5. (18) [2,2,6,5,3] Consider the utility function U(x, y) = (1+ y)vx and the budget constraint p x + py = I, where x 2 0 and y 2 0. Answer the following and show your derivations. (a) Is the utility function quasi-linear? Prove or disprove. (b) Is the utility function homothetic? Prove or disprove. (c) Does the utility function exhibit DMU and DMRS? Prove or disprove. (d) Let x and y" denote the optimal consumption of x and y. Calculate x " and y". (e) Let V(x, y) = x 1+ y . Is V(x, y) a monotonic transformation of U(x, y) ? Explain