Ali Tutupoho, S.E., M.Si. Dosen EP-FE_UP

Sabtu, 26 Oktober 2013

SURPLUS KONSUMEN & SURPLUS PRODUSEN

D → q = √( 52 – p ) , S → p = 7 + ¼ q²
D → q² = 52 – p
S → p = 7 + ¼ q²
         ¼q² = p – 7 
            q² = 4p – 28
E → D = S
52 – p = 4p – 28
-5p = -80
p = 16
q² = 4p – 28
    = 4 (16) – 28
    = 36
q =  √36
   = 6
Maka titik E = (6 , 16)
D → q = √( 52 – p ) → q² = 52 – p → p = 52 – q²
S → p = 7 + ¼ q²
            6
Sk =    ∫ ( 52 – q² ) dq – p.q
0                       6                     
     = 52q – ⅓ (q3) ]  - p . q
                              0
     = [ 52 (6) – ⅓ (63)  ] – 0 – p . q
     = ( 312 – 72 ) – 0 – (16) (6)
     = 240 – 0 – 96
     = 144
Maka Surplus Konsumen: 144
                      6
Sp =    p . q - ∫ ( 7 + ¼ q² ) dq
              0                                          6
     = (16) (6) – ( 7q – 1/12 (q3) ]                         
                                                  0
     = 96 – [ 7 (6) – 1/12 (63) ] – 0
     = 96 – ( 42 – 18 )
     = 36
Maka Surplus Produsen: 36
D → 3q² =  75 – p  →  p = 75 - 3q²
S → 6q = p – 3 → p = 6q + 3
E → D = S
75 – 3q² = 6q + 3
-3q² - 6q = 3 – 75
-3q² - 6q = -72
-3q² - 6q + 72 = 0
q² + 2q - 24 = 0
( q + 6 ) ( q – 4 )
q = -6 atau q = 4
q = -6 (tidak memenuhi) jadi q = 4
p = 6q + 3
   = 6 (4) + 3
   = 27
Maka titik E = ( 4 , 27 )
            4
Sk =    ∫ ( 75 - 3q² ) dq – p.q
0                  4                      
     = ( 75q – q3 ) ]  - p . q
                           0
     = [ 75 (4) – 4³ ] – 0 – p . q
     = 300 – 48 – 0 – ( 27 . 4 )
     = 144
Maka Surplus Konsumen: 144
                      4
Sp =    p . q - ∫ ( 6q + 3 ) dq
              0                                 4
     = ( 27 . 4 ) – ( 3q² + 3q ) ]                        
                                             0
     = ( 27 . 4 ) – [ 3 (4)² + 3 (4) ] – 0
     = 108 –  ( 48 + 12 ) – 0
     = 108 – 60 – 0
     = 48
Maka Surplus Produsen: 48
D → p – 100 + 2q = 0 → p = 100 – 2q
S → p – 20 – 2q = 0 → p = 20 + 2q
E → D = S
100 – 2q = 20 + 2q
-4q = -80
    q = 20
p = 100 – 2q
   = 100 – 2(20)
   = 60
Maka titik E = ( 20 , 60 )
           20
Sk =    ∫ ( 100 – 2q ) dq – p.q
0              20                     
     = 100q – q² ]  - p . q
                         0
     = [ 100 (20) – (20)² ] – 0 – (60) (20)
     = ( 2000 – 400 ) – 0 – 1200
     = 1600 – 1200
     = 400
Maka Surplus Konsumen: 400
                     20
Sp =    p . q - ∫ ( 20 + 2q ) dq
              0                      20
     = p . q – ( 20q + q² ) ]                        
                                      0
     = (60) (20) – [ 20(20) + (20)² - 0]
     = 1200 – ( 400 + 400 )
     = 400
Maka Surplus Produsen: 400
D → q = √100 – p → p = 10 – q
S → q = p – 2 → p = q + 2
E → D = S
10 – q = q + 2
-2q = -8
    q = 4
p = 10 – q
   = 10 – 4
   = 6
Maka titik E = ( 4 , 6 )
            4
Sk =    ∫ ( 10 – q ) dq – p.q
0                  4                     
     = 10q – ½ q² ]  - p . q
                           0
     = [ 10 (4) – ½ (4)² ] – 0 – (6) (4)
     = ( 40 – 8 ) – 0 – 24 
     = 32 – 24
     = 8
Maka Surplus Konsumen: 8
                      4
Sp =    p . q - ∫ ( q + 2 ) dq
              0                           4
     = p . q – ( ½ q² + 2q ) ]                        
                                         0
     = (6) (4) – [ ½ (4)² + 2 (4) ] – 0
     = 24 – ( 8 + 8 )
     = 8
Maka Surplus Produsen: 8

Dosen Pengajar Mata Kuliah Teori Ekonomi Mikro
ttd
   Ali Tutupoho, S.E., M.Si.

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