アトキンソン・スティグリッツの定理
∂ V 2 ∂ C 2 + λ 2 ∂ V 2 ∂ C 2 − λ 1 ∂ V 1 ∂ C 2 − γ N 2 = 0 , {\displaystyle {\frac {\partial V_{2}}{\partial C_{2}}}+\lambda _{2}{\frac {\partial V_{2}}{\partial C_{2}}}-\lambda _{1}{\frac {\partial V_{1}}{\partial C_{2}}}-\gamma N_{2}=0\;,}
∂ V 2 ∂ Y 2 + λ 2 ∂ V 2 ∂ Y 2 − λ 1 ∂ V 1 ∂ Y 2 + γ N 2 = 0 {\displaystyle {\frac {\partial V_{2}}{\partial Y_{2}}}+\lambda _{2}{\frac {\partial V_{2}}{\partial Y_{2}}}-\lambda _{1}{\frac {\partial V_{1}}{\partial Y_{2}}}+\gamma N_{2}=0\;}
となる。
λ 1 = 0 {\displaystyle \lambda _{1}=0} かつ λ 2 = 0 {\displaystyle \lambda _{2}=0} となるケースでは、
∂ V i / ∂ Y i ∂ V i / ∂ C i + 1 = 0 , {\displaystyle {\frac {\partial V_{i}/\partial Y_{i}}{\partial V_{i}/\partial C_{i}}}+1=0\;,}