### Question

How do we calculate “real” prices, adjusting for inflation?

Uses monthly price data of a commodity and a monthly consumer price index (CPI) to adjust prices for inflation. The result is a set of real prices that show the trends in the commodity price after removing the effect of general inflation.

### Data Requirements

• Monthly price data
• Monthly consumer price index for the same period
The consumer price index is usually calculated by the Ministry of Finance in each country, but CPI data for each country are also available from the International Monetary Fund.

### Background

Economic decisions are mostly based on relative prices, not absolute prices. In other words, if all prices and income doubled, there would be no effect on purchasing decisions because relative prices would not have changed. Similarly, planting decisions of farmers are largely determined by the relative prices of different crops.

Inflation describes a general increase in all prices, although the rate of increase varies across products. Inflation is usually measured by the consumer price index (CPI), which describes the prices in a given month as a percentage of prices in a base period. If the CPI has a base month of January 2000, then by definition the CPI for that month is 100. If the CPI is 150 in January 2002, this means that prices were 50 percent higher in January 2002 than they were two years before. This implies that the annual inflation rate over this period is (1.5)1/2 = 1.225 or 22.5%. (See Footnote 1) Variables
i commodity
Pi nominal price of commodity
CPIt comsumer price index for month t

Real prices are defined as prices that have been adjusted for inflation. The real price in a given month is calculated by dividing the nominal price (the price observed in the market) by the CPI of that month, where the CPI is expressed as a ratio and not a percentage. In other words, a CPI of 150 is expressed as 1.5.

Usually, we are most interested in the changes in real prices over time rather than the level of real prices at one time. For example, it is not very useful to know that the real price of maize in June 2008 was xxx birr/quintal. It is more interesting to know that, although nominal prices of maize in 2008 increased by 80%, the real prices of maize increased by only 45%. This implies that, relative to other prices in the economy, the price of maize rose by 45% over the year.

### Example

This spreadsheet (link) shows the calculation of real prices using nominal prices and a consumer price index. Column A has the month and year (See Footnote 2 below). Column C contains the price data for each month. In this example, we are working with wholesale maize prices from Addis Ababa, Ethiopia. Column D contains the consumer price index with a base period of January 2007. Column E calculates the real price of maize in wholesale markets of Addis Ababa, using a base period January 2007.

The graph plots the nominal and real prices of maize in Ethiopia. This graph illustrates two general patterns: The nominal price and the real price always cross at the base period, January 2007 in this example. This is because in the base period, the CPI is 100 so the real price is equal to the nominal price. Generally, the real price rises more slowly than the nominal price. The higher the rate of inflation, the greater the divergence between nominal and real prices (the only exception to this is in rare cases where the inflation rate is negative).

This example also demonstrates the importance of calculating real prices. For example, between September 1997 and September 2007, the nominal price of maize almost doubled from 114 birr/quintal to 226 birr/quintal. Without deflating prices, one might be tempted to think that consumers would shift from maize to other grains and that maize has become a very profitable crop for farmers. However, after adjusting for inflation, the real price barely changed, rising only slightly from 189 to 196 birr/quintal. In other words, over this ten year period, maize prices rose but only at the same rate as other prices in the economy. Therefore, over this period, maize did not become any more expensive relative to other goods.

Footnotes:

1. If prices rise by 50% over two years, the annual inflation rate is not 25% because of compounding. If prices increased by 25% each year for two years, the total increase would be (1.25)2 = 1.5625 or 56.25%.

2. This column can be easily created in Excel by typing in the first two months and years, marking these two cells, and then dragging the frame down the column to automatically fill in the remaining cells.

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