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Index Numbers Index numbers Index numbers measure the magnitude of economic changes over time. They express these changes as percentages of a predetermined period (usually a particular year, known as the base year). The Index of Retail Prices, which attempts to measure the change in price of the goods and services we buy, is one of the most important indexes because It measures the cost of living, inflation It enables governments to monitor inflation It is used in pay determination and in wage negotiations It is linked to increases in social welfare and pensions. Price Relative This is a simple index that shows the price of a single item over a period of time as a percentage of the price in the base year. Example: The price of Product A over 3 years is as follows: 2003 €4.50 2004 €4.70 2005 €4.89 The price relatives, using 2003 as base year, are 2003 = 100 2004 (4.70/4.50)x100 = 104.4 2005 (4.89/4.50)x100 = 108.7 This index tells us that the price of Product A rose by 4.4% between 2003 and 2004 and by a further 4.3% between 2004 and 2005. Laspeyre’s Index The Laspeyre Index uses the quantities of the base year to give relative importance to the different products. This is known as weighting. The index is calculated by the formula: Laspeyre Index = Pn Qo *100 P0Q0 Laspeyre Advantages 1. Weights (the quantities) are only needed for one year, the base year 2. Because of this it is cheaper to construct 3. The indexes for each year can be compared directly Pn is the price in the year for which the index is being calculated and P0 and Q0 are the price and quantities in the base Year Laspeyre Disadvantages 1. Tends to overstate price increases 2. Does not take account of changes in demand. The Laspeyre Index tells us what we would have paid in year n for a collection of goods assuming we bought the base year quantities. Walter Fleming Page 1 of 5 Index Numbers Paasche Index This calculates an index using the quantities of the year for which the index is being calculated. This index takes changes in consumption into account. Pn Qn *100 Paasche Index = Qn are the Quantities P0Qn in the year in which the index is being calculated Paasche’s Advantages 1. Uses current quantities (weights) and 1. so takes changes in consumption patterns into account. 2. Does not overstate price increases Paasche’s Disadvantages 1. Not a pure index as price and quantities change 2. Long and expensive to update weights 3. The indexes for each year cannot be compared directly since the quantities change 4. Tends to understate price changes The Paasche tells us what we would pay in the base year for the amount of goods we bought in the current year. Limitations of Laspeyre and Paasche indexes The Laspeyre Index tends to overstate price increases, whereas the Paasche Index tends to understate increases. Indices give only a general indication of change over a wide geographical area. The choice of base year can affect the indices. The base year should not be too far in the past. It should also be a fairly unexceptional period, not one of say very high or very low inflation. Fisher’s Index As said above, the Laspeyre Index tends to overstate the changes in price while the Paasche Index tends to understate price changes. The Fisher Index attempts to correct this. Fisher’s index = (Laspeyre's Ιndex) x (Paasche's Index) Fisher’s index lies between the other two indexes. It is referred to as an “ideal” index because it correctly predicts the expenditure index. Walter Fleming Page 2 of 5 Index Numbers Example: 2003 Product A B C 2005 Price 1.15 0.80 2.50 Quantity 20 90 10 Price 1.30 1.04 2.90 Laspeyre Index for 2005 using 2003 as base year Paasche Index for 2005 Σpnq0 1.30 x 20 = 26.00 1.04 x 90 = 93.60 2.90 x 10 = 29.00 Total = 148.60 Σpnqn 1.30 x 50 = 65.00 1.04 x 60 = 60.24 2.90 x 15 = 43.50 = 168.74 Σp0q0 1.15 x 20 = 23.00 0.80 x 90 = 72.00 2.50 x 10 = 25.00 = 120.00 Index for 2005 = 148.60/120.00 = 124 Fisher’s index = Quantity 50 60 15 Σp0qn 1.15 x 50 = 57.50 0.80 x 60 = 48.00 2.50 x 15 = 37.50 = 143.00 Paasche Index for 2005 = 168.74/143.00 = 118 (124) x(118) 120.96 The Consumer (Retail) Price Index The Consumer Price index (CPI) is designed to measure the change in the level of prices paid for consumer goods and services. It measures inflation. The Central Statistics Office (CSO) collects the prices of a fixed representative group of goods and services every month. Over 50,000 prices are collected from shops, supermarkets, petrol stations, service outlets, etc as well as from utilities, transport companies, doctors, dentists, etc. The prices are combined into a single index measuring the overall level of prices. Not all goods and services are treated equally. The CSO decides what weight to apply to a product by determining the average weekly expenditure of an average household on the product or service. This information is got through the Household Budget Survey, which is carried out every 5 years. This survey also determines which goods and services should be included or dropped. The survey involves over 7000 households chosen at random from all private households in the state. STAGES INVOLVED IN THE CONSTRUCTION OF THE CPI Selection of Component Commodities: Walter Fleming Page 3 of 5 Index Numbers The commodities and services purchased by the great majority of households should be used, e.g. food, housing, transport and vehicles, etc. Selection of Weights: Each component group should be weighted “annually” according to the expenditure of a typical family. Collection of Data: Usually involves continuous investigation to find prices and weights for commodities. Selection of a Base Time Period: A base period should be chosen which is not too far in the past. USES OF CONSUMER PRICE INDEX 1. To measure the rate of inflation 2. Wage negotiations 3. Widening of the tax bands - used by Government as the yardstick by which tax bands are widened in the annual budget. 4. Maintaining the real value of social welfare payments. 5. To maintain the real value of savings 6. International competitiveness - a comparison of our inflation rate with those of our trading partners indicates whether our international competitiveness is improving or worsening. Other uses of the CPI 1. To find "Real" wages The "real" wage is an indication of how much purchasing value wage increases give us. If for example, my wage was €200 in 1998 and it was €400 in 2001, it would appear my wages had doubled. However if the CPI had increased from 100 in 1998 to 110 in 2001 then my real wage in 2001 would be €363.63, that is it took €400 in 2001 to buy the same goods that cost €363.63 in 1998. To find real wages: (Wage divided by Index Number) * 100 Walter Fleming Page 4 of 5 Index Numbers 2. Changing the base year of an index From time to time it is necessary to change the base year to prevent the index becoming too unwieldy. We need to be able to change from "old" index numbers to "new" index numbers. Example: Year 1979 1980 1981 Index (Base 1968 =100) 340 346 351 If the Base Year is changed to 1980 = 100 what is the new index for 1981? New Index =(Index for required year) divided by ( index of New Base Year) *100 New index for 1981 = 351/346 * 100 = 101.4 OTHER COMMONLY USED INDICES 1. The agricultural output price index 2. The wholesale price index 3. Industrial production index 4. Import price index 5. Export price index 6. Shares Indices e.g. Financial Times Share index. LIMITATIONS OF INDEX NUMBERS 1. Index numbers give only general indications of changes therefore they will not cater for minority groups generally. 2. Weights become out of date. 3. The information used might be biased. 4. Open to misinterpretation. Walter Fleming Page 5 of 5