Brett, Art, and Isabel reside on a tiny island in the Pacific. All three of them have a utility function given by U = Y^0.5, where Y is income per day. Suppose that Brett earns $7 per day, Art earns $25 per day, and Isabel earns $36 per day. What happens to the value of the utilitarian social welfare function If the government takes $9 of Art's income and gives it to Brett?

Question

Quizplus · Accepted Answer

First, we need to find the initial utility level for each person:

- Brett: U = 7S1^(1/2)S1^0 = 7
- Art: U = 25S1^(1/2)S1^0 = 25
- Isabel: U = 36S1^(1/2)S1^0 = 36

Then, we can calculate the initial utilitarian social welfare function as the sum of the individuals' utility:

USW = U_Brett + U_Art + U_Isabel = 7 + 25 + 36 = 68

Next, we need to calculate the new utility levels after the income transfer:

- Brett: U = 16S1^(1/2)S1^0 = 16
- Art: U = 16S1^(1/2)S1^0 = 16 ($9 less than before)
- Isabel: U = 36S1^(1/2)S1^0 = 36

The new utilitarian social welfare function is:

USW_new = U_Brett + U_Art + U_Isabel = 16 + 16 + 36 = 68

Therefore, the utilitarian social welfare function remains unchanged at 68. However, this assumes that the $9 taken from Art's income does not affect his utility function. It is possible that the loss of income could decrease Art's utility and therefore decrease the overall utilitarian social welfare function.

Brett, Art, and Isabel Reside on a Tiny Island in the Pacific