3
拟线性效用：帕累托最优意味着总效用最大化？
我读到，如果我们对所有消费者都有准线性效用，那么任何对等的最优分配都会使所有消费者的效用水平之和最大化。那是： What we know:What we know:\textbf{What we know:} 1)ui(mi,xi)=mi+ϕi(xi)∀i=1,...,I1)ui(mi,xi)=mi+ϕi(xi)∀i=1,...,I1)\quad u^i(m^i,x^i)=m^i+\phi^i(x^i)\; \quad \forall i=1,...,I 2)ϕi()is continous and strictly increasing (but not necessarily differentiable)2)ϕi()is continous and strictly increasing (but not necessarily differentiable)2)\quad\phi^i(\;)\;\text{is continous and strictly increasing (but not necessarily differentiable)} 3)An allocation,xsatisfies¬∃x^s.t.m^i+ϕi(x^i)≥mi+ϕ(xi)∀i3)An allocation,xsatisfies¬∃x^s.t.m^i+ϕi(x^i)≥mi+ϕ(xi)∀i3)\quad \text{An allocation,}\,x\, \text{satisfies}\;\neg\,\exists\,\hat{x}\; s.t. \;\hat{m}^i+\phi^i(\hat{x}^i)\geq m^i+\phi(x^i)\;\forall i andm^i+ϕi(x^i)>mi+ϕ(xi)for someiandm^i+ϕi(x^i)>mi+ϕ(xi)for …