Figure 2.3, titled 'The distribution of spoils: pirates and the British navy,' provides a graphical comparison of income distribution between eighteenth-century pirates and the British navy using Lorenz curves. The curve for the pirate ship *Royal Rover* is positioned very near the 45-degree line of perfect equality, reflecting the egalitarian rules for distributing booty. In contrast, the curves for the naval ships *Favourite* and *Active* are bowed significantly away from the equality line, indicating that ordinary crew members received a much smaller portion of the spoils. The graph also visually confirms that the distribution on the *Favourite* was more unequal than on the *Active*.

Figure 2.3: Lorenz Curves for Spoils Distribution on Pirate and Naval Ships

The Gini coefficient can be calculated geometrically from a Lorenz curve diagram. It is the ratio of the area between the line of perfect equality and the Lorenz curve (designated as area A) to the total area of the triangle formed under the line of perfect equality (designated as area A + B). The formula is: $$ \text{Gini} = \frac{\text{A}}{\text{A + B}} $$

Gini Coefficient Formula (Based on Lorenz Curve Areas)

Figure 2.4b is a visual representation that displays the Gini coefficients for several previously illustrated Lorenz curves. All the Gini coefficients shown in this figure were calculated using the area method, which is based on the geometry of the Lorenz curve diagram.

Figure 2.4b: Gini Coefficients from Various Lorenz Curves

Figure E2.1 is a diagram that illustrates the method for calculating the Gini coefficient based on the geometry of a Lorenz curve graph. It visually demonstrates the relationship between the area enclosed by the Lorenz curve and the line of perfect equality, which is used to quantify income inequality.

Figure E2.1: Calculating the Gini Coefficient from a Lorenz Curve Diagram

Figure 2.4a illustrates the relationship between the Lorenz curve and the Gini coefficient in the context of wealth distribution. It provides a visual example of how the Gini coefficient, a measure of inequality, can be derived from the areas on a Lorenz curve diagram representing the distribution of wealth.

Figure 2.4a: The Lorenz Curve and Gini Coefficient for Wealth Ownership

An increase in the shaded area between the Lorenz curve and the line of perfect equality directly results in a higher Gini coefficient. This area serves as a visual representation of inequality, and its size is causally linked to the numerical value of the Gini coefficient.

Causal Link Between Lorenz Curve Area and Gini Coefficient

The degree of inequality represented by a Lorenz curve can be quantified by the area between the curve and the 45-degree line of perfect equality, with a larger area indicating greater inequality. The Gini coefficient provides a close approximation of this inequality, calculated as the ratio of the area between the Lorenz curve and the line of equality to the total area of the triangle under the 45-degree line.

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The Lorenz curve provides a visual measure of how much a distribution deviates from the line of perfect equality, making it a powerful tool for comparing inequality between different groups. A notable historical example is the comparison of spoils distribution on eighteenth-century pirate ships versus naval vessels. The Lorenz curve for a pirate ship like the Royal Rover lies much closer to the 45-degree line of perfect equality than the curve for a typical naval ship, graphically illustrating the more egalitarian economic system established by pirate institutions.

Using the Lorenz Curve to Compare Pirate and Naval Inequality

To cite the ebook, use The CORE Econ Team 2023 The Economy 2.0: Macroeconomics Open access e-text https://core-econ.org/the-economy/.

To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Macroeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

CORE Econ - The Economy 2.0: Macroeconomics

Relationship Between the Lorenz Curve Area and the Gini Coefficient

The significant inequality in the division of spoils on British Royal Navy ships, such as the 'Favourite' and 'Active', is vividly illustrated by their Lorenz curves. Following the capture of the Spanish treasure ship 'La Hermione', these curves show a large deviation from the line of perfect equality, with ordinary sailors receiving only about a fourth of the prize money. The remainder was distributed among a few officers and the captain. The inequality was even more pronounced on the 'Favourite' compared to the 'Active'.

Unequal Spoils Distribution on the Royal Navy's 'Favourite' and 'Active'

Based on the distribution rules from the articles of the pirate ship Royal Rover, the resulting Lorenz curve for income from captured booty lies very close to the 45-degree line of perfect equality. This graphical representation illustrates the highly egalitarian nature of the pirates' economic system, where the institutional rules ensured that ordinary crew members received a significant share of the spoils.

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