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6. Assume that you have two agents with the following utility functions: u1(x,y)-21n(x)+In(y) and uz(x,y)-In(x)+3 1n(y). The
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U L ........ ... . u,lx, y) = Рxx + 2lnxtlny 9 9 = m, ou - more = 2 Ox 002 - moy - MRSxy = mux = 2 y moy 312 = 24 At optimalх = 2 х1 = от ) Agent 2 Ч2 (x, 92 = OU2 = lnx+ 31я7 M Ox = 2 О Х о, - мая MRS²x, y = mox моя = + ось - P4х + P Q = м 2 At optm2 4 px 1. x2 = M2 ups Y = 6 3 1 m y2 = 302 upy mi= - ex Px + eypy 5 x + upy = m2 = ese Pret e²y Py = 2P2t opg alhatatodermat= 7 px - 4110 Px + 8 Py) + 3 (2 Px + 6Py) 12 yopx + 32Py + 6Px + 18 Py = 84 px 46 Px + 50Py = 84 Px 50PY = su px - 46 px 50PY

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