Interpreting Indexed Data
Two researchers are analyzing the same historical data on wheat prices. Researcher A creates an index with the year 1750 as the base period (value = 100). Researcher B uses the same data but sets the year 1850 as the base period (value = 100). When they plot their respective indices on separate graphs, Researcher A observes that their entire graphed line is positioned lower on the vertical axis than Researcher B's line. Researcher A concludes that their choice of an earlier base year demonstrates a less dramatic overall price trend. Is Researcher A's conclusion correct? Explain your reasoning.
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Real Wages of London Craftsmen and British Population (1264-2001)
An economist creates a graph showing a country's average income from 1980 to 2020, represented as an index with the year 1990 set as the base period (value = 100). The graph reveals a distinct 'U' shape, indicating a period of decline followed by a period of recovery and growth. If the economist decides to replot the exact same data but changes the base period to the year 2010, what effect will this have on the shape of the graphed line?
Interpreting Indexed Data
Consider two individuals, Priya and David, whose preferences for goods X and Y are represented by the following utility functions:
- Priya: U(X, Y) = X^0.3 * Y^0.7
- David: U(X, Y) = X^0.6 * Y^0.4
Based on these functions, which of the following statements accurately compares their preferences?
An economic analyst observes that a country's GDP index for the year 2015 is 120 when the base year is 2010 (set to 100). After changing the base year to 2015 (set to 100), they note that the index for 2010 is now approximately 83.3. The analyst concludes that this change in index values proves that the rate of economic growth between 2010 and 2015 appears slower when 2015 is used as the base year. This conclusion is correct.
Interpreting Indexed Economic Data
Advising a Junior Analyst on Index Charts
An analyst is studying the price of a specific commodity from 2000 to 2020. They create two graphs using the same raw price data, but with different reference periods for the price index.
- Graph A uses the year 2000 as the base period (index = 100).
- Graph B uses the year 2010 as the base period (index = 100).
Visually, the entire plotted line in Graph B is positioned lower on the y-axis than the line in Graph A. What is the most accurate conclusion that can be drawn from this observation?
Analyzing Indexed Data Interpretations
Evaluating a Manager's Performance Review
An analyst presents a chart of a company's quarterly sales from 2010 to 2020, indexed with 2010 as the base year (value = 100). The chart displays a dramatic 'hockey stick' growth pattern, with a sharp increase in the final two years. A manager, concerned by the visual severity of this recent spike, suggests changing the base year to 2018 to make the overall trend appear more stable. What will be the actual effect of changing the base year to 2018 on the visual representation of the data?