The serial assembly model is considered. The problem is formulated to find sets of cost inputs for which solutions found by a recursion procedure remain valid. For simplicity a solution of this problem is provided for the two-stage problem. The paper shows that the stability region of cost inputs forms a convex cone in R⁴ and consists of a system of linear inequalities. An algorithm is provided to compute the parameters of this cone and several cases of changing only two parameters are displayed graphically.