Mathematical formulation of optimal choice and the Lagrangian

Summary

• Mathematical formulation of optimal choice:

\[\max_{x_1,x_2} u\left( x_1,x_2 \right) s.t. p_1x_1+p_2x_2=m\]

• Lagrangian

\[L\left( x_1,x_2 \right)=u\left( x_1,x_2 \right)-λ\left( p_1x_1+p_2x_2-m \right)\]

• First order condition

\[ \frac{MU_1}{MU_2}= \frac{p_1}{p_2}\]