Question

19. If f(x, y, z) = 4x2 + 3xyz + 2y3z + Vz, find the value of °(3.) Y2) when x = 1, y=2, z= 3. дх 20. If u(x1, x2) = 18x1 + 3x2, find the value of MRS(8,13). (Don't forget to include a minus sign when entering your answer!) unit unit unit 21. Bryan consumes only goods 1, 2, and 3 (in quantities X1, X2, and xz respectively) and as preferences over (X1, X2, X3) bundles that are captured by the utility function UB (X1, X2, X3). When prices were P1,= $2,P2 = $4, P3 = $6 and 1 = $120, Bryan chose to purchase the bundle (10, 10, 10). How much good 1 will Bryan choose to purchase at prices P1 = umie, P2 = wie, Pz = nie and I = $240? (Assume Bryan makes purchases so as to maximize his utility). [If the answer cannot be determined with only this information, enter 99.]

Answer 1

6 flasy, z) = 42 ² + 3y2 + 2y z + 2 Sflary,2) partial derivative wrta keeping all variable construit = $ 142°4 2942 4 ng®2 + VE I flangiz) = 8 x + 3y z 1 Jflary, z) = 8 2 + 3y z At 7 = 1, y = 2, Z=3 put in equ o we Gel Sf (204,2)= 8(0) +363)(8) = 26 Ja MRSE - MUY MU UMUM paule dealvative of 'u(2, 122) Wortar IM With a pautial derivative of U (1 & j wert de MRS = -5/187, +372) 5 11821+34) MRSI MRS : 6

RD Budget Line (inihad) Piast P Q2 + P₂ 23 = I > 28, +4.72 +673 = 1207 - 0 bininal Budget-line Son of himal Bunde ? = 10,7-10,73= 10 Multiply equ@by 2 Both side 2 Roth Side 2 (22, + 47, + 623 ) = 2 (120) - 481 + 8X₂ + 1292 = 240 Heli P = 4, P2 = 8, P2 = 12 which previous optimal Bundle. statisfy Hence, the good I will Bayan choose to purchase 1. be x1=10 klew optimall Bundle Remoun same ie (10,10,10)