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

$$\frac{MU_1}{MU_2}= \frac{p_1}{p_2}$$