�The Consumer Price Index�

• The consumer price index (CPI) measures the change in prices for a fixed market basket of goods and services from one period to another.
• In constructing the CPI, the universe or group of commodities to be included should be defined, then a sample is chosen to represent the universe.
• The aggregate expenditure (Laspeyres) is used.

Example 1

• The table below shows the prices and quantities of the basket of goods used in the calculation of CPI in a country.
• (a) Construct the CPI for the years 2003 to 2007.
• (b) Interpret your results in 2007

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solution

• The CPI for 2007 is 189.13% which means that on the average the prices of the basket of goods have gone up by 89.13% compared to the base year price.
• Example 2
• An enquiry into the expenditure of middle class families in a certain city gave the following information:

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• Construct the CPI using the weights provided using 2022 as the base year and interpret your results.

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Solution

• For 2022: Food = (35/100)x150 = 52.5; Fuel = (10/100)x25 = 2.5 etc. Same computation is done for the year 2023.
• Total amount is the row sum for each year.
• CPI = (total amount/total amount of base year)x 100

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�Uses of the CPI – Calculating Inflation�

• Inflation is the persistent increase in the general price levels whiles deflation is the persistent decrease in the general price levels.
• Mathematically, inflation or deflation for the years t is computed as:
• (CPI_t – CPI_t-1)/(CPI_t-1)x100 where CPI_t-1 is the consumer price index year for t-1.
• If this value is greater zero, then there is inflation. But if it is less than zero, then is deflation.

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• Example 1
• The table below shows the CPI for a country from 2000 to 2010. Calculate the level of inflation/deflation for each year and interpret your results for the year 2009.

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Prices of goods and services in 2009 have gone up by 6.5 percent compared to that of 2000.

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�Uses of the CPI – Deflating�

• Real income is the income of an individual, organization or a country, after taking into consideration the effects of inflation on purchasing power.
• The process of calculating real income from current (nominal) income is called deflating.
• Mathematically, if RI is real income and NI is nominal income, then:
• RI = (NI/CPI)x100

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�Example 1�

• The CPI in a country is 300% in 2005 (2000 = 100). If an employee earned GHC 7000 in 2000 and GHC 21,000 in 2005.
• (a) Calculate his real income his real income in 2005
• (b) Comment on the welfare of the employee.
• Soln:
• (a) Recall RI = (NI/CPI)x100; thus
• RI₂₀₀₅ = (21,000/300)x100 = 7000.
• (b) Although the employee’s nominal income tripled over the period, his standard of living or purchasing power is the same as it was in 2000.

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�Example 2�

• The table below shows the annual income of a teacher and the CPI from 2001 to 2009.
• (a) Calculate the real income of the teacher.
• (b) Prepare a series of index number to show the changes in his/her real income
• (c) Comment on the welfare of the teacher.

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solution

• (a) Recall RI = (NI/CPI)x100, see calculation in table below
• (b) A simple income index from the real income of the teacher is given as
• I_n/0 = (I_n/I₀)x100. See computation of real income index number in table below.

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• (c) The nominal income increases but his/her real income decreases. This means that the teacher has been worse of over the years.
• Related to the calculation of real income is the calculation of purchasing power of a currency or income.
• Rise in price levels means a reduction in the purchasing power of money or the amount of goods and services that you can buy.
• Suppose the price of rice increases from GHC 10 per bag in 2010 to GHC 20 in 2020. This means in 2020 if you had GHC10, you could buy only half bag of rice.
• Mathematically, if PP is the purchasing power of the cedi, then PP = (1GHC/CPI)x100

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Reading Assignment

• Read on:
• (i) use of Index numbers
• (ii) Limitations of Index numbers.