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Unformatted text preview: The individual preferred level is given by: G = αY i N b) The second derivative is given by: ∂ 2 U i ∂ 2 G = Y i G N 1 α G α (1 α ) 1 Y i N G + α 1 G 2 + Y i G N 1 α G α (1 α ) 1 ( Y i N G ) 2 α 1 G 2 = Y i G N 1 α G α 1 Y i N G + 1 G 2 α (1 α ) < 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 ) which is a contradiction. d) With the singlepeakness 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: NonForProfits (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 counterbalancing weights to employer organizations and firms that have competing interests....
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 Fall '12
 Sieg
 Fiscal Policy, Utility, Yi, Household income in the United States

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