LECT 1 2018 2019 Index Numbers PDF

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INDEX NUMBERS An index is used to express the relative change in a value from one period to another. In economics, they are intended to measure the degree of changes in economic variables over time. Index numbers are values stated as a percentage of a single base figure. Therefore, an index number is a number that expresses the relative change in price, quantity, or value compared to a base period. Importance of index Numbers Index numbers are important in economic statistics for the following reasons i.

The study the change in the effects of such factors which cannot be measured directly. Bowley stated that "Index numbers are used to gauge the changes in some quantity which we cannot observe directly".

ii.

Index numbers are usually applied in statistical device to measure the combined fluctuations in a group related variables.

iii.

With the support of index numbers, the average price of several articles in one year may be compared with the average price of the same quantity of the same articles in a number of different years.

iv.

Index numbers may be categorized in terms of the variables that they are planned to measure. In business, different groups of variables in the measurement of which index number techniques are normally used are price, quantity, value, and business activity.

v.

Index numbers for instance the Consumer Price Index is important because it measures the change in the price of a large group of items consumers purchase. The Producer Price Index, on the other hand measures price fluctuations at all stages of production. The ruling authorities need knowledge of these fluctuations to stabilize the economy.

Types of Index Numbers a. Simple Index Number: A simple index number is a number that measures a relative change in a single variable with respect to a base. These type of Index numbers are constructed from a single item only. b.

Composite Index Number: A composite index number is a number that measures an average relative changes in a group of relative variables with respect to a base. A composite index number is built from changes in a number of different items.

c.

Price index Numbers: Price index numbers measure the relative changes in prices of a commodity between two periods. Prices can be either retail or wholesale. Price index number are useful to comprehend and interpret varying economic and business conditions over time.

d.

Quantity Index Numbers: These types of index numbers are considered to measure changes in the physical quantity of goods produced, consumed or sold of an item or a group of items.

Characteristics of index numbers: a.

Index numbers are specialised averages.

b.

Index numbers measure the change in the level of a phenomenon.

c.

Index numbers measure the effect of changes over a period of time.

d.

Index numbers are reported as percentages but the sign is usually omitted in computations

e.

Index numbers are related to a base year

f.

Most economic index numbers are reported to the nearest whole number or to the nearest 10th of a percent e.g. 8.3, 118.6

Uses of Index number 1.

Index numbers has practical significance in measuring changes in the cost of living, production trends, trade, and income variations.

2.

Index numbers are used to measure changes in the value of money. A study of the rise or fall in the value of money is essential for determining the direction of production and employment to facilitate future payments and to know changes in the real income of different groups of people at different places and times.

3.

By using the technical device of an index number, it is possible to measure changes in different aspects of the value of money, each particular aspect being relevant to a different purpose.

4.

Basically, index numbers are applied to frame appropriate policies. They reveal trends and tendencies.

5.

Index numbers are beneficial in deflating inflated values.

Problems associated with index numbers 1. 2. 3. 4. 5.

Choice of the base period. Choice of an average. Choice of index. Selection of commodities. Data collection.

ILLUSTRATIONS Simple Index Numbers This considers comparison for a single commodity or variable. Therefore, if the index number is used to measure the relative change in just one variable, such as hourly wages in manufacturing, we refer to this as a simple index. The current value is converted into a percentage relative to the base value in simple index. Illustration 1 1. According to the Bureau of Labour Statistics, in 2010 the average hourly earnings of production workers was ₦800. In 2015, it was ₦1,300. What is the index of hourly earnings of production workers for 2015 based on 2010 data? 𝐼=

𝑃𝑡 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 (𝑃𝑟𝑖𝑐𝑒) = ∗ 100 𝐵𝑎𝑠𝑒 𝑉𝑎𝑙𝑢𝑒 (𝑃𝑟𝑖𝑐𝑒) 𝑃0

Or =

𝑉𝑎𝑙𝑢𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒 𝑡 ∗ 100 𝑉𝑎𝑙𝑢𝑒 𝑖𝑛 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑡𝑖𝑚𝑒 𝑜𝑟 𝐵𝑎𝑠𝑒𝑠 𝑃𝑒𝑟𝑖𝑜𝑑

By how much does current wage increase relative to the base price?

Illustration 2 Assume the population of students in Babcock University (BU) in 2016 was 10,000 and for Clifford University (CLU) it was 1,875. i. ii.

What is the population index of BU compared to CLU? What is the population index of CLU compared to BU?

Illustration 3 Suppose the price of a plate of food in BUGH was ₦1,000 in 2014 and in 2017 it is ₦1,800. What is the price index for 2017 using 2014 as the base year? By how much did price increase between 2014 and 2017? Illustration 4 The prices of Bread for four years is presented in the table below Year 2015 2016 2017 2018

Price 200 230 280 300

Determine the simple price index using i. ii. iii.

2015 as the base year 2017 as the bas year Chain based method

Unweighted Index Numbers Sometimes it is necessary to compare the index number of a group of items. This can be done using a. The arithmetic mean as average b. Median as average c. Geometric mean as average Illustration 4 Consider the table below, compute the index numbers. (2010 = 100) Year Items Ex. Book Calculators Math. Set

2010 Price 24 47 24

2017 Price 25 51 40

2018 Price 27 60 56

Simple Aggregate Index This can also be achieved by summing the prices (rather than the index numbers) in the two periods and taking their ratio. 𝑃𝐼 =

∑ 𝑃𝑡 ∗ 100 ∑ 𝑃0

The problem with this method is that it is influenced by the unit of measurement. For instance if exercise books were measured in cartons and not in prices, the value of the index would differ significantly.

WEIGHTED INDEX NUMBERS There are two common methods for computing weighted index numbers i. ii.

Laspeyres method Paasche method

Laspeyres Price Index This is computed as shown

𝑃𝐼 =

∑ 𝑃𝑡 𝑄0 ∗ 100 ∑ 𝑃0 𝑄0

Where PI = Price Index Pt = Price in year t or current year P0 = Price in Base year Q0 = Quantity in Base year Paasche Price Index This is an alternative to the Laspeyres index. The procedure is similar, but instead of using base-period quantities as weights, it uses current-period quantities as weights. This index has the advantage of using more recent quantities. The formula for the Paasche Index is 𝑃𝐼 =

∑ 𝑃𝑡 𝑄𝑡 ∗ 100 ∑ 𝑃𝑜 𝑄𝑡

Where Pt = Price in the current period Qt = Quantity in the current period Po = Price in the base period. Advantages and Disadvantages of Laspeyres and Paasche Method Laspeyres Advantages i. Requires quantity data from only the base period. ii. It allows a more meaningful comparison over time. iii. The changes in the index can be attributed to changes in the price. Disadvantages i. Does not reflect changes in buying patterns over time. ii. It may overweight goods whose prices increase. Paasche Advantages i. Because it uses quantities from the current period, it reflects current buying habits. Disadvantages i. It requires quantity data for the current year. ii. Because different quantities are used each year, it is impossible to attribute changes in the index to changes in price alone. iii. It tends to overweight the goods whose prices have declined. iv. It requires the prices to be recomputed each year.

Fisher’s Ideal Index In an attempt to overcome the shortcomings associated with the Laspeyres and Paasche methods of computing price index, Irving Fisher developed another method called Fisher’s ideal index. It is the geometric mean of the Laspeyres and Paasche indexes. The index number is computed as shown below. 𝐹𝑖𝑠ℎ𝑒𝑟 ′ 𝑠 𝐼𝑑𝑒𝑎𝑙 𝐼𝑛𝑑𝑒𝑥 = √(𝐿𝑎𝑠𝑝𝑒𝑦𝑟𝑒𝑠)(𝑃𝑎𝑎𝑠𝑐ℎ𝑒 𝐼𝑛𝑑𝑒𝑥) Fisher’s index seems to be theoretically ideal because it combines the best features of both Laspeyres’ and Paasche’s. That is, it balances the effects of the two indexes. However, it is rarely used in practice because it has the same basic set of problems as the Paasche index. It requires that a new set of quantities be determined for each period. Illustration 5 An index of bread prices for 2016 based on 2010 is to be constructed. The prices and quantities for each year are given below. Use 2010 as the base period and 100 as the base value. Year

2010

2016

2010

2016

Type of Bread Enriched Whole Wheat Val U Butter Cup Blessed Loaf

Quantity (Qo) 10 20 30 40 50

Quantity (Qt) 30 40 50 60 70

Price (N) (Po) 30 50 60 70 48

Price (N) (Pt) 50 70 90 80 60

i. ii. iii. iv. v.

Determine the simple price indexes for the items. Determine the aggregate price index for the years. Determine Laspeyres’ price index. Determine the Paasche price index. Determine Fisher’s ideal index....