Consider the utility-maximisation problem, maxu(x1,x2) subject to p1x1+p2x2=m. Let v(p1,p2,m) be the indirect utility function and be the Lagrange multiplier. a. Show that =m(x1u)x1+(x2u)x2 b. Show that p1v=x1,p2v=x2. c. Show that =m(p1v)p1+(p2v)p2. d. Prove that if u(x1,x2) is homogeneous of degree r in (x1,x2), then v(p1,p2,m) is homogenous of degree r in (p1,p2) Consider the utility-maximisation problem, maxu(x1,x2) subject to p1x1+p2x2=m. Let v(p1,p2,m) be the indirect utility function and be the Lagrange multiplier. a. Show that =m(x1u)x1+(x2u)x2 b. Show that p1v=x1,p2v=x2. c. Show that =m(p1v)p1+(p2v)p2. d. Prove that if u(x1,x2) is homogeneous of degree r in (x1,x2), then v(p1,p2,m) is homogenous of degree r in (p1,p2)