Question

Hi there, I am struggling to understand how to complete these economics questions and was wondering if you could please explain in detail how to work them out? Is it possible to please hand write the answer so I can understand thanks.

1. Consider the following exchange economy. There are two goods Cl and 2) and two consumers (A and B), Preferences and endowements are as follows: UA (XC, A, X2A) = xc, A SCA SCA = (1,1) us (x, 8, x 3) = 5x Box B 5c 8 = (2, 2) a) Depict the economy in an edgeworth box diagram. Your diagram should include the autarkic allocation and each consumers in difference curves through autarky. b) Identify the set of Pareto efficient allocations and add them to your diagram. C) Find the warrasian equilibrium allocation (WEA) for the economy by completeing the following steps. we use T to denote the exchange rate, pilp2. To show banore consume that consumer A's optimal consumption plan, as a function of T, is to Ź + 271 units of good 1 and 2 Ž units of good 2 ii. show that consumer B's optimal consumption plan, as a function of T, is to consume It Ĥ units of good 1 and I t X units of good 2. iii. Find the equilibrium value for m e iv. Using your answers to (i) - (iii) idenify the WEA and draw another Edgeworth box diagram to illustrate your answer.

Answer 1

for 2) MRSI, B = PilP2 =T + x3x, B = T, X2B = TXIB DATE: 1 PAGE NO' 20 from Bc. Pixß + P2 X 2 B 2 Pi + QP2 PIXIB +X28 = 2 PilP2+2 PM P2 TX B + TX, B = 25+2 pe 2xx, B=2012 X, B = @=T +2)/30 = 1+ 1/A Ang l xqB = + 1 = {(A+TA = 7+7)] il at Eqm i XIA + x, B = 3 5+ yg +1+v0 =3 105+-5/15 + YA =3 05/+ Ya = 3-105 105/8= 3-165 , col won = 1 105/01 = l•50 T Th 1 Ang facup Pull Now. WEA . (Xin Xa) A = (-57-5, +5+5) = (1,1 p XX X 1,x2) B = (2,2). - Ang Budget Constraint BC & X, A + X2B = 2. Ane

Graph

(0,3) x1_B IC_A set of pareto effecient allocation x2_B - (1,1) 12 x1_A.

(0,3) x1_B IC_A set of pareto effecient allocation x2_B – (1,1) budget Constraing 2 x1_A