アトキンソン・スティグリッツの定理
最適解を得るための基本条件は
μ ∂ V 1 ∂ C 1 − λ 2 ∂ V 2 ∂ C 1 + λ 1 ∂ V 1 ∂ C 1 − γ N 1 = 0 , {\displaystyle \mu {\frac {\partial V_{1}}{\partial C_{1}}}-\lambda _{2}{\frac {\partial V_{2}}{\partial C_{1}}}+\lambda _{1}{\frac {\partial V_{1}}{\partial C_{1}}}-\gamma N_{1}=0\;,}
μ ∂ V 1 ∂ Y 1 − λ 2 ∂ V 2 ∂ Y 1 + λ 1 ∂ V 1 ∂ Y 1 + γ N 1 = 0 , {\displaystyle \mu {\frac {\partial V_{1}}{\partial Y_{1}}}-\lambda _{2}{\frac {\partial V_{2}}{\partial Y_{1}}}+\lambda _{1}{\frac {\partial V_{1}}{\partial Y_{1}}}+\gamma N_{1}=0\;,}