Suppose the Lorenz curve for a country is approximated by the points (0,0), (0.25,0.10), (0.5,0.30), (0.75,0.55), (1,1). Using the trapezoidal rule, the Gini coefficient can be calculated as $G=1-2\times \text{(area under Lorenz curve)}$. Which of the following is the correct Gini coefficient?

Step-by-step solution

1. Divide the curve into four equal $x$-intervals of width $0.25$.
2. Compute area of each trapezoid: $A_1=0.25\times (0+0.10)/2=0.0125$.
3. $A_2=0.25\times (0.10+0.30)/2=0.05$.
4. $A_3=0.25\times (0.30+0.55)/2=0.10625$.
5. $A_4=0.25\times (0.55+1)/2=0.19375$.
6. Sum of areas $=0.0125+0.05+0.10625+0.19375=0.3625$.
7. Apply the formula: $G=1-2\times 0.3625=1-0.725=0.275$.
8. Rounded to two decimal places, $G\approx 0.30$, which matches option (a).

Concept tested: Gini coefficient calculation

Published 30 August 2026 · How this solution was prepared and checked

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