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Paul's utility function is given by the formula UP(xP1,XP2)=xP11/3xP22/3 and John's utility function is UJ(x11, xJ2)=x111/2x121/2. Paul disposes of an initial endowment P1=1 and P2=0,

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Paul's utility function is given by the formula UP(xP1,XP2)=xP11/3xP22/3 and John's utility function is UJ(x11, xJ2)=x111/2x121/2. Paul disposes of an initial endowment P1=1 and P2=0, while for John it is J1=0 and 32=1. Their only income comes from selling some of the initial endowments. Assuming that prices p1 and p2 of goods x1 and x2 are determined by an impartial arbiter-auctioneer, at what ratio of these prices will the equilibrium for the exchange between Paul and John take place

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