Ch10 Monopoly¶
核心概念¶
for comepetition, 不管產量多少，價格都一樣
→ MR = P
but for monopoly, 產量提高時，價格降低
→ MR = P - △P×先前Q
Will set price/quantity to where marginal profit = 0 i.e. MR = MC.
Calculation tips
Remember when calculating equilibrium price/quantity with MR = MC, do the partial derivative of Q instead of P, as the corresponding P on MR curve != the actual P on demand curve. If you want to calculate the equilibrium with P, calculate with marginal profit = 0 instead.
Lerner Index¶
the elasticity of the demand curve
it's negative
Monopoly vs. Competition¶
subsidy monopoly¶
理論上可以補助 monopoly 使 monopoly 產出到 Q~C~ (最 efficient 產量)
使 social gain 跟 competitive 時一樣
C+D+F+G 必> F+G+H
否則 monopoly 原本就會選擇產出到 Q~C~ 而非 Q~M~
Price Ceiling¶
Zero Profit Monopoly¶
如果要求 monopoly 跟 competition 一樣 zero economic profits
natural monopoly¶
if AC crosses demand curve when slope < 0
→ competitive 下的 P (\(P_C\), where MC = D) < AC
→ earn negative profit if competitive
→ competitive industry 不可能存在
所以會給 limited time 的 patent，兼顧廠商的 profit & 社會福利
e.g.
- 一家軟體廠商
開發完軟體之後的複製費用幾乎為零
因此 AC i.e. \(\dfrac{開發費用}{產量}\) 斜向下
demand curve 交 AC 於 AC 斜向下處
又 MC 交 AC 於 AC 最小值處
- 台電花大錢架好供電網路之後的 MC 就很小了
因此形成 natural monopoly
innovation for natural monopoly¶
不是一定會造成正向 social gain
e.g.
花 $50M 增加一個小小功能，使自家產品比他牌強，因而獲得大量客戶，
但實際上對客戶造成的 gain 只有 $10M 的價值
→ good for company, bad for society ( $-40M social gain)
Price Discrimination¶
charge different price for identical items
First-Degree¶
- 完全知道每個人的需求曲線並依此定價，榨光所有 consumers' surplus
- monopolist 會生產至 competition quantity (D=MC) → social welfare maximized, no deadweight loss
Second-Degree¶
price depends on quantity, no individual differences
前 \(Q_0\) 賣 $10 (where MR=MC)，\(Q_0\) 之後賣 $10 > P > MC (e.g. \(Q_0\) - \(Q_1\) 賣 competitive price $7)
→ 深藍色三角形的 producer's surplus & 淺藍的 consumers' surplus
quantity & PS & CS & social welfare increases
Third-Degree¶
different price in different markets
Man City 的人願意用 $7 買 whatever quantity → \(MR_{city}=\$7\)
黃曜霆的 mail
Two-Part Tariff¶
e.g. monopoly 入場後商品，再用入場費吸光 consumers' surplus
Homework¶
注意¶
N~2~ c
