UNLOCKING THE VALUE OF MONEY
Index Numbers and Inflation Challenges
Class Key Points
• Simple Relative: The base period is always set at 100. It is calculated as I = (P / P ) × 100,
n 0
comparing current prices or quantities against the past.
• Points vs. Percentages: Never confuse a change in index points with the actual percentage
change. The true variation is: ((In − Im) / Im) × 100.
• Rebasing: Shifts the series to a new base year without losing proportionality: Rebased Index =
(Old Index / In) × 100 (where In is the value in the new base year).
• Weighted Indices: These simulate a basket of goods (Σ p · q).
◦ Laspeyres: Assumes static consumption habits (anchored in q ). It tends to overestimate
0
inflation.
◦ Paasche: Assumes dynamic consumption (anchored in q ). It tends to underestimate
n
inflation.
• Measuring Inflation: The rate at which general prices change. Inflation = ((I
current −
Iprevious) / Iprevious) × 100
Independent Practice Laboratory
CHALLENGE 1: SIMPLE RELATIVE (RAW MATERIALS)
Context: The cost per ton of a specialized agricultural fertilizer was $450 in the 2019 base year.
Due to supply chain disruptions, the cost spiked to $531 in 2021, and further increased by exactly
15% in 2022 compared to the 2021 price.
Question: What is the index number for the year 2022, and what is the total percentage increase
from the base year?
Answer: Index 2022 = 135.7 | Total increase = 35.7%
Applied Mathematics and Statistics Elaborado por. Ing. Dario Becerra
Index Numbers and Inflation Challenges
Class Key Points
• Simple Relative: The base period is always set at 100. It is calculated as I = (P / P ) × 100,
n 0
comparing current prices or quantities against the past.
• Points vs. Percentages: Never confuse a change in index points with the actual percentage
change. The true variation is: ((In − Im) / Im) × 100.
• Rebasing: Shifts the series to a new base year without losing proportionality: Rebased Index =
(Old Index / In) × 100 (where In is the value in the new base year).
• Weighted Indices: These simulate a basket of goods (Σ p · q).
◦ Laspeyres: Assumes static consumption habits (anchored in q ). It tends to overestimate
0
inflation.
◦ Paasche: Assumes dynamic consumption (anchored in q ). It tends to underestimate
n
inflation.
• Measuring Inflation: The rate at which general prices change. Inflation = ((I
current −
Iprevious) / Iprevious) × 100
Independent Practice Laboratory
CHALLENGE 1: SIMPLE RELATIVE (RAW MATERIALS)
Context: The cost per ton of a specialized agricultural fertilizer was $450 in the 2019 base year.
Due to supply chain disruptions, the cost spiked to $531 in 2021, and further increased by exactly
15% in 2022 compared to the 2021 price.
Question: What is the index number for the year 2022, and what is the total percentage increase
from the base year?
Answer: Index 2022 = 135.7 | Total increase = 35.7%
Applied Mathematics and Statistics Elaborado por. Ing. Dario Becerra
