$($a$)$ Derive the indirect utility function in case of a Cobb$-$Dauglas utility function $u(x,y)=x^{}{y}^{}.$ Where $+=1$ and the budget equation is given by : $I=P_x*x+P_y*y.$

$($b$)$ Derive the compensated demand function for the utility function $u=q_1{q}_2$ and the expenditure function $E=p_1{q}_1+p_2{q}_2.$ Verify the Shephard's Lemma.

$4+(3+3)$