clear all;

%pset1 problem3c using brute force method
beta = 1.01^(-1);
sigma = 4;
epsilon = 0.01;
gamma = 0.8;

initial = [0,100];
diff = 1;
i = 0;
while diff > 0.000000001
    lambda = sum(initial)/2;
    bc = 0;
    
    for t = 0:1000
        cB = -lambda^0.5 + (lambda + 4*(1 + epsilon)+lambda^0.5)^0.5;
        cR = -lambda^0.5 + (lambda + 4*(1 - epsilon)+lambda^0.5)^0.5;
     
        bc = bc + 0.5*cB^(-3) + 0.5*cR^(-3) - gamma*(cB^(-4)*(1+epsilon) + cR^(-4)* (1-epsilon));
    end
    
    if bc > 0 initial(1) = lambda;
    else initial(2) = lambda;
    end
            
    diff = abs(bc);
    
   i = i+1; 
end
    
lambda  
boom = cB/2
recession = cR/2

psB = 0.5*(beta/(1-beta))*(((cB)^(-sigma)*(1+epsilon) + (cR)^(-sigma)*(1-epsilon) )/(cB)^(-sigma))
psR = 0.5*(beta/(1-beta))*(((cB)^(-sigma)*(1+epsilon) + (cR)^(-sigma)*(1-epsilon) )/(cR)^(-sigma))

rBB = (psB + (1+epsilon))/psB;
rBR = (psR + (1-epsilon))/psB;
rRB = (psB + (1+epsilon))/psR;
rRR = (psR + (1-epsilon))/psR;

r = 0.25*(rBB + rBR + rRB + rRR)