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
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