Purchase Solution

Lorenz curve

Not what you're looking for?

Ask Custom Question

Author's explanation of a Lorenz curve: Economists use a cumulative distribution called a Lorenz curve to describe the distribution of income between households in a given country. Typically, a Lorenz curve is defined on [0,1] with endpoints (0,0) and (1,1) and is continuous, increasing, and concave upward. The points on this curve are determined by ranking all households by income and then computing the percentage of households whose income is less than or equal to a given percentage of the total income of the country. For example, the point (a/100, b/100) is on the Lorenz curve if the bottom a% of the households receive less than or equal to b% of the total income. "Absolute equality" of income distribution would occur if the bottom a% of the households receive a% of the income, in which case the Lorenz curve would be the line y=x. The area between the Lorenz curve and the line y=x measures how much income distribution differs from absolute equality. The "coefficient of inequality" is the ratio of the area between the Lorenz curve and the line y=x to the area under y=x.

a) Show that the coefficient of inequality is twice the area between the Lorenz curve and the line y=x; that is, show that the coefficient of inequality = (2)the integral from 0 to 1 of [x-L(x)]dx.

b)The income distribution for a certain country is represented by the Lorenz curve defined by the equation L(x)=(5/12)x^2+(7/12)x. What is the percentage of total income received by the households? Find the coefficient of inequality.

Purchase this Solution

Solution Summary

The solution provides a discussion regarding a Lorenz curve and the coefficients of inequality.

Solution Preview

See the attached file.

The illustrative function I include in the document is the cubic behavior for x between 0 and 1 but any line through the triangle proves the point.

Author's explanation of a Lorenz curve: Economists use a cumulative distribution called a Lorenz curve to describe the distribution of income between households in a given country. Typically, a Lorenz curve is defined on [0,1] with endpoints (0,0) and (1,1) and is continuous, increasing, and concave upward. The points on this curve are determined by ranking all households by income and then computing the percentage of households whose income is less than or equal to a given percentage of the total income of the country. ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.