市场理论#

边际收益曲线#

1. 需求曲线为直线

$P = a - bQ$ $TR = P \cdot Q = -bQ^2 + aQ$ $MR = \frac{dTR}{dQ} = -2bQ + a$ $\text{令}MR = 0\text{则，有} MR = -2bQ + a = 0$ $Q = \frac{a}{2b}$ $\text{令}P = 0\text{则，有} P = a -bQ = 0$ $Q = \frac{a}{b}$ 因此边际收益曲线在纵轴截距为需求曲线在纵轴的截距
边际收益曲线在横轴截距为需求曲线在横轴截距的一半

2. 需求曲线为非直线 $D: P(Q)$
   $TR = P(Q) \cdot Q$
   $AR = \frac{TR}{Q} = P(Q)$ $MR = \frac{dTR}{dQ} = \frac{dP(Q)}{dQ} \cdot Q + P(Q) = P(\frac{dP(Q)}{dQ}\cdot \frac{Q}{P} + \frac{P(Q)}{P}) = P(1-\frac{1}{Ed})$

$\because \frac{dP(Q)}{dQ} = -b < 0 , Q>0$ $\therefore MR < P = AR$