Microeconomics 2nd Edition by Douglas Bernheim

Exercise 2

Charles has two children, Thomas and Harry. He wants to divide $10,000 between them. He makes such decisions by maximizing a social welfare function: W ( U T , U H ) = 4 U T + 3 U H , where U T is Thomas's utility and U H is Harry's. Furthermore,
and
where T is the amount of money Thomas receives and H is the amount Harry receives. How will Charles divide the money