Edgeworth box. apples. F-f. A-a. trade. f f F. fig leaves

Transcription

1

2 Chpters 9 nd 1

3 pples Edgeworth box F-f trde A- A f f F fig leves

4 pples Edgeworth box F-f trde A- A Adm gets (f,) Eve gets (F-f, A-) f f F fig leves

5 pples Edgeworth box F-f endowment A- A Adm hs (,A) Eve hs (F,) f f F fig leves

6 pples Edgeworth box Adm s indifference curves f fig leves

7 pples Edgeworth box Eve s indifference curves f fig leves

8 pples Edgeworth box not Preto efficient f fig leves

9 pples Edgeworth box not Preto efficient Preto efficient f fig leves

10 pples Edgeworth box endowment point f fig leves

11 pples Edgeworth box contrct curve f fig leves

12 pples Edgeworth box Q Eve is fully discriminting monopolist f fig leves

13 pples Edgeworth box Adm is fully discriminting monopolist f fig leves

14 pples Edgeworth box All the trdes possible t fixed price f fig leves

15 pples Edgeworth box Adm s supply nd demnd f fig leves

16 pples Edgeworth box Adm s supply nd demnd Eve s supply nd demnd f fig leves

17 pples Edgeworth box Wlrsin equilibrium perfect competition supply = demnd f fig leves

18 pples Edgeworth box Q Eve is fully discriminting monopolist f fig leves

19 pples Edgeworth box 9.5 Q Eve is clssicl monopolist? f fig leves

20 pples Edgeworth box 9.5 P Q Adm s demnd t given price f fig leves

21 pples Edgeworth box 9.5 P Q locus of Adm s demnds for ll possible prices f fig leves

22 pples Edgeworth box 9.5 M P Q Eve s choice s clssicl monopolist f fig leves

23 pples Edgeworth box 9.5 M Q W Perfect competition nd fully discriminting monopoly re Preto efficient but clssicl monopoly is not. f fig leves

24 Imperfect competition 1.2 Alice mkes hts t cost of $c per ht. Her profit is π 1 = p c price Alice s

25 Imperfect competition 1.2 Alice mkes hts t cost of $c per ht. Her profit is π 1 = p c price With the demnd eqution p = K b Alice s other totl production under perfect competition is K-c becuse the price is given by p = c. Alice s profit is zero. price = mrginl cost

26 Imperfect competition 1.2 Alice mkes hts t cost of $c per ht. Her profit is π 1 = p c price Alice s With the demnd eqution other p = K b With imperfect competition, Alice s profit is π 1 = (K b c)

27 Bob s b Imperfect competition 1.2 Alice s isoprofit curves Alice s

28 Imperfect competition If Alice is monopolist, b = nd her profit is π 1 = (K c) dπ 1 d = K 2 c = = 1 2 ()

29 Imperfect competition If Alice is monopolist, b = nd her profit is π 1 = (K c) dπ 1 d = K 2 c = = 1 2 () So Alice mximizes profit when = 1 () 2 p = 1 2 (K + c) { } 2 π 1 = 1 () 2

30 Bob s b Imperfect competition perfect competition monopoly b = 1 () 2 Alice s

31 Imperfect competition Alice nd Bob re duopolists who mke hts t cost of $c per ht. Under Cournot competition, they choose their s simultneously. Their profits re π 1 = (p c) π 2 = (p c)b The price is determined by the demnd eqution, which in this cse is p = K b

32 Imperfect competition Alice nd Bob re duopolists who mke hts t cost of $c per ht. Under Cournot competition, they choose their s simultneously. Their profits re π 1 = (p c) π 2 = (p c)b The price is determined by the demnd eqution, which in this cse is p = K b Alice s nd Bob s profits become: π 1 = ( b) π 2 = ( b)b

33 Imperfect competition Alice s profit is: π 1 = ( b) π 1 π 2 = ( b)b = 2 b = = 1 ( b) 2 π 1 2 b = = 1 ( b) 2 π 2 π 2 b 2b = b = 1 2 ( ) b = R 1 (b) = 1 2b (K = c b) 2 b = 1 ( ) 2 R 2 () = 1 ( ) 2

34 Bob s b Imperfect competition B b = B Alice s

35 Bob s b Imperfect competition B b = B A = R 1 (B) Alice s

36 Bob s b Imperfect competition B b = B A = R 1 (B) Alice s

37 Bob s b Imperfect competition Alice s

38 Bob s b Imperfect competition Alice s rection curve: = R 1 (b) Alice s

39 Bob s b Imperfect competition Alice s rection curve: = R 1 (b) Bob s rection curve: b = R 2 () Alice s

40 Bob s b Imperfect competition Nsh equilibrium Alice s

41 Imperfect competition To find the Nsh equilibrium, solve the simultneous equtions: = R 1 (b) = 1 ( b) 2 b = R 2 () = 1 ( ) 2 π 1 = 2 b = = 1 ( b) 2 π 2 b = 2b = b = 1 ( ) 2 R1(b) = 1 2 ( b) R 2 () = 1 ( ) 2

42 Imperfect competition To find the Nsh equilibrium, solve the simultneous equtions: = R 1 (b) = 1 ( b) 2 b = R 2 () = 1 ( ) 2 π 1 = 2 b = = 1 ( b) 2 Becuse of the symmetry, = b nd so π 2 b = 2b = b = 1 ( ) 2 = b = 1 3 () R1(b) = 1 p = 1 3 K c { } 2 π 1 = π 2 = 1 () 3 2 ( b) R 2 () = 1 ( ) 2

43 Imperfect competition To find the Nsh equilibrium, solve the simultneous equtions: = R 1 (b) = 1 ( b) 2 b = R 2 () = 1 ( ) 2 π 1 = 2 b = = 1 ( b) 2 Becuse of the symmetry, = b nd so π 2 b = 2b = b = 1 ( ) 2 = b = 1 3 () R1(b) = 1 p = 1 3 K c { } 2 π 1 = π 2 = 1 () 3 2 ( b) R 2 () = 1 ( ) 2 Totl lrger, price lower, nd totl profit less thn in the cse of monopoly.

44 Bob s b Imperfect competition perfect competition Cournot equilibrium monopoly 1 () 3 1 () () Alice s

45 Imperfect competition 1.3 Alice nd Bob re duopolists who mke hts t cost of $c per ht. Under Stckelberg competition, Alice chooses her first. Their profits re π 1 = (p c) π 2 = (p c)b The price is determined by the demnd eqution, which in this cse is p = K b

46 Imperfect competition 1.3 Alice nd Bob re duopolists who mke hts t cost of $c per ht. Under Stckelberg competition, Alice is chooses her first. Their profits re π 1 = (p c) π 2 = (p c)b The price is determined by the demnd eqution, which in this cse is p = K b Alice s nd Bob s profits become: π 1 = ( b) π 2 = ( b)b

47 Imperfect competition 1.3 π 1 = ( b) π 2 = ( b)b Bob observes Alice s nd mkes the best reply b = R 2 () = 1 2 ( )

48 Bob s b Imperfect competition 1.3 Bob s rection curve: b = R 2 () Alice s

49 Imperfect competition 1.3 π 1 = ( b) π 2 = ( b)b Bob observes Alice s nd mkes the best reply b = R 2 () = 1 ( ) 2 Alice predicts Bob s choice, which mkes her profit: π 1 = ( R 2 ()) = 1 2 ( )

50 Imperfect competition 1.3 π 1 = ( b) π 2 = ( b)b Bob observes Alice s nd mkes the best reply b = R 2 () = 1 ( ) 2 Alice predicts Bob s choice, which mkes her profit: π 1 = ( R 2 ()) = 1 2 ( ) Alice s predicted profit is hlf monopolist s profit nd so her optiml is the sme s monopolist s = 1 () 2 b = 1 2 ( ) = 1 4 ()

51 Bob s b Imperfect competition 1.3 Bob s rection curve: b = R 2 () 1 4 () Alice s isoprofit curve 1 2 () Alice s

52 Bob s b Imperfect competition 1.3 perfect competition Cournot equilibrium Stckelberg equilibrium monopoly () () 1 () () Alice s

53 Bob s b Imperfect competition perfect competition No such thing s Stckelberg No such thing s Stckelberg equilibrium. It is relly the pth equilibrium. It is relly the pth followed in subgme-perfect followed in subgme-perfect equilibrium of Stckelberg gme. equilibrium of Stckelberg gme () () Cournot equilibrium Stckelberg equilibrium monopoly 1 () () Alice s

54 Bob s b Imperfect competition 1.3 perfect competition Wht kind of competition do Wht kind of competition do consumers like best? consumers like best? Cournot equilibrium Stckelberg equilibrium monopoly () () 1 () () Alice s

55 Bob s b Imperfect competition 1.3 perfect competition Wht kind of competition do Wht kind of competition do consumers like best? consumers like best? Cournot equilibrium Stckelberg equilibrium monopoly () () 1 () () Alice s

56 Ford Imperfect competition 1.4 Generl Motors Cournot competition consumers

57 Imperfect competition 1.4 Mcdonlds Burgerking Cournot competition? consumers

58 Imperfect competition 1.4 Mcdonlds Burger King derer price cheper price Bertrnd competition consumers

59 Bob s b Imperfect competition 1.4 perfect competition Bertrnd equilibrium is most like perfect competition Cournot equilibrium Stckelberg equilibrium monopoly () () 1 () () Alice s