i mananged to solve until d), but how I use the envelope theorem to find out when reduction in Px is better than a reduction in Py?

4 Constrained optimization in two variables Anthony seeks to maximize the following utility function no, y) = sales/3 subject to the budget constraint pea: + 19in = I where pm, pg, 9:, y, I > 0. a) Find Anthony's utility-maximizing bundle (55*, y*) as a function of pm, pm and I. b) Show that if is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is Spent on a"? What share is Spent on y? In other words, * I" I I calculate \"f and 3%. Are these shares a functlon of prlces? Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the exponents. d) What is the impact of a change in pm on Anthony's utility? e) When is a reductiOn in pm better for Anthony than a reduction in 333; of the same size? Hint: use the envelope theorem