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- SWI if ( 1)( 63+18 +390 2+20 3 455 4+154 5) 8(3 )2(1+3 )( 3 3 +2 2)2 > 0; which is positive for 0 < < 0:4090 and negative otherwise: Next, SWI > SWH if 8( 2c)2 ( + )(6 2 3 2) ( +3 )(9 2 2)2 > 0 and this is always true. Finally, SWC > SWC+ i 360 8 + 1008 7 + 420 6 2 750 5 3 533 4 4 127 3 5 33 2 6 + 65 7 + 38 8 > 0 which is the case for all 2 (0; 1): Therefore, the highest SW is: SWC > SWI if 0 < < 0:4090 SWI > SWC if 0:4090 < < 1 Consumer Surplus. First to prove CSC > CSH is equivalent to (45 5 +162 4 +306 3 2+236 2 3+41 4 22 5) 8(3 + )2(3 2 +3 2 2)2 > 0 which is always true: Next, CSC > CSI if ( 1)( 45 90 +114 2+220 3+59 4 66 5) 8(3 )2(1+3 )( 3 3 +2 2)2 > 0; which holds for 0 < < 0:6259: Next, CSI > CSH if 24( 2c)2 ( + )2 ( +3 )(9 2 2)2 > 0 and this is always true. Finally, CSC > CSC+ i 72 8 + 288 7 + 480 6 2 + 570 5 3 + 413 4 4 17 3 5 163 2 6 45 7 + 2 8 > 0 which is the case for all 2 (0; 1).
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