Question

A social welfare function is thought to be additive along the lines proposed by Bentham and Mill: W=U1+U2 + ... + Un where U; is individual i's utility and there are n individuals. Suppose an economy is made up of two individuals, John and Jane. John's utility function is UJohn = 127 and Jane's utility function is Ujane = 3x. There is a fixed quantity of 140 units of good X. What allocation of good X between John and Jane maximizes social welfare? units of good X and Jane consumes units of good X. (Enter numeric responses using Social welfare (W) is maximized when John consumes integers.)

Answer 1

U1=Ujohn=127

U2=Ujane=3x

W=U1+U2

U1=127

U2=3x

W=Q=140

140=127+3x

13=3x

X=13/3=4.3

Allocation to maximize welfare:

John=127; Jane=3(4.3)

John=127; Jane=12.9 is the maximized social welfare when John consumes integers.