公平貿易?

考慮以下的demand curve:

Q = 10/P^2


R --- revenue 利潤
P --- price 價格
sqrt. --- square root 開方根
Q --- quantity 數量
M --- marginal 邊際

當marginal cost 是$1 的時候, 專利的營利是 MR = MC = 1
R = PQ = 10/P
P = sqrt. (10/Q)
R = 10*sqrt. (Q/10) = sqrt. (10Q)
MR = 0.5sqrt.10/sqrt.Q  = 1
0.5 sqrt.10= sqrt. Q
10*0.25 = Q
Q = 2.5
P = sqrt. 10/2.5 = 2
R = 2*2.5 = 5

當marginal cost 是$3 的時候, 專利的營利是 MR = MC = 3

R = PQ = 10/P
P = sqrt. (10/Q)

R = 10*sqrt. (Q/10) = sqrt. (10Q)
MR = 0.5sqrt.10/sqrt.Q  = 3
0.5 sqrt.10=3 sqrt. Q
10*0.25 = 9Q
Q = 5/18
P = sqrt. (10*18/5) = 6
R = 30/18 = 5/3 = 1.66666667

但是當marginal cost 上升的時候, 如果他可以導致一個demand 上升的話,
如demand curve 變成

Q = 40/P^2

那麼
R = PQ = 40/P  P = sqrt. (40/Q)

R = 40*sqrt. (Q/40) = sqrt. (40Q)
MR = 0.5sqrt.40/sqrt.Q  = 3
0.5 sqrt.40=3 sqrt. Q
40*0.25 = 9Q
Q = 10/9
P = sqrt. (40*9/10) = 6

R = 60/9 = 6.66666666.....

所以為什麼有些企業自稱要搞公平貿易?