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Suppose a concave utility function has two peaks g 1

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c) You can easily see that the concavity implies single peakedness. Suppose a concave utility function has two peaks G 1 and G 2 , and G 1 < G 2 . Since G 1 and G 2 are local maxima, the slop of utility function is zero. ∂U i ∂G ( G 1 ) = ∂U i ∂G ( G 2 ) = 0 However, concavity implies that the slope decreases as G increases: ∂U i ∂G ( G 1 ) > ∂U i ∂G ( G 2 )
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which is a contradiction. d) With the single-peakness the median voter is the decisive voter. Let Y Med be the median income of the member of society, the outcome is given by median voter’s preferred level: αY Med N Problem 3: Non-For-Profits (20 percent) a) If municipal unions control the voting behavior of their members, then they can endorse a candidate and swing close elections. Moreover, they can provide local manpower to a political campaign or donate money to a campaign. b) You can require unions to hold an internal votes before they can endorse a politician. You can try to pass laws that restrict political contributions to individuals (is that con- stitutional?). Of course, unions may just serve as counter-balancing weights to employer organizations and firms that have competing interests.
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