Question

help me with question 4 all pleasee..please show your step :')

with three goods. 1 .*y, and and 3. There are 200 4. (20 points) Consider a pure exchange economy with three goods, consumers who are either of type A or of type B. w.A.WA) (1,1,0) as his or her initial • Type A Each consumer of type A holds w1 - (wit.w.wg)-(1,1,0) endowment, and has the following utility function: • Type B: Each consumer of type B has w" -(wi w endowment, and has the following utility function: WS) (0,1,1) as his or her his or her initial Suppose 100 consumers are of type A, and other 100 consumers are of type B (a) Derive demand functions aí (1.7.), (p. p,pa), and ag um.pa) of type-A con sumers. (b) Derive demand functions of (11.22.ps), (1,2,ps), and a .pa) of type B com sumers. (c) Derive Walrasian equilibrium prices. You may normalize pi= 1.

Answer 1

1. Let p = 1, & P2, P3 → Prices of Good 2 & 3 endowment Income MA = 1P,+ 1 P2 + opz = 1+P2 MB = opit IP2 + 1P3 = P2+83 I UCX1, X21X3) = xlnxit Bln x2 + y lnxz. . then xi = XM. X2= BM (& HB ty)P, (2+B+7) P2? 13- a18+7)83 then a) XIA = OMA = x(1+P2) XA = B (1412) (&+B+Y) I T2+B+7) 9. &tß + Y) P2 for A &= 1/4 , & ß= 1/4 x = 42 then xxß +2 = 1/4+1/4+1/2 = 1. z = YM a) X = + (1+2), K, = 4c1f92)» | x3 = 1 b) X= 42 , B=14, 1=!4 , +p+Y= 4

then [X1B = $s (Peats) ja Ves = (Pzf9 | .] *3* = + (fotfa) ] (1) Now at walsasian eam excess dem and in all Mkts are cleared off XA #XB: 4, xxx@ = +1=2, x* x3 = 1. then f(1+82) + f (P 2+3) = 1. + P3) = 2 HP2 + P2 + 12 = 8P2 1 +212 + P3 = 812 T1+P3= 6/2 & { (Tppet Petfe) = 1. 211+P2) + P2 +83 = 413 2+QP2 + P2 + P3 = 4B3.. 2+382 = 313 @ Solving 1 60 3/2 = 3/3 -2 6P2 = 6/3 - 4 80 tpz = 613-4 5= 513 P₂ = 1, then P2 * = _ & P=1. (P1, P2, P3) = (1, 1/3, 1) Ang