Index Numbers and Price Measurement

1. What is an Index Number?

An index number is a dimensionless ratio that measures the relative change in a variable (usually price) over time.
$$I_t=\frac{P_t}{P_0}\times 100$$
where $P_t$ is the price level at time $t$ and $P_0$ is the base‑year price level.
The index is always expressed as 100 in the base year.

1.1 Why Use Index Numbers?

• Comparability: Prices of different goods and services are measured on a common scale.
• Simplicity: A single number summarizes complex price movements.
• Policy: Governments and central banks use indices to set wages, adjust taxes, and design monetary policy.

2. Key Price Indices

2.1 CPI – The Most Widely Used Index

CPI tracks the price changes of a fixed basket of goods and services that represent typical household consumption.

• Base year: 2018 (for Nepal).
• Weights: Derived from expenditure shares in the latest national expenditure survey.

2.1.1 Worked Example – CPI Calculation (2022)

Step 1 – Compute Laspeyres price relatives
$${\text{Price Relative}}_i=\frac{P_{2,i}}{P_{0,i}}$$

Step 2 – Weighted sum
$${\text{CPI}}_{2022}=100\times \sum _i{w}_i\times {\text{Price Relative}}_i$$
$$=100\times (0.30\times 1.1667+0.20\times 1.10+0.25\times 1.20+0.25\times 1.05)$$ $$=100\times (0.3500+0.2200+0.3000+0.2625)=100\times 1.1325=113.25$$

Interpretation
CPI increased from 100 (base 2018) to 113.25 in 2022, indicating a 13.25 % rise in the cost of living.

2.2 PPI – Producer Price Index

PPI measures the average change in selling prices received by domestic producers. It uses a fixed basket of production inputs and is often used to anticipate future CPI movements.

2.3 GDP Deflator – A Broad Price Index

Unlike CPI, the GDP deflator uses a variable basket weighted by the current period’s output. It captures price changes for all final goods and services, including investment goods and government purchases.

$${\text{GDP Deflator}}_t=\frac{{\text{Nominal GDP}}_t}{{\text{Real GDP}}_t}\times 100$$

3. Index Number Formulas

3.1 Chain‑Weighted Indices

Chain indices update weights every period, reducing bias from changing consumption patterns.

$$C_t=\prod _{k=1}^t{\left(\frac{\sum w_{k,i}{P}_{k,i}}{\sum w_{k-1,i}{P}_{k-1,i}}\right)}^{1/2}$$

4. Advantages & Disadvantages

4.1 Substitution Bias

Because CPI uses a fixed basket, it may overstate inflation when consumers switch to cheaper substitutes. Chain‑weighting mitigates this.

5. Real‑World Applications

5.1 In the Real World

• eSewa: Adjusts transaction fee thresholds annually using the CPI to maintain purchasing power for users.
• Ncell: Revises mobile data tariffs based on the PPI to reflect rising wholesale costs.
• NEPSE: Uses the CPI to index dividend payouts for listed companies, ensuring dividends keep pace with inflation.

5.2 Worked Real‑World Example – Bank Loan Interest

A Nepali bank offers a nominal loan interest rate of 12 % per annum. The CPI indicates an inflation rate of 6 % over the same period.
$$\text{Real Interest Rate}=\frac{1+0.12}{1+0.06}-1\approx 5.66\%$$
Thus, the borrower effectively pays a 5.66 % real cost of borrowing.

6. Visualizing Inflation Dynamics

flowchart TD
  "Base Year Prices" --> "Compute Price Relatives"
  "Compute Price Relatives" --> "Apply Weights"
  "Apply Weights" --> "Sum Weighted Relatives"
  "Sum Weighted Relatives" --> "Multiply by 100"
  "Multiply by 100" --> "Index Number"

7. Comparison of Index Types

8. Chain‑Weighting in Practice

sequenceDiagram
  participant Base as Base Year
  participant Current as Current Year
  participant Index as Index Number
  Base->>Index: Provide base basket
  Current->>Index: Provide current basket
  Index->>Index: Compute Laspeyres & Paasche
  Index->>Index: Take geometric mean
  Index->>Index: Update weights

9. Index Numbers in Nepal’s Economy

• CPI Base Year: 2018 (latest revision).
• GDP Deflator Base Year: 2015 (for consistency with national accounts).
• PPI: Updated quarterly by the Central Bureau of Statistics.

9.1 Recent Data Snapshot

10. Summary

Index numbers translate complex price movements into a single, comparable figure. CPI, PPI, and GDP deflator each serve distinct purposes, from measuring consumer cost of living to adjusting producer prices and calculating real GDP. Understanding their construction, strengths, and limitations is essential for interpreting inflation data, making policy decisions, and evaluating real economic performance.

In the real world

• eSewa: Uses CPI to adjust transaction fee thresholds, ensuring fees reflect current purchasing power.
• Ncell: Revises mobile data tariffs annually based on PPI, aligning consumer prices with wholesale cost changes.
• NEPSE: Indexes dividend payouts to CPI, protecting shareholders from inflation erosion.

Exam tip

• Know the formulas: Laspeyres, Paasche, Fisher, and chain‑weighted indices.
• Practice calculations: Use sample baskets to compute CPI and GDP deflator.
• Understand bias: Be able to explain substitution bias and why chain‑weighting helps.
• Interpret data: Relate index changes to real‑world scenarios (e.g., wage adjustments, loan rates).
• Use visuals: Draw CPI trend, inflation rate, and GDP deflator charts to support answers.