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Unformatted text preview: 1 Question 5 Suppose D d and R d are asset positions for Daisy of democratic and republican assets, while D r and R r are those of Robert. Then, a ) U d = 0 . 6 ln D d + 0 . 4 ln R d and U r = 0 . 2 ln D r + 0 . 8 ln R r 5 points were assigned for a completely correct answer and a partial credit was only rarely given. b ) pD d +(1- p ) R d = 1000 (Since p +1- p = 1 we can assume that all money are spent on assets as one dollar and a bundle, which consists of one asset of each type, yield same payoffs in both states) 5 points were assigned for a completely correct answer and a partial credit was only rarely given. c ) To get demand functions one can maximize a Lagrangian for both Daisy and Robert or note that utility functions are monotone transformation of a Cobb-Douglas utility function, hence, D d = . 6 · 1000 p andR d = . 4 · 1000 1- p and D r = . 2 · 1000 p andR r = . 8 · 1000 1- p Now in a equilibrium markets have to clear, so 600 p + 200 p = 2000 and p = 0 . 4 . Thus ( D d ,R d ,D r , R r ) = ( 1500 , 2000 3 , 500 , 4000 3 ) 5 points were assigned to finding correct demand functions and 5 points were assigned to finding equilibrium p and asset positions d ) For this utility functions all Pareto efficient allocations must be interior except for two allocations where all assets go to one person. This is so because when, say, D d = 0 and R d > 0 Daisy is willing to sacrifice almost entire...
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