Imagine the following (which is a rough approximation of the income distribution in the U.S.)

There are 100 people with the following incomes.

10 earn 14

10 earn 25

10 earn 37

10 earn 50

10 earn 63

10 earn 80

10 earn 100

10 earn 130

10 earn 184

9earn 360

1earn 1300

A well-established assumption in economics is there is diminishing marginal utility to income.A common utility function is Utility for a person = ln(income).Assume each person has that same utility function.

Assume social welfare function is the sum of each individual's Utility. (NOT INCOME)

1.(5 points) Given the distribution above what is total social welfare.

2.(5 points) What distribution of income would maximize the Social welfare function?

3.(5 points) What is total social welfare under that distribution?

4.(5 points) People argue that redistribution would shrink the size of the pie or total income.Currently total income in my example is 11370.What could total income fall to but with optimal redistribution total social welfare be unchanged from its level without redistribution?