3. In the country of Barumbia, the average per capita consumption of people in the richest 10
percent of the consumption distribution is $10000, and the average per capita consumption
of people in the poorest 40 percent of the consumption distribution is $1000. Further
suppose that utility is equal to the natural logarithm of consumption, so that the marginal
utility of one dollar of consumption is 1/C, (where C is consumption measured in dollars).
Given the information about Barumbia stated in the question, what is the maximum
percentage leak in the redistributive bucket that a utilitarian would be willing to accept
before deciding that further redistribution from the richest 10 percent of people to the
poorest 40 percent of people in this country would be bad? Show your work.
