. 利 1. ( ) 8 w, 利率 r, 量 Q0 K 勞 L min C = wl + rk s. t. Q0 = f ( K, L) C = C(Q) P ( 數量 Q 利 max π = PQ C( Q) 2. 量 max π = PQ C( Q) = R( Q) C( Q) F.O.C.

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1 . 利. 8 w, 利率 r, 量 K 勞 L min C wl + rk s. t. f K, L C C 數量利 max π C. 量 max π C R C F.O.C. π / R / C / R C MR MC MR MC 量 S.O.C. π / R / C / R C < R MR 率 C MC 率 MR 率 MC 率利 R 3. 數力來類類數力易度數力絶力數力異數異.. 數裡行不不

2 3 利 π > 數 n 利 π < 4 perfect information 數 n. TR R p n i i MR AR 若量 n R p MR p R p AR p 3 d p S p p p d D 3. 數 max π p C ; K F.O.C. π / p C ; K p MC 量 i MR MC F C < R C < R F F E C > R E SMC SAC MR AR p ˆ

3 iitc TR π TR TC TR TC AR AC π > TR > TC AR AC > AC > > AC AR π < AC > > AVC TR > TVC 不 AR π < < AVC TR < TVC 不 AR 3

4 不利 π N TFC 利 π TR TVC TFC TR TVC + π π > π TR > TVC N N 3 p SAVC p SMC p SAVC p < SAVC 4 p SAVC SMC p 不數量不量 p 數量量 S ε / C A S S S A S p / p p A o p C o p p A S S ε A > o C 例 SMC 4 + SMC 4 + p d p d 3 練數 C p 58 利 3 量利練 p 數 C + 4 量利 4

5 4. p, K p, n 數 LMC p LAC K K SAC SMC p SMC a 數量 K SAC b 若 K 降 SAC c K K K K SAC SMC 量不 p SMC d 數量 K SAC e 若 K 3 降 SAC 3 f K K 3 K K 3 SAC3 SMC3 量不 p SMC3 g 3 了降 p SMC, K LMC LMC 5

6 3 數 max π, K p C, K π F.O.C. p SMC, K π K C K C, K C K 不 K C K min C, K C K K 數 C S, K K S L C, K C max π K p C L π F.O.C. p LMC 3 例 C S K +.5K 6 K 4 LAC LMC LMC 5. LAC LMC n S LMC i n S LMC i D 6

7 利 π > n n n n S LMC i i π π TR TC LAC LMC LAC 例 94 C n 6. 不 w, r 不 n K 不 w, r LAC, LMC 不 n w, r TC wl + rk 若不若降不 n LAC w, r n LAC 不 w, r 不 n LAC w, r A LAC LMC π > 數 n LAC LMC 7

8 n S LMC w r LAC 不 n S LMC w r 不 LAC 不 C n S LMC w r LAC 7. T T π C T TR TC C TR T C C + T C T T A C + AC + C M C C MC π C T π C MC MC C C AC MC C T n n π 不 π T 不 MC 不 π < n S w, r 不 T, n,, π 8

9 量 T t t 金例 t T 來量 TC C T C C + t AC C / A C C / + t AC + t MC C / M C C / + t MC + t M C LAC LMC t 度 t 度 S < LAC n n S π π C t TC t C TR AR T R t AR t AR t 9

10 AR t 度量 t 量 > t 3 t 例 t % π C t t C TR T R t AR TR / A R t t AR

11 量 Step min C wl + rk L, K s. t. f L, K C C Step. maxπ C s. t. 若數量 maxπ wl rk s. t., f K, L maxπ f K, L wl rk K, L K, L 練兩兩 8 數 TC + + 利? 練 LAC 5 5 數練 LTC C 數

12 price-taker price-maker d, K, K 4. 例 LAC 例律利 n D..TR min 數 s. t. 利量 max π C s t.. C wl + rk f K, L C C TR. AR, MR TR AR TR MR + D + ε D ε D ε MR D ε > MR > D ε < MR <

13 數 TR MR 不 AR MR. 量. max π C, K R C, K π F.O.C. R C MR SMC π S.O.C. R C <. max π R C π F.O.C. R C π < 不 π π >

14 3. 數 L α K β 量 α + β LAC α + β < LAC 率 3 α + β > LAC 練數 34 C 利量利 3

15 4.. 力數 Lerner Index M MC MR D ε ε D D ε 力 < M < M 不 D MR MC > ε > M D < ε. 利. SWsocial welfarecs+s 利

16 SW S CS S D 3 SW m MC D m MR 4 兩 SW c A SW m deadweight loss m c E C S MC j j 量 m c MR D d j j. 利 m AR MR A R M R m D AR MR m > > c M R MC, SW SW SW m MC 5

17 c SW g 3 < c AC MC i > ii AC 利利 iii SW S CS SW SW c AC c f b c a AC 3. MC 率 AC 利 > MC 率利 MC 率六. 不. 離利 i 理易了離 ii 了離 iii 離離利 3 不不. 類來來 MR 6

18 例 TR MR 3 4 TR MR 異 i 量 ii 利 SW 異 i 不 ii CS S CS S c 不不 3 不不例 i 數 Max Π + C ; +, Π TR C F.O.C. MR MC 7

19 Π TR C 聯立 MR MC MR MR MC, MR ε ε ε ε ε 若 ε < ε 不 < > ε > ε ε ε ε, ε, 練數 C 兩離數 8. 5 兩 ii 8

20 利利練兩數 4 數 C 若兩量利若兩量利練兩數 45 9 數 C + 若兩量若兩量練 3 力 C 兩數兩量兩量利 9

21 . 量量量 + 利 Max, π TR + TC TC π TR + TC F.O.C. MR MC π TR + TC MR MC 量 MR MC MC MC MC 例 6 TC 5 + TC. π 5 練 TC TC. 5.. T π C T π F.O.C. MR MC C C + T M C MC A C AC + T / 不量不不 π 不

22 . 量 T t π C t [ C + t] [ t] C C C + t TR TR t M C MC + t A C AC + T / MR MR t AR AR t 3. T t π C t t C TR TR t MR MR t AR AR t 量, 不利 T tπ 利 π C 利 π t π t[ C ] MR MC 量不練 C 利量若量量若利利量

23 Oligopoly.. 數若兩 duopoly 若若. 行行了量 3. 異 4.. 量. 量 + F +. 異不不, / < / >, / > / <.. uasi-competition model MC 量 MR MC 量不 π C F + C π C F + C Max π Max π MR, MC MR, MC 利 MC F + MC MC MC MC MC MC MC + MC F + +

24 例. 5 C 5 C. 5 量 F + MC MC π , π Collusion model Cartel 利 π + π 類 Max π π + π F + C + F + C F + + C C F π TR C π TR C C TR C C C MR MC MR MC 兩 MR MC MC MC MC MC + MC MR + F MR MC MC 不 Maxπ π + π π π 利 Cartel Max π + π 不 Maxπ Maxπ 例. 5 C 5 C. 5 量 MR MC MC π , π Cournot 利 a b + C c + e + f π [ a b + ] c e f a e b + f b c

25 3 利 π b c b f b b e a + π + 率 b c b f b π 率, 率 >, 率 <, 率 b c b f b π f b c + + π 3 < + b c π π 利 b c b f b b e a + π + π 利利 f b c + + π π 利利數 relation function, C R C F C Max + π.. t s 量量不 π 量 i j i 量 j 量 Cournot 量零 c b f b e a + π + b f b e a π f b b e a + φ 數例 5. 5 C 數 π 5.5 π 5. 95

26 數 Max π C R, C s. t. π R C / φ 例. 5 C. 數 π π Cournot Cournot solution Max π s. t. φ Max π s. t. φ 數來行兩數 Cournot 例兩 π 3 π 9 練 3 + MC C Cournot 練 Cournot 4

27 4.Stackelberg Leader Follower Leade 數數來行數來利 Followe 了數量數來量 A I Leade Max π R, C Leade s. t. φ 量不零 / φ Cournot s. t. / Follower Leade 量數來量 φ 例 Max π [.5 + ] 5 s. t 數 Max π [ ] 5 π π 366, π I Follower Max π R, C Leade s. t. φ Follower Leade 量數來量 φ φ π π π φ 例 Max π [.5 + ]. 5 s. t Max π [ ]. 5 / π , π 33.5, π π π π 5

28 C I Follower φ φ Cournot D I Leader F ˆ ˆ, 兩 Leader C, 兩 Follower E ˆ, I Leade II Follower G, ˆ I Followe II Leade ˆ πˆ G π F C π ˆ π I Leader 8 / π , π π π E ˆ II Leader Follower I Leader F 877.8, 64.7 E 366.6, 7. Follower G 33.5, C 3, 9 5 Max π + 不 π C A π 不 π C π 不 π C E π π AE A 利利 E A C 練 + TC TC 領 6

29 領 3 領 5.ertrand ertrand Cournot 數量了 / given / 3 MC TC j i I > d ε II > 利 d Max π Max TR ε 數 II > 來 < < 練 3 + 兩 MC ertrand 兩量 6. 領 rice-leadership model 量量利來 7

30 A MC D 度 MC A 連 MR MR MC 量量 MC 量 A MC MC D 數 MR MC Dˆ MC 例.5 + TC 5 TC. 5 領練 A 領 MC r 49 3 A 量量. 異.Cournot F + 異不 F, F, 利 π F, C F, C 8

31 不, π 不, π 數數 Max π, s. t. / F.O.C. 數 φ, 數數 Max π, s. t. / F.O.C. 數 φ, 數 3Cournot Cournot solution 數 φ φ 聯立 9

32 .Stackelberg I Leade Max π, s. t. φ / φ II Leade Max π, s. t. φ / φ 例 + C C 8 數 φ φ 若 Followe 量 3. 率 Market share model 率 k k + Leade Max π, k s. t. k k, 數 Follower k π C F, F,,,, π C Max π, C

33 k s. t. k F.O.C. 數例異 A 率 / 3 數 A TC 5 A 量量利 4.Sweezy Kinky demand curve Sweezy 說不易 i 量量不 i 不 / i 降 / > j j i i 不 i 量降 i 量不. 理論 game theory 參行略便參略理論便略. i 參 player ii 略 strategy iii payoff

34 . i ii 行 A L R T,,,, 參不略略 Simultaneous Gam 理論 Cournot ertrand Simultaneous Gam 參例 A A 行 Seuential Gam 列理論 Stackelberg 領 Seuential Gam 3. 零 zero sum game A 5, -5 -, A -8, 8 6, -6 若 A saddle point 參行 max min a A A 不利略 A A 不利略兩 A A 不利 A A 略不利 A A 略兩若 A max min min max i j ij max min a min max a i j ij aij A A A A j i ij A 5 A 8

35 A A A A A A A A 不略 A 5 3 A 4 例 A 3, 3-7, 7 A -8, 8 6, -6 A 4 9 A 7 4. 零略 Dominant strategy 不略不略略 A,, A,, L R T 4, 4, 8 8,, Nash 略 Nash L R T,,,, L R T, 3, 3,.5, 4 3

36 Nash i 不 ii iii pareto efficient outcome Left Right Top,, - utton, -, 3 A 4, 4 3, A, 3 8, 8 War eace War, 3, eace, 3,,,,, 3 列 Seuential Game 類 Stackelberg Leader Follower Left Right Top, 9, 9 utton,, 4

37 練 Leade Follower 不不, 9, 9,, 不不, 9, 9,, 練 low price high price low price,, 6 high price -, 7, Nash 若 A Leade 5

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. 利 1. ( ) 8 w, 利率 r, 量 Q0 K 勞 L min C = wl + rk s. t. Q0 = f ( K, L) C = C(Q) P ( 數 量 Q 利 max π = PQ C( Q) 2. 量 max π = PQ C( Q) = R( Q) C( Q) F.O.C.

. 利 1. ( ) 8 w, 利率 r, 量 Q0 K 勞 L min C = wl + rk s. t. Q0 = f ( K, L) C = C(Q) P ( 數量 Q 利 max π = PQ C( Q) 2. 量 max π = PQ C( Q) = R( Q) C( Q) F.O.C.