Week 20: Income Distribution

 Lorenz Curve and Gini Coefficient

🔹 1. What is Income Distribution?

Income distribution refers to how a nation’s total income is divided among its population. It shows whether income is shared equally or concentrated among a small group.

➤ Key Concepts:

  • Perfect equality: Everyone earns the same income.

  • Perfect inequality: One person earns all the income; others earn nothing.

  • Most real-world economies lie somewhere in between.

🔹 2. The Lorenz Curve

The Lorenz Curve is a graphical representation of income distribution.

➤ How it works:

  • Horizontal axis (X-axis): Cumulative % of households (from poorest to richest).

  • Vertical axis (Y-axis): Cumulative % of income earned.

➤ Interpretation:

  • A straight diagonal line (Line of Equality) shows perfect equality.

  • The further the Lorenz Curve bends below the Line of Equality, the greater the income inequality.

🔹 3. The Gini Coefficient

The Gini Coefficient is a numerical measure of income inequality, derived from the Lorenz Curve.

➤ How it is calculated:

  • It measures the area between the Lorenz Curve and the Line of Equality, divided by the total area under the Line of Equality.

  • Formula:

    Gini=AA+B

    (Where A = area between the line of equality and Lorenz curve; B = area under the Lorenz curve)

➤ Gini Coefficient Scale:

Gini ValueInterpretation
0Perfect equality
0.2–0.3Low inequality
0.3–0.5Moderate inequality
0.5–0.7High inequality
1Perfect inequality

🔹 4. Real-World Examples

CountryGini CoefficientIncome Equality Status
Sweden0.27Very equal
Germany0.31Relatively equal
USA0.41Moderate inequality
Brazil0.53High inequality
South Africa0.63Very high inequality

🔹 5. Why Does It Matter?

  • Helps governments design tax and welfare policies.

  • Can guide economic reforms and income redistribution.

  • Indicates social stability—greater inequality often leads to unrest.

🇹🇷 20. Hafta: Gelir Dağılımı

Lorenz Eğrisi ve Gini Katsayısı

🔹 1. Gelir Dağılımı Nedir?

Gelir dağılımı, bir ülkedeki toplam gelirin bireyler veya hanehalkları arasında nasıl paylaşıldığını gösterir. Gelirin eşit veya dengesiz dağılmış olup olmadığını analiz eder.

➤ Temel Kavramlar:

  • Tam eşitlik: Herkes aynı geliri alır.

  • Tam eşitsizlik: Tüm geliri sadece bir kişi alır.

  • Gerçek hayattaki ülkeler bu iki uç arasında bir yerde bulunur.

🔹 2. Lorenz Eğrisi

Lorenz Eğrisi, gelir dağılımının grafiksel bir gösterimidir.

➤ Nasıl Çalışır:

  • X ekseni: Kümülatif hanehalkı yüzdesi (en fakirden en zengine).

  • Y ekseni: Kümülatif gelir yüzdesi.

➤ Yorumlama:

  • 45°'lik doğru (Eşitlik Doğrusu), tam eşit gelir dağılımını gösterir.

  • Lorenz eğrisi bu doğrunun altında ne kadar eğilirse, gelir eşitsizliği o kadar fazladır.

🔹 3. Gini Katsayısı

Gini Katsayısı, Lorenz Eğrisi'nden türetilen ve gelir eşitsizliğini sayısal olarak ölçen bir göstergedir.

➤ Nasıl Hesaplanır:

  • Eşitlik doğrusuyla Lorenz eğrisi arasındaki alanın, tüm üçgenin alanına oranıdır.

  • Formül:

    Gini=AA+B

    (A = Eşitlik doğrusu ile Lorenz eğrisi arasındaki alan, B = Lorenz eğrisinin altındaki alan)

➤ Gini Katsayısı Ölçeği:

Gini DeğeriAnlamı
0Tam eşitlik
0.2–0.3Düşük eşitsizlik
0.3–0.5Orta düzeyde eşitsizlik
0.5–0.7Yüksek eşitsizlik
1Tam eşitsizlik

🔹 4. Gerçek Hayattan Örnekler

ÜlkeGini KatsayısıGelir Dağılımı Durumu
İsveç0.27Çok eşit
Almanya0.31Görece eşit
ABD0.41Orta düzeyde eşitsizlik
Brezilya0.53Yüksek eşitsizlik
Güney Afrika0.63Çok yüksek eşitsizlik

🔹 5. Neden Önemlidir?

  • Vergi ve sosyal politika tasarımı için yol gösterir.

  • Gelir adaleti ve yeniden dağıtım politikaları için referans sağlar.

  • Toplumsal istikrarı etkiler: Eşitsizlik arttıkça huzursuzluk riski artar.

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