�What is an Index number (IN)?�

• An IN is the percentage ratio of prices, quantities and values comparing two time periods – base period and current period.
• Base period is period against which comparisons are made – indicated by the subscripts 0. Value of IN at the base period is always 100, I₀ = 100.
• Current of given period on the other hand is the period being compared with the base period. Period could be weekly, monthly, quarterly, semi-annually, biannually etc.
• Values of the IN in subsequent years can be more than or less than the value of the base year depending on whether the values of the actual number increased or decreased.

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• Example:
• Assuming the IN of industrial production in 2020 is 85% and 120% in 2023 compared to that of 2015 which is the base year (100%).
• Interpretation
• There is a net decrease in industrial production by 15% (85%-100%) compared to that of 2015
• There is a net increase in industrial production by 20% (120%-100%) compared to that of 2015

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�Classification of Index numbers�

• (i) Simple price, quantity and value indices
• (ii) Aggregate (weighted) indices
• Simple aggregated price, quantity and value indices

- Laspeyres price and quantity index

- Paasche price and quantity index

- Fisher ideal index

• (iii) Special purpose indices – combine other indices to show changes in business activities or any important occurrence from period to another. Example, composite index of economic activity by BoG.

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�Simple price, quantity and value indices�

• Simple Price Index – measures the percentage change in the price of a good or commodity from a given base period to another year. Its purpose is to measure the rise or fall in price of the commodity from the base year to the current year. Example: price index of cocoa.
• Simple Quantity Index – measures the percentage in the quantity of a good or output from a base period to current period. Example: production index of gold.
• Simple Value index – measures the percentage in the value of a good from one period to another. Note that value = quantity x unit price. Example: value index of cocoa.

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�Construction of simple price, quantity and value indices�

• Let us denote the base year price of cocoa by P₀ and the price of cocoa in the current year by P_n. Then the simple price index of cocoa Pn/0 is given as P_n/₀ = (P_n/P₀)x100.
• Analogically, we can define the simple quantity and value indices as:
• Q_n/o = (q_n/q₀)x100 and V_n/0 = (v_n/v₀)x100 respectively. Where q₀ is the quantity of the commodity in the base year, q_n is the quantity in current year, v₀ = p₀q₀ is the value in base year and v_n = p_nq_n is the value in the current year.

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• Example:
• In 2010, the price of a car was GHC 25000 and in 2020, the same car cost GHC 35000. If the base year is 2010, find the price index of the car in 2020.
• Interpret your results.
• Soln:
• P₀ = 25000, P_n = 35000, implies the simple price index, P₂₀₂₀ = (P_n/P₀)x100 = (35000/25000)x100 = 140
• This means that the price of the car has increased by 40% (140% - 100%) compared to the base year price.

• Example 2
• The table below shows the price and output of cocoa for Ghana from 2012 to 2021. Using 2012 as the base year construct the:
• (a) Simple price index of cocoa for the years
• (b) Simple quantity index of cocoa for the years.
• (c) Value index for cocoa
• (d) Interpret the price, quantity and value indices for 2021

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Solution

• (d) Compared to the base year, the price, the quantity and the value of cocoa has gone up by 16%, 33% and 55% respectively.
• Construction of Aggregated (Weighted) Indices
• Aggregated Index (AI) is a measure of the percentage ratio of the sum of the prices, quantities and values of a group of commodities from one period to the other.
• The objective of constructing aggregated index is to provide basis for comparing the general price, quantity and value of a group of commodities.

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Example

• The table below shows the prices (in cedis) of a group of commodities for 2020 and 2021. Construct a simple aggregated price index for 2021 taking 2020 as the base year.

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Example 2

• The table below shows the production (in tons) and unit prices (in cedis) of some selected commodities in Ghana for 2015 – 2019.
• (i) Using 2015 as the base year, calculate:
• (a) The simple aggregated price index
• (b) The simple aggregated quantity index
• (c)The value index
• (ii) Interpret your results for the year 2018.

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Solution

• Compared to 2015, the aggregate prices, quantities and values of the commodities have seen a net increase of 91.09%, 104.38% and 266.39% respectively in 2018.

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�The Laspeyres Index�

Example 1

• The prices of three food items for 2010 and 2020 and the quantities consumed by a certain community in 2010 are shown in the table below.
• Construct the Lespeyres price index using 2010 as the base year.
• Interpret your results.

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