Question

Consider U=q²+q²

Derive the Mashallian dd function from q1 and q2.

Answer 1

$$\frac {\delta u}{\delta q_1}=2q_1$$ $$\frac {\delta u}{\delta q_2}=2q_2$$

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

$$\frac {2q_1}{p_1}=\frac {2q_2}{p_2}$$

$$I=p_1q_1+p_2q_2$$

$$q_2=\frac {p_2}{p_1}q_1$$

$$q_1^*=\frac {Ip_1}{p_1^2+p_2^2}$$

$$q_2^*=\frac {Ip_2}{p_1^2+p_2^2}$$