经济学题目求解

(a) 边际成本 = dC(X)/dX = d(2X²)/dX = 4X
(b) 利润 = P*XD - C(XD) = P*(12-0.25P) - 2*(12-0.25P)² = -0.375P² + 24P - 288

对P求导得
-0.75P + 24 = 0
P = 32
产出 = 12 - 0.25*32 = 4

利润 = -0.375*32² + 24*32 - 288 = 96
(c) 供给曲线由P=边际成本决定
PS = 4X
需求曲线为
PD = 48 - 4X

社会总剩余 = X*(PD - PS) = X*(48-8X)
对X求导得
48 - 16X = 0
X = 3
(d)
PS = 4*3 = 12
PD = 48 - 4*3 = 36
即出厂价为12，零售价为36
(e) 利润 = (P + s)*XD - C(XD) = (P + s)*(12-0.25P) - 2*(12-0.25P)²
= -0.375P² + (24 - 0.25s)P - 288 + 12s
对P求导得
-0.75P + 24 - 0.25s = 0
P = 32 - s/3
产出 = 12 - 0.25*(32 - s/3) = 4 + s/12