Suppose there are two individuals and two goods. Preferences are given by

u₁ (x,y) = Max{x,y}

and

u₂ (x,y) = xy

Consider the allocation w₁ = (10,0) and w₂ =(0,10) Note that the

allocation is best (resp. worst) for individual 1 (resp. 2) among feasible

set. Now show that

(a) The allocation is Pareto-efficient.

(b) The allocation is envy-free.