Question

Suppose you have follow ing utility function : UX1,X2)-Xx2 where 0<0<1; 0<B< 1; 0<B+0<1 The price of commodity X, is P, >0; the price of good X, is P, >0 a) Set up the expenditure minimizati on problem. b) Obtain compensated demand curves c) Calculate cross price elasticiti es of demand curves d) Calculate marginal cost of utility e) Obtain the optimal expenditure function Is the expenditure function increasing with respect to prices and utility?

Answer 1

aX1 O UCX6Xq) = xoxzB , a) Min Pixi + P272 - St. u= X, 8x23 L (X1gX2) = Pixit P2X2 +2 [ u-x, Ox23] b.) foci al 7 p - 2 X₂B ox, 0-1 =0 22/ax2 = P2 - 7 B x2 B-1 x 0 =0. thug = Ах„Box 91 = Xo 9 - PR x B xz By Xie XB I BRxI= P2 X 2 BO 2 ß Pixi = 0 P2 X2 X= (0P242) / BP, from constraint, u = x10 X2B rar u= (0 Pax 2 ] 0 XzB ū= @jo (28) 8x2840 top x2 = [(BP, Joto (u) to /BR /Bto wisto = (u) BTO (OP2./BpJ8%) Cross ca Price elasticity. Pl ax 24 = alnX2 - X2*ap a lap, eriya = Inflw Yoto ]+ kollee, 59640] 16. Once) thus der er da fanen. 2 x cm = fope). (80) 1786, (u BPI Bto I denxia = d en P2 ß ßto. = 6,2 cross price elasticity of xi wot P2 Any

le) optimal expenditure furch e = Pixi Cat P2TOCH ВРо Twitter og *fat los como hoy e- abftet (o 12 foro. (0,3 %* + (PP) 9810 , P4840] ome 70, & de yol are yo H 80 Yes expenditure funch a wot P& T Ang