Question

In: Economics

One type of function often used to model Lorenz curves is f(x) = ax+(1-a)xp. Suppose that...

One type of function often used to model Lorenz curves is f(x) = ax+(1-a)x^p. Suppose that and that the Gini index for the distribution of wealth in a country is known to be 4/9, and assume that a= 1/3

(a) Use the given information to determine the correct value of p.

(b) According to this model, how much of the wealth is owned by the wealthiest 5% of the population?

Expert Solution

The function for Lorenz curve is given as , and for the given a, it would be or .

(a) The Gini index is given to be G=4/9. The Gini index would be computed as or .

We have or or or .

Now, , and hence, for , we have

or or or or or or .

(b) For the Lorenz curve be , the cumulative lower 95% of population would own cumulative income of or or or 83.25%. Hence, the wealthiest 5% of the population would own an income of or 16.75% of income.

Rahul Sunny answered 2 years ago

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