Anthony seeks to maximize the following utility function u(x, y) = x/3y2/3 subject to the budget constraint Pxx + Pyy = I where px, Py, x, y, , I > 0. a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of px, py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pax and Pvy/*. Are these shares a function of prices? 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 px on Anthony's utility?