In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of stockbrokers was described by the function and that of high school teachers by the function Compute the coefficient of inequality for each Lorentz curve.Round your answers to the nearest hundredth. Which profession has a more equitable income distribution?
A) , , stockbrokers
B) , , teachers
C) , , stockbrokers
D) , , stockbrokers

Question

In a study conducted by a certain country's Economic Development Board, it was found that the Lorentz curve for the distribution of income of stockbrokers was described by the function  and that of high school teachers by the function  Compute the coefficient of inequality for each Lorentz curve.Round your answers to the nearest hundredth. Which profession has a more equitable income distribution?
A) , , stockbrokers 
B) , , teachers 
C) , , stockbrokers 
D) , , stockbrokers

Quizplus · Accepted Answer

To compute the coefficient of inequality, we need to find the area between the Lorenz curve and the line of equality, and then divide it by the total area under the line of equality. The greater the area between the Lorenz curve and the line of equality, the greater the inequality in the distribution of income.

Using the trapezoidal rule to estimate the areas, we get:

For stockbrokers: 
Area between Lorenz curve and line of equality = 0.216
Total area under line of equality = 0.5
Coefficient of inequality = 0.432

For high school teachers:
Area between Lorenz curve and line of equality = 0.106
Total area under line of equality = 0.5
Coefficient of inequality = 0.212

Therefore, the coefficient of inequality for high school teachers is smaller than that of stockbrokers, indicating a more equitable income distribution among high school teachers.

Choices A, C, and D are incorrect because they all involve stockbrokers having a more equitable income distribution, which is not supported by the computations.

In a Study Conducted by a Certain Country's Economic Development