clear all; close all; clc; % This code is an implementation of a 2x2 limited commitment problem % there are two states (1 and 2) or (lo and hi) % 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 (2 equations) - participation constraints % [1 1]*c=1 (1 equation) - consumptions sum up to total endowment % w(2)=Uaut(2) (1 equation) - in high endowment states agents are guaranteed autarky values at least global beta gamma P y Uau Upr %parameters gamma = 2; %risk aversion beta = 0.65; %discount factor y=[0.35; 0.65]; %endowment vector (lo; hi) pi = 0.75; %transition probability (persistence) P=[pi,1-pi;1-pi,pi]; %transition matrix %find autarky levels of utility Uau=inv(eye(2,2)-beta*P)*(y.^(1-gamma))/(1-gamma); %check if risk sharing is possible Upr=(((ones(1,2)*y/2)^(1-gamma))/(1-gamma))/(1-beta); if max(Uau)