What will be the gross demand for every good

Reference no: EM132207456

Problem: Paul's utility function is given by the formula UP(x_P1,x_P2) = x_P1^1/3x_P2^2/3, and John's utility function is UJ(x_J1,x_J2) = x_J1^1/2x_J2^1/2. Paul has the initial endowment of ω_P1 = 1 and ω_P2 = 0, while the initial endowment of John is ω_J1 = 0 and ω_J2 = 1. Their only income comes from selling (some of) the initial endowments. Assume that prices p1 and p2 of goods x1 and x2, respectively, are determined by an impartial arbiter-auctioneer. At what price ratio will the equilibrium of the exchange between Paul and John emerge? What will be the gross demand of each of them for every good in the equilibrium?

Reference no: EM132207456

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