99台大商研:獨佔兩市場與消費者剩餘 - 經濟

字有點多，抱歉。
題目是這樣的:
A monopolist serves an aggregate market with a damand function given by
q=36-2p. This market can be partitioned into submarket 1 and 2 with
submarket demandfunctions given by
q1=16-1/2P1 and
q2=20-3/2P2.
Marginal cost is constant and equal to 4. Determine the profit-maximinizing
monopolist's uniform aggregate price?
What prices will the monopolist set if the decides to price discriminate?
Comment on the folloing statement and provide an economic rationale
for your answer:Price discrimination always hurts consumers?

小弟我算到最後面時，想說統一訂價下的總消費者剩餘可以用個別市場下的消費者剩餘
加總起來。(此題統一訂價有兩組解:(P*,Q*)=(11,14)或是(18,7))
我計算消費者剩餘的方法:
用P*=11算出q1=10.5, q2=3.5，再利用三角型面積公式算出
第一個市場的消費者剩餘(32-11)*10.5/2=110.25
第二個市場的消費者剩餘(40/3-11)*3.5=4.0833
CS=CS1+CS2=114.333

可是解答是這樣算的
總需求函數為P=18-1/2Q, P*=11,Q*=14 (P*=18,Q*=7算出來也是49)
CS=(18-11)*14/2=49

我不懂為什麼個別市場的消費者剩餘加總為什麼不會等於總消費者剩餘，想不透
求高手幫我解答，拜託了。

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