In a study conducted by a certain country's Economic Development Board regarding the income distribution of certain segments of the country's workforce, it was found that the Lorentz curve for the distribution of income of college professors is described by the function
Compute the coefficient of inequality of the Lorentz curve. Round to the nearest thousandth. Hint: Use the formula
A) 0.331
B) 0.809
C) 0.589
D) 0.31

Question

In a study conducted by a certain country's Economic Development Board regarding the income distribution of certain segments of the country's workforce, it was found that the Lorentz curve for the distribution of income of college professors is described by the function ​  ​
Compute the coefficient of inequality of the Lorentz curve. Round to the nearest thousandth. Hint: Use the formula 
A) 0.331 
B) 0.809 
C) 0.589 
D) 0.31

Quizplus · Accepted Answer

Using the formula for the coefficient of inequality, we have:

G = (A - 0.5B)/A

where A is the area under the line of perfect equality and B is the area between the Lorentz curve and the line of perfect equality.

To find A, we need to find the area of the triangle with vertices at (0,0), (1,1), and (0,1):

A = 0.5(1)(1) = 0.5

To find B, we need to integrate the Lorentz curve function from 0 to 1:

B = ∫0^1 11eb651f_cb00_5424_b0a1_c7218d00c766_TB8255_11 dx

Using integration by substitution with u = x^(2), du = 2x dx, we get:

B = 1/2 ∫0^1 (1 - e^(-u/2)) du

B = 1/2 (-2e^(-u/2))|0^1 = 1 - e^(-1/2)

Thus, the coefficient of inequality is:

G = (0.5 - 0.5(1 - e^(-1/2))) / 0.5 = 0.809 (rounded to the nearest thousandth)

Therefore, the best choice is B, with the coefficient of inequality being 0.809.

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