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An index is a statistical measure that represents the value of a specific quantity in relation to its value during a designated base period. This base period value is typically set to a standard of 100 for ease of comparison.

Definition of Index

When data is represented using an index, the visual shape of the plotted curve does not change if the reference period is altered. The selection of a different base year, which is typically normalized to a value of 100, will only result in a vertical shift of the entire graph, leaving the underlying trend, such as a 'hockey stick' pattern, intact.

Invariance of Index Graph Shape to Reference Period

This figure presents a comparison of the ratio of laborers' wages to the cost of using capital goods in England and France from the late 1500s to the early 1800s. While this ratio was comparable in both nations during the mid-17th century, it began to diverge afterward. In England, labor became progressively more expensive relative to capital, creating a growing economic incentive to substitute workers with machinery. This trend was not observed in France, where, conversely, the incentive for labor-saving innovation was actually stronger in the late 16th century than it was two centuries later.

Figure 2.13: Wages Relative to the Cost of Capital Goods in England and France (Late 16th to Early 19th Century)

To create a nominal wage index, a specific baseline year is chosen and its value is set to 100. For any subsequent year, the index value is calculated by applying the percentage change in the nominal wage to the index value of the preceding year. This method converts wage data from currency units into a standardized index, making it easier to track growth relative to the baseline.

Constructing a Nominal Wage Index

An economic index is created to track the price of a specific basket of goods. In the base year, the price of the basket was $200, and the index was set to 100. The following year, the price of the same basket of goods increased to $250. What is the index value for the second year?

An economist is creating a price index for a new technology product that has seen rapid price decreases since it was introduced a decade ago. The economist chooses the most recent year as the base period for the index. Critically evaluate this choice. Is this an effective choice for illustrating the product's price history? Justify your reasoning.

Evaluating the Choice of a Base Period

A country's nominal wage index is reported to be 125 for the year 2022, using the year 2010 as the base period where the index was 100. This value of 125 directly indicates that the average nominal wage in 2022 was $125.

Analyze the provided data on housing price indices for two cities. Based on this information, which city experienced a greater percentage increase in housing prices between 2010 and 2023? Explain your reasoning and also clarify whether you can determine which city has the higher average house price in 2023.

Interpreting Housing Price Indices

A researcher has collected data on the average price of a loaf of bread every year from 1980 to the present. Instead of presenting the raw price data (e.g., $0.50 in 1980, $2.50 in 2020), they decide to convert it into a price index with the year 1980 set as the base period (value = 100). Explain the primary advantage of using this index for analyzing the change in bread prices over time compared to using the raw dollar amounts.

Justifying the Use of an Index

The table below shows a price index for a basket of consumer goods over three years, with Year 1 serving as the base period.

| Year   | Price Index |
|--------|-------------|
| Year 1 | 100         |
| Year 2 | 110         |
| Year 3 | 115.5       |

Based on this index, what can be concluded about the change in prices between Year 2 and Year 3?

An economist is tracking the price of a standard loaf of bread. The prices for three consecutive years are shown in the table below. Using Year 1 as the base period (where the index is 100), calculate the price index for Year 2 and Year 3.

| Year   | Price of Bread |
|--------|----------------|
| Year 1 | $2.00          |
| Year 2 | $2.20          |
| Year 3 | $2.50          |

Provide the calculated index values for Year 2 and Year 3.

Constructing a Price Index

Match each term related to the construction of an economic index with its correct description.

The Consumer Price Index (CPI) is a metric designed to track the average price level that consumers pay for a representative 'shopping basket' of goods and services. This basket typically includes items such as food, beverages, utilities, rent, healthcare, education, and financial services. Consequently, an increase in the CPI signifies a rise in the economy's overall price level.

Definition of Consumer Price Index (CPI)

A research report on a country's agricultural productivity uses an index where the year 2010 is the base period (value = 100). For the year 2020, the index value is reported as 92. Explain what this index value of 92 signifies about the country's agricultural productivity in 2020 compared to 2010.

Interpreting an Index Value Below the Base

Critically evaluate the politician's claim. In your evaluation, explain how the choice of a base period can influence the interpretation of an index. Is the politician's claim a fair representation of the housing situation? Justify your answer.

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