Question

2. Assume that the price of good 2, P2 = $1 and my income is M = $60. Derive the demand for X, as a function of p, for each of the following utility functions. a) U(x1, x2) = 3x1 + 2x2. b) U(x1, x2) = min {2x1,3x2}. c) U(x1,x2) = 3x1 + x2. d) U(x1, x2) = x1x2. e) U(x1, x2) = min (3x1,x2).

answers to the questions

Answer 1

Answers 2 (a) ll (x,x) = 3x + 2x2, MRS12 = Mv/mv₂= 3/2. then If MRS. 2 > P.P = P, only x, is consume So x = SMP, If 3/2 >P, lo If 3/2 <P, x = {bolp, 3728, lo , 3 <2P (B) u (x,x) = min (2x, , 3X2), at eam 2x, = 3x2 from Bil P, x, + x2 = 60 x 2 = 2 x 1 put x₂= 2x, /3, P,x, + 2x1 = 60 3P, x, +2x = 180, xt = 180 3P, + 2 2

(C) 4(x,x) = 3x + x2, MRs1, 2 = 3, IF MRS>P, IP, only x, is consumed, x, = {bole ,33 (di u = x.x, MRS., 2 = Mv. /mv₂ = x2(x, at can X2lx, = Pala , x = P, x,. from B. - P. x + x₂ = 60, 2P,x, = 60, [x; = 60/2P, Answer (e) u= min. (3x,,x2). at egn, 3x = x2, fromBec - P, x, + 3x = 60 ** Foto - -) Answer - Answer