qo = the quantity bought (or sold) in the base period pn = price in current period po = price in base period 20-18
18. 18. The 1990 party Drink The 2000 party Unit price Quantity Unit price Quantity po qo pn qn wine 2.50 25 3 30 beer 4.50 10 6.00 8 soft drinks 0.60 10 0.84 15 pnqo = (3 x 25) + (6 x 10) + (0.84 x 10) = 143.4 poqo = (2.5 x 25) + (4.5 x 10) + (0.6 x 10) = 113.5 So, Laspeyre's price index = (143.4/113.5) x 100 = 126.3 20-19
19. 19. Laspeyres Index Requires quantity data from only the base period. This allows a more meaningful comparison over time.
20. 20. Laspeyres index assumes that the same amount of each item is bought every year. If I bought a radio one year, the index assumes I bought one the next year. If I bought 35 kg of oranges in Po, the index assumes I bought the same amount every year, when in reality if the price went up, one might buy less. Does not reflect changes in buying patterns over time. Also, it may overweight goods whose prices increase.
21. 21.  Paasche index    The Paasche index uses the consumption in the current period It measures the change in the cost of purchasing items, in terms of quantities relating to the current period The formal definition of the Paasche index is: pnqn Paasche index = × 100 poqn ∑ ∑ Where: pn = the price in the current period po = the price in the base period qn = the quantity bought (or sold) in the current period 20-22
22. 22. ∑ pq P= ∑pq t t 0 t \$811.60 (100) = (100) = 135.64 \$598.36
23. 23. Paasche Index Because it uses quantities from the current period, it reflects current buying habits.
24. 24. Paasche Index It requires quantity data for the current year. Because different quantities are used each year, it is impossible to attribute changes in the index to changes in price alone. It tends to overweight the goods whose prices have declined. It requires the prices to be recomputed each year.
25. 25.  Fisher’s ideal index  Fisher’s ideal index is the geometric mean of the Laspeyres and Paasche indexes  The formal definition is: Fisher' s index = ( Laspeyres index )( Paasche index ) ∑p q ∑p q ∑p q ∑p q 20-26 n o n n o o = o n × 100
26. 26. i) Index numbers are economic barometers. They measure the level of business and economic activities and are therefore helpful in gauging the economic status of the country. (ii) Index numbers measure the relative change in a variable or a group of related variable(s) under study. (iii) Consumer price indices are useful in measuring the purchasing power of money, thereby used in compensating the employees in the form of increase of allowances.
27. 27. 20-28
28. 28. 20-29