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Heyy chegg community can anyone explain this to me with clear steps. Appreciate it. (An Exchange Economy) Consider and economy with two goods, 1 and

Heyy chegg community can anyone explain this to me with clear steps. Appreciate it.
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(An Exchange Economy) Consider and economy with two goods, 1 and 2, and two consumers, A and B. Consumer A 's utility function is UA(x1A,x2A)=min{x1A,x2A}. Consumer B's utility function is UB(x1B,x2B)=x1Bx2B. Consumer A is endowed with Y units of good 2 (and no good 1 ) and consumer B is endowed with Z units of good 1 (and no good 2). Assume that Y0x1B0,x2B=0andx2B0,x1B=0ifU=0 The picture of the indifference curves are omitted. [b] Using our notation on endowments, we know that 1A=0,2A=Y,1B=Z and 2B=0, with Y0, consumer B solves the following problem s.t.p1x1B+p2x2B=x1Bmaxx2Bx1Bx2Bp1Z Using the familiar budget and tangency conditions, we can find optimal demands as x1B(p1,p2)=2p1p1Z=2Zandx2B(p1,p2)=p2p12Z. Given p1,p2>0, consumer A solves the following problem max1A,x2Amin{x1A,x2A}s.t.p1x1A+p2x2A=p2Y Calculus cannot help in solving this problem sinoe again the stilify function is not differentiable. Howener, it is clear from the indifference curves that the optimal consumptions of treo goods are the same, or x1A(p1,p2)=x2A(p1,p2). Substifuting this into the budget condition, we hate x1A(p1+p2)=x2A(p1p2)=P1+P2P2Y [d] Given p1=1, the marlet clearing conditions for goods I and 2 are repectirely x1A(1,p2)+x1B(1,p2)=Zandx2A(1,P2)+x2B(1,P2)=Y. By Walrus' law it is enough to clear only one market, the other one then clears astomatically. Clearing the first market using the demand functions derived in part [C], we hate 1+p2p2Y+2Z=Zp2=2YZZ This will lead to the following compertitive equilibriam for the exchange cconomg: p1x14=1,p2=2YZZ=2YZ,x2A=2YnZ+x1n=2Zx2n=Yn2Z It can be verified that all these ralues are feasible giren the assumption Z2Y. We calculated abote the equilibrium price is be negative. What is the problem? From part [c]. tre know that B's demands for the turo goods as a function of p2 look like this (ure still set p1=1 ) Therefore. B's demand for good 1 is alrays half of his endosment. In addition, since A never demands more good I than good 2, the largest A's demend for good I conld erer be, no matter what the price, is Y, which is the total amount of good I in the cconomy. When Z>2Y, or cyuiralently. Y

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