Suppose that all the people in a country are ranked according to their incomes, starting at the bottom. Let x represent the fraction of the community making the lowest income (0 less than or equals x less than or equals 1 ); x equals 0.4, therefore, represents the lower 40% of all income producers. Let I(x) represent the proportion of the total income earned by the lowest x of all people. Thus, I(0.4) represents the fraction of total income earned by the lowest 40% of the population. The curve described by this function is known as a Lorenz curve. Suppose Upper I (x )equals 0.94 x squared plus 0.06 x. Find and interpret (0.1).

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pedrocarratore pedrocarratore · Answer 1 · 2020-05-06T06:39:32+02:00

Answer:

I(0.1) = 0.0154

The 10% of the community with the lowest income hold 1.54% of the total income earned in the community.

Step-by-step explanation:

The Lorenz curve is given by:

[tex]I(x) = 0.94x^2+0.06x[/tex]

If x = 0.1 (representing the 10% of the community with the lowest income), their total aggregate income is given by:

[tex]I(x) = 0.94*0.1^2+0.06*0.1\\I(x) = 0.0154=1.54\%[/tex]

This means that the 10% of the community with the lowest income hold 1.54% of the total income earned in the community.