Optimal choice for Cobb-Douglas preferences

Summary

Cobb-Douglas utility function

• $u\left( x_1,x_2 \right)=x_1^ax_2^b$
• $MRS=- \frac{ax_2}{bx_1}$
• $x_1^*= \frac{a}{a+b} \frac{m}{p_1}$
• $x_2^*= \frac{b}{a+b} \frac{m}{p_2}$