ufp_ps2_12_sol

The individual preferred level is given by g = αy i

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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 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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The individual preferred level is given by G = αY i N b...

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