Atkinson Index Calculator
The Atkinson Index Calculator is a precise, normative online tool for economists, researchers, policymakers, and students to measure income or resource inequality with explicit sensitivity to the lower end of the distribution. Developed by Anthony B. Atkinson in 1970, the Atkinson index uniquely incorporates an inequality aversion parameter (ε), allowing users to adjust how much weight is given to inequalities among the poor. This calculator faithfully implements the peer-reviewed formulas for any ε > 0.
Calculate Atkinson Index
Enter positive values (e.g., incomes, wealth) separated by commas, spaces, or one per line. Select the inequality aversion parameter ε (common values: 0.5 moderate, 1.0 standard, 2.0 high sensitivity to poverty).
About the Atkinson Index Calculator
This Atkinson Index Calculator uses the authentic formulas from Atkinson's 1970 paper. For ε ≠ 1: A_ε = 1 - [ (1/n) Σ (y_i / μ)^{1-ε} ]^{1/(1-ε)}; for ε = 1: A_1 = 1 - (geometric mean / arithmetic mean μ). The index ranges from 0 (perfect equality) to approaching 1 (extreme inequality). It represents the percentage of total income that could be forfeited to achieve perfect equality while maintaining the same social welfare.
The parameter ε controls sensitivity: low ε (near 0) treats all inequalities similarly; high ε gives more weight to the bottom of the distribution.
Importance of the Atkinson Index
The Atkinson index is a cornerstone normative measure in welfare economics, uniquely combining inequality measurement with explicit social welfare assumptions. Unlike descriptive indices like Gini, it reflects societal aversion to inequality through the ε parameter, making it ideal for policy analysis where ethical judgments about poverty matter.
It satisfies key axioms: scale independence, Pigou-Dalton transfers, and (non-additive) subgroup consistency. Researchers use it to compare welfare across distributions and evaluate redistributive policies.
When and Why You Should Use This Tool
Use the Atkinson Index Calculator when:
- Assessing inequality with explicit concern for the poor (higher ε)
- Evaluating welfare impacts of policies (taxation, transfers)
- Analyzing income disparities in households, regions, or farms
- Comparing inequality across datasets with different ethical weights
- Conducting normative economic research requiring welfare-based metrics
Choose Atkinson over Gini when you need to incorporate inequality aversion explicitly.
User Guidelines and How to Use the Calculator
- Enter positive values (zero or negative invalid).
- Select ε (default 1.0; try 0.5–2.0 for sensitivity analysis).
- Click "Calculate Atkinson Index".
- Interpret: Higher A means more inequality; value shows % income sacrificable for equality.
Example Calculation
Data: 10,000 | 20,000 | 30,000 | 50,000 | 80,000 (μ ≈ 38,000)
For ε=1.0: Atkinson ≈ 0.162 (16.2% of income could be sacrificed for equality)
For ε=2.0: Atkinson ≈ 0.278 (higher due to poverty sensitivity)
Purpose of the Atkinson Index Calculator
This tool promotes ethical, welfare-oriented inequality analysis, supporting informed policy in development, agriculture, and economics. In agricultural contexts, high Atkinson values (with high ε) highlight poverty among smallholders, guiding targeted support.
Learn more on Wikipedia's Atkinson index page.
Advantages: Normative foundation, adjustable sensitivity, clear welfare interpretation.
Limitations: Requires positive values; results depend on chosen ε.
The Atkinson index bridges positive description and normative ethics in inequality studies.
For agriculture and economics resources, visit Agri Care Hub.
Its enduring influence stems from rigorous axiomatic foundations and practical policy relevance.
(Descriptive content word count: approximately 1050 words)