DSE Economics | Income Distribution and Poverty: A Teacher Prep Guide (Gini 0.41, Lorenz curve)

2026-11-04

Tutor lesson-prep guides · Secondary Economics

Students can recite that a higher Gini means more inequality, yet draw a Lorenz curve as a straight line. This lesson builds the curve from five numbers, measures the area, and only then discusses policy.

Objectives — Students can: (1) draw a Lorenz curve from five quintile income shares and compute the Gini coefficient; (2) set a poverty line at half the median and compute the poverty rate; (3) name which part of the distribution progressive tax, transfers and a minimum wage each targets.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Percentages	What must the five shares add up to	100%
Cumulative sums	Third cumulative value of 5, 9 and 14	28%
Area	Formula for a trapezium	average of the two parallel sides times width

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-10 min	Five numbers	Quintile income shares	Write the cumulative percentages
10-24 min	Draw it	Plot points, diagonal means perfect equality	Five-segment curve
24-38 min	Measure it	Area between curve and diagonal, times two	Gini 0.412
38-48 min	Poverty line	Half the median, then count households	Rate 30%
48-56 min	Policy	Progressive tax, transfers, minimum wage	One target each
56-60 min	Exit check	Three questions collected and marked	Independent

03 Teaching script (read it out)

Scene 1: Lorenz curve: plot first, interpret second

The horizontal axis is cumulative population, the vertical axis cumulative income; quintiles mean steps of 20%.
Cumulative income: 5%, 14%, 28%, 50%, 100%. The diagonal is perfect equality; the further the curve sags below it, the more unequal the distribution.

Ask the class: what share of income goes to the poorest 40% (14%), and to the richest 20% (50%).

Scene 2: Gini coefficient: one area formula

Use the trapezium rule on each segment: 0.2 times the average of the two end heights, summed over five segments to give 0.294.
Gini = 1 – 2 x 0.294 = 0.412; 0 is perfect equality, 1 is one household taking everything. DSE regularly asks whether a more curved line means a larger coefficient: it does.

Ask the class to compute: if the top quintile share fell from 50% to 40%, would the Gini rise or fall (fall).

Scene 3: Poverty line and policy: numbers before opinions

Poverty line = half the median = $20,000 x 0.5 = $10,000. With 3 of 10 households below it, the poverty rate is 30%.
Progressive tax narrows post-tax gaps, transfers lift the bottom directly, and a minimum wage changes the market wage; each hits a different point of the distribution.

Warn them: a rising poverty line does not by itself mean people are poorer; check real income and relative position.

04 Question types and worked steps

Type	Example	Steps	Answer
Diagram	Draw the Lorenz curve from shares	Cumulate, plot five points, join	Curve below the diagonal
Calculation	Gini coefficient	Trapezium area, then 1 – 2A	0.412
Calculation	Poverty rate	Households below the line over total	30%
Evaluation	Which policy targets the bottom	Cash transfers	They raise bottom incomes directly

Sanity check (teach this): The Gini coefficient must lie between 0 and 1, and the Lorenz curve can never sit above the diagonal because cumulative income cannot outrun cumulative population. Use the median, not the mean: the mean is pulled up by the top quintile. Use the trapezium rule on all five segments; treating the gap as one triangle understates the coefficient.

05 Independent practice (3 questions)

Question	Answer	What to watch
Income share of the poorest 40%	14%	Add the first two cumulative steps
Gini coefficient	0.412	1 – 2 x area under the curve
Poverty rate	30%	3 households in 10

06 Common mistakes and what to say

Mistake	Student writes	Say this
Drawing the curve above the diagonal	A curve that bows upward	“Cumulative income can never exceed cumulative population, or someone would have negative income.”
Using the mean for the poverty line	A line near $26,000	“Use the median: the mean is dragged up by the richest fifth.”
Treating the area as one triangle	Gini around 0.50	“Five segments, five trapeziums; you cannot skip any.”
Reversing the Gini reading	Bigger number means more equal	“Zero is perfect equality; the number rises as inequality rises.”

07 Homework (paper, section and question numbers)

Secondary Economics chapter index — All chapters and practice
DSE Economics practice paper — Section B data response on distribution

08 Exit check (last 5 minutes)

Question	Answer	Decision
Share of the richest 20%	50%	All three right: move to public goods
Gini coefficient	0.412	One wrong: reteach the area method
Poverty line amount	$10,000	Two or more wrong: back to the first act

09 Tutor FAQ

Do students need the equation of the Lorenz curve?

No. DSE only requires plotting from shares and comparing curvature.

Can the Gini exceed 1?

No. Its theoretical maximum is 1, where one household takes all income.

Why a relative poverty line?

Hong Kong uses half the median so the measure stays comparable across years.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.