3. (1) Given a general constrained minimization problem as the following: min f(x,, .".x,a) s.t. g(x,, ...x,,a)=0, mathematically illustrate the envelope theorem as the following. (Hint: Show that *=y*, then take a total differentiation of * and make use of the FOCs) (12 points) dy of (x , ". x , a) dog(x , .x , a ) da da da (2) If the constraint is modified as g(x,, ...x,, a) = c, rewrite the Lagrangian function and repeat the above procedure to show that dy*/de . = 1", i.e., 1* measures the effect on the extreme value due to the relaxation of the constraint. (12 points)