Suppose all investors have shifted CRRA utility with the same coefficient > 0. Suppose w m

Suppose all investors have shifted CRRA utility with the same coefficient

ρ > 0. Suppose w˜ m > ζ . Consider an allocation w˜ h = ζh + bh(w˜ m −ζ )

where H h=1 bh = 1. Show that the allocation is Pareto optimal. Hint: Show that it solves the social planner’s problem with weights λh defined as λh = b

ρ

h .