SUPPORT CENTRE - University of Sheffield

1 MATHEMATICS SUPPORT CENTRE Title: Simple Index numbers Target: On completion of this worksheet you should be able to calculate simple index numbers, and a weighted index. Index numbers make a comparison between a value (quantity or price) in the current period and the corresponding value in a base period. All calculations are given in percentages without the % sign. 100 =valuebasevaluenumberindex Example. A pint of milk cost 26p in January 1988, 29p in 1990, 36p in 1997 and 34p in 1999. The milk price index in 1990 with 1988 as base is 51111002629 = Exercise Find the milk price index in each case: 1. For 1999 with 1988 as base. 2. For 1999 with 1997 as base. Answers: The index in 1999 with base 1988 is 130 8 The index in 1999 with base 1997 is 94 4 Index numbers can go down as well as up! Notice that milk went up by 5p between 1990 and 1999 (a increase) but the index increased from 111 5 to 130 8, or 19 3 points.

2 An increase of so many points in the index number does not mean a percentage increase of the same amount, unless you are referring back to the base period. Exercise. 1. The price of a laptop computer in 1997 is 3 000 in 1999 is 2 000 in 2000 is 1 000 Construct a price index for a laptop with base year 1999. 2. The price of a car in 1990 is 6 000, in 1995 is 8 000, and in 2000 is 9 000. Construct a price index for the car with base year 1990. 3. The price of a train ticket to London from Lanchester in 1995 is 30 1996 is 40 1997 is 50 2000 is 60 Construct a price index for the ticket with base year 2000. 4. Using the information in the table construct index numbers for Prices in pence Item 1998 1999 2000 White bread 51 51 52 Carrots 24 22 19 Cod fillets /lb 277 324 374 a.

3 Bread for the 3 years with 1998 as base. b. Carrots for the 3 years with base year 1999. c. Cod fillets for the 3 years with base year 2000. Answers: 1) 150,100,50; 2) 100,133 3,150; 3) 50,66 7, 83 3, 100 4a) 100,100,102 0; 4b) 109 1,100,86 4; 4c) 74 1,86 6,100; S3 Often we look at the price of a group of goods in various quantities - 'baskets'. Quantities and prices can vary from year to year, so to make 'fair' comparisons the Laspeyres Price Index uses the base year quantities throughout. The Laspeyre Price Index = 100 yearbaseingoodsofbasketofpriceyearcurren tingoodsofbasketofprice Example. My friend eats only brown bread and honey, and each week in 1999 ate 7 loaves of sliced brown bread and 2kg of honey.

4 Now she eats 8 loaves and 1 5kg of honey. We can calculate the Laspeyres Index for her food consumption for Jan 2000 with Jan 1999 as base as follows. Loaf of bread 1kg honey Price in Jan 1999 52p 1 68 Price in Jan 2000 54p 1 96 The price of the basket in Jan 1999: (7 x 0 52) + (2 x 1 68) = 3 64 + 3 36 = 7 00 The price of the basket in Jan 2000: (7 x 0 54) + (2 x 1 96) = 3 78 + 3 92 = 7 70 11010011100007707= = =Index Exercise. 1. I enjoy going to the cinema and theatre. Here are details of tickets I bought and prices. price Jan 99 Qty Jan 99 price Jan 00 Qty Jan 00 cinema tickets 3 8 3 50 6 theatre tickets 8 2 10 1 Calculate a Laspeyre's Price Index for January 2000 with base January 1999. Answer: 120 Example. The Paasche Price Index for my cinema and theatre tickets for January 2000 with base January 1999 is 21191002631100)36()81()5036()101( = = + + Exercise.

5 Calculate the Laspeyres and the Paasche Price Index for January 2000 for each of the following with base January 1999. 1. For my travel costs. My weekly travel costs are train fares to and from work, and bus fares to and from the town CENTRE . The cost and number per week are as follows: price Jan 99 Qty Jan 99 price Jan 00 Qty Jan 00 train fare 1 85 10 2 6 bus fare 0 75 4 1 4 2. For my share portfolio. My shares in Company A and B are: price Jan 99 Qty Jan 99 price Jan 00 Qty Jan 00 Company A 1 70 1000 2 00 1500 Company B 1 90 200 1 00 200 3. For the Coffee Club. price Jan 99 Qty Jan 99 price Jan 00 Qty Jan 00 Tea bags 250g 1 56 1kg 2 01 1 5kg Instant coffee 100g 1 51 2kg 1 86 2 5kg 4. For my shares. I have a small portfolio of shares in Companies A , B and C. price Jan 99 Qty Jan 99 price Jan 00 Qty Jan 00 Company A 0 90 100 1 200 Company B 1 200 0 90 100 Company C 2 200 4 300 Answers: question Laspeyres Paasche 1 111 6 113 5 2 105 8 109 2 3 124 1 124 3 4 156 5 169 3 People tend to change to cheaper goods, and buy less, when prices go up so may well not buy the same quantities each year.

6 To account for this another index, the Paasche Price Index, updates the quantities and calculates the index using this year's quantities throughout.