(Inequality) The average income in a country is $50,000. (a) What is the largest

Question

(Inequality) The average income in a country is $50,000.
(a) What is the largest fraction of the population that can make $100,000 or more?

(b) What is the largest fraction of the population that can make $150,000 or more?

(c) Suppose that it is in fact possible for someone to have negative income, but that no one will have an income below -$50,000 (but the average income is still $50,000). What is the largest fraction of the population that can make $100,000 or more?

(d) Now suppose that not only is everyone’s income positive, but that an especially generous country guarantees that everyone makes at least $25,000 per year. Assuming the average income is $50,000 as before, now find the largest fraction of the population that can make $100,000 or more.

Explanation / Answer

A) Assume that x is the proportion having $100,000 income and remaining have 0 income. This will give maximum value of x.

So, 100,000x = 50,000

x = 0.5

B) 150,000x = 50,000

x = 1/3

C) -50,000(1-x) + 100,000x = 50,000

150,000x = 100,000

x = 2/3

D) 25000(1-x) + 100,000x = 50,000

75000x = 25000

x = 1/3

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