A village consists of 100 households. 90 of these households own no land, while the remaining 10 households each own an equal share of the total land in the village. A graph is constructed by ordering the households from least to most land owned. The horizontal axis shows the cumulative percentage of households, and the vertical axis shows the cumulative percentage of total land they own. Which of the following coordinates representing (cumulative % of households, cumulative % of land) correctly lies on this graph?

Describing a Lorenz Curve for Land Distribution

Consider a village where 90% of the population owns no land, and the remaining 10% of the population owns all the land equally. When plotting a graph of the cumulative percentage of the population (ordered from least to most land) versus the cumulative percentage of land owned, the segment representing the landowners (from the 90th to the 100th percentile of the population) is a straight line.

Statement: If the land were redistributed among this 10% so that their ownership was no longer equal, this segment of the graph would remain a straight line.

Match each land ownership scenario in a hypothetical village with the corresponding description of its Lorenz curve. For each curve, assume the population is ordered from least to most land owned.

Analyzing Changes in a Lorenz Curve

In a community of 100 households, 90 households own no land, while the remaining 10 households own all the land, with each of these 10 owning an equal share. A graph is created by plotting the cumulative percentage of households (ordered from least to most land owned) on the horizontal axis and the cumulative percentage of total land they own on the vertical axis. The final segment of this graph, representing the landowners, is a straight line. The slope of this line is ____.

Arrange the steps in the correct order to construct a graph representing land distribution in a village where 90% of the population is landless and the remaining 10% owns all the land equally. The graph plots the cumulative percentage of the population on the horizontal axis against the cumulative percentage of land they own on the vertical axis.

Evaluating a Claim about Land Inequality

Consider a village with 100 households where 90 are landless and 10 own all the land in equal shares. A graph is plotted with the cumulative percentage of households (ordered by land ownership) on the x-axis and the cumulative percentage of land owned on the y-axis. A student incorrectly draws this as a single, smooth curve that starts at the origin and bows away from the 45-degree line of perfect equality. What is the fundamental conceptual error this student has made?

A community has 100 households. Consider two scenarios for land ownership:

• Scenario A: 90 households own no land. The remaining 10 households own all the land, with each of these 10 owning an equal share.
• Scenario B: 90 households own no land. Of the remaining 10 households, one household owns 50% of the total land, and the other nine households own the remaining 50% of the land in equal shares.

A graph is created for each scenario, plotting the cumulative percentage of households (ordered from least to most land owned) on the horizontal axis and the cumulative percentage of land they own on the vertical axis. How does the graph for Scenario B differ from the graph for Scenario A?

Figure 2.2: Lorenz Curve for Land Ownership in a Village with High Inequality