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Problem Set 2: Solutions Problem 1 (Marginal Rate of ...

Problem Set 2: SolutionsECON 301: Intermediate MicroeconomicsProf. Marek WeretkaProblem 1 (Marginal Rate of Substitution)(a)For the third column, recall that by definitionMRS(x1, x2) = ( U x1)( U x2).Utility Function U x1 U x2 MRS(x1, x2)MRS(2,3)(i)U(x1, x2) =x1x2x2x1 x2x1 32(ii)U(x1, x2) =x31x523x21x525x31x42 3x25x1 910(iv)U(x1, x2) = 3 lnx1+ 5 lnx23x15x2 3x25x1 910(b)MRS(2,3) = 9/10 for utility functionU(x1, x2) =x31x52has the following interpre-tation: At bundle (2,3), to remain indifferent about the change ( , remain at the sameutility level), a consumer is willing to give up 9/10 ofx2for one additional unit ofx1. (Or,after losing one unit ofx1, he must receive 9/10 of a unit ofx2to be as well off as he wasat bundle (2,3).)

{ Note: These types of preferences are not \well behaved" like Cobb Douglas pref-erences are, so we use a di erent second secret of happiness for these preferences. We can no longer use MRS = p 1 p 2 since the MRS of the indi erence curve is not de ned at the kink. To nd the demand for both milk (x 1) and strawberries (x 2) we solve the ...

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