A social welfare function (A social welfare function reflects how much weight to give the preferences of various members of society.) is thought to be additive along the lines proposed by Bentham andMill:

W=U₁+U₂+...+U_n

where U_i is individuali's utility and there are n individuals.

Suppose an economy is made up of twoindividuals, John and Jane. John's utility function is U_John=24X^0.5

andJane's utility function is U_Jane=2X.

There is a fixed quantity of 120 units of good X.

What allocation of good X between John and Jane maximizes socialwelfare?

units of good X and Jane consumes

Social welfare(W) is maximized when John consumes .... units of good X and Jane consumes .... units of good X.