M2E@Fudan

**Duality I

locally non-sotiated preference relation (L.N.S.) + an allocation {Xt}i given a price sequence {Pt} solving UMP => {Xt}i given {Pt} solves EMP

**Duality II

lower hemi-continuous preference relation (L.H.C.) + EMP => UMP

**Duality II:

L.H.C. + A Price quasi-Equilibrium with transfers + (Each wealth level m>0) => A Price Equilibrium with Transfers

**1st Fundamental Welfare Theorem

L.N.S. + A Price Equilibrium with Transfers =>Pareto Optimality

(It is already EMP, according to Duality I)

**2nd Fundamental Welfare Theorem

a> An allocation that is Pareto Optimal + all preference relations CONVEX + L.N.S =>

A Price quasi-Equilibrium with Transfers

b> Duality II

(The corresponding price sequence {Pt} is guaranteed by Separating Hyperplane Theorem)

http://www.econ.umn.edu/~tkehoe/classes/8105-11.html

Homework1.m

function ALPHA=f(n)
N=10^n;
beta=0.95;
alpha=0:1/N:1;
t1=4*alpha/(1-beta)-(3+beta)/(1-beta^2);
[p,q]=min(abs(t1));
ALPHA=1/N*(q-1)