A graph can be used to visualize how wealth is distributed within a group. On this graph, a straight 45-degree diagonal line represents perfect equality, where every cumulative percentage of the population holds the same cumulative percentage of the wealth (e.g., the bottom 20% of the population holds 20% of the wealth). A curve that bows away from this line indicates inequality; the further the curve bows, the greater the inequality.

Consider two ships with different institutional rules for dividing treasure:

• Ship A: The captain and quartermaster each receive 2 shares. Key officers receive 1.5 shares. All other crew members receive 1 share.
• Ship B: The captain receives 10 shares. Key officers receive 5 shares. All other crew members receive 1 share.

Two curves are plotted to represent these two systems. Curve 1 bows significantly away from the line of perfect equality. Curve 2 lies very close to the line of perfect equality.

Based on an analysis of their distribution rules, which statement correctly identifies the curve for each ship?

Evaluating a Proposed Change to Treasure Distribution

Comparative Analysis of Pirate Economic Systems

A historian makes the following claim: 'The rules for dividing treasure on the pirate ship Royal Rover—where the captain received two shares, some officers received one and a half or one and a quarter shares, and a regular crew member received one share—created a system of extreme wealth inequality. Therefore, a graphical representation of this distribution would show a curve that bows significantly far away from the 45-degree line of perfect equality.' Evaluate whether this claim is true or false.

Explaining the Shape of a Wealth Distribution Curve

A graphical representation can be used to show how wealth is distributed within a population. A straight 45-degree line on this graph represents perfect equality, where everyone receives the same amount. A curve that bows away from this line indicates inequality; the further the curve bows, the more unequal the distribution. Below are four different systems for distributing treasure. Arrange these systems in order from the most equal (whose curve would be closest to the 45-degree line) to the least equal (whose curve would bow furthest from the 45-degree line).

Analyzing Crew Morale and Stability

A graph is used to show how treasure is distributed among a 100-person crew. A straight 45-degree line on the graph represents perfect equality (e.g., the lowest-paid 70 people receive 70% of the treasure). The curved line on the graph represents the ship's actual distribution rules. A specific point on this curve shows that the 70 lowest-paid crew members collectively received 50% of the total treasure. What does this single data point reveal about the ship's distribution system?

A graph can be used to visualize how wealth is distributed within a group. On this graph, a straight 45-degree diagonal line represents perfect equality. A curve that bows away from this line indicates inequality; the further the curve bows, the greater the inequality. Match each of the following treasure distribution systems to the description of its corresponding curve.

A graph can be used to visualize how treasure is distributed among a ship's crew. On this graph, a straight 45-degree line represents a system of perfect equality. A second, curved line represents the actual distribution. The more unequal the distribution, the larger the area between the curved line and the 45-degree line becomes. Given a system where the captain receives two shares and a regular crew member receives one, the area between the two lines is relatively small. If the rules were changed so the captain received twenty shares while a regular crew member still received only one, the area between the two lines would significantly ____.