%euler equation

function ee = ee(a);

global nA A nY Y k j r beta pi aprime

lhs = (Y(j) + (1+r)*A(k) - a).^(-2);
rhs = beta*(1+r)*(pi(j,1)*(Y(1) + (1+r)*a - bf(a)*aprime(:,1)).^(-2) + ...
    pi(j,2)*(Y(2) + (1+r)*a - bf(a)*aprime(:,2)).^(-2) + pi(j,3)*(Y(3) + (1+r)*a - bf(a)*aprime(:,3)).^(-2));

ee = rhs - lhs;