clear all; close all; clc; % This code is an implementation of a 7x2 limited commitment problem % there are seven states and two agents % there are also promised utilities w and consumption values c, % corresponding to each state % % The equations we need to solve in general look the following way: % w=u(c)+beta*P*w (7 equations) - participation constraints % M*c=1 (4 equations) - consumptions sum up to total endowment % w(hi)=max(Uaut(hi),U(1/2)) (3 equations) - in high endowment states agents are guaranteed autarky values at least global beta gamma P y Uau Upr %parameters gamma = 2; %risk aversion beta = 0.75; %discount factor %y=[0.35; 0.4; 0.45; 0.5; 0.55; 0.6; 0.65]; %endowment vector (lo; hi) y=[0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8]; %endowment vector (lo; hi) pi = 0.75; %transition probability (persistence) P=(ones(7,7)-eye(7,7))*(1-pi)/6+eye(7,7)*pi; %find autarky levels of utility Uau=inv(eye(7,7)-beta*P)*(y.^(1-gamma))/(1-gamma); %check if risk sharing is possible Upr=(((ones(1,7)*y/7)^(1-gamma))/(1-gamma))/(1-beta); if max(Uau)