function h_s = crossing_helper(h_0, rho, gamma, theta, omega, alpha, x_y)
    options = optimset('Display','Final','TolX',1e-10,'TolFun',1e-10);
    h_s = fsolve(@(h_s) (1-x_y-alpha)*(1+(1/omega)*((((1-gamma)*theta)/(gamma*h_s))^(1-rho))) - alpha*((theta - h_s)/((1-theta)*h_s)) , h_0,options);
end