北京大学：《微观经济学》Chapter Twenty-Seven Oligopoly 寡头垄断

Chapter twenty-Seven Oligopoly 寡头垄断

Chapter Twenty-Seven Oligopoly 寡头垄断

Structure Non-collusive moves Simultaneous moves Quantity competition -Cournot model Price competition Bertrand model Sequential moves Quantity leadership- Stakelberg model Price leadership Collusion

Structure Non-collusive moves – Simultaneous moves Quantity competition –Cournot model Price competition – Bertrand model – Sequential moves Quantity leadership – Stakelberg model Price leadership Collusion

Oligopoly A monopoly is an industry consisting a single firm a duopoly is an industry consisting of two firms An oligopoly is an industry consisting of a few firms. Particularly, each firm's own price or output decisions affect its competitors'profits

Oligopoly A monopoly is an industry consisting a single firm. A duopoly is an industry consisting of two firms. An oligopoly is an industry consisting of a few firms. Particularly, each firm’s own price or output decisions affect its competitors’ profits

Oligopoly How do we analyze markets in which the supplying industry is oligopolistic? Consider the duopolistic case of two firms supplying the same product

Oligopoly How do we analyze markets in which the supplying industry is oligopolistic? Consider the duopolistic case of two firms supplying the same product

Quantity Competition Assume that firms compete by choosing output levels If firm 1 produces y, units and firm 2 produces y2 units then total quantity supplied is y1+ y2. The market price will be p(y,+ y2) The firms total cost functions are C,, and c2y2)

Quantity Competition Assume that firms compete by choosing output levels. If firm 1 produces y1 units and firm 2 produces y2 units then total quantity supplied is y1 + y2 . The market price will be p(y1+ y2 ). The firms’ total cost functions are c1 (y1 ) and c2 (y2 )

Quantity Competition Suppose firm 1 takes firm 2s output level choice y2 as given. Then firm 1 sees its profit function as I1(y1iy2)=p(y1+y2y1-c1(y1) Given 2, what output level y1 maximizes firm 1s profit?

Quantity Competition Suppose firm 1 takes firm 2’s output level choice y2 as given. Then firm 1 sees its profit function as Given y2 , what output level y1 maximizes firm 1’s profit? 1 1 2 1 2 1 1 1 (y ;y ) = p(y + y )y − c (y )

Quantity Competition; An Example Suppose that the market inverse demand function is p(yT)=60-OT and that the firms' total cost functions are C1(y1=yi and C2(y2)=15y2+y2

Quantity Competition; An Example Suppose that the market inverse demand function is and that the firms’ total cost functions are p(yT) = 60 − yT c1 y1 y1 2 ( ) = c2 y2 y2 y2 2 and ( ) = 15 +

Quantity Competition; An Example Then, for given y2, firm 1's profit function is I(y1;y2)=(60-y1-y2y1-y1 So, given y2, firm 1s profit-maximizing output level solves =60-2y1-y2-2y1=0. dy1 I. e firm 1's best response to y2 Is y1=k1(y2)=15、1 y2

Quantity Competition; An Example (y ;y ) ( y y )y y . 1 2 1 2 1 1 2 = 60 − − − Then, for given y2 , firm 1’s profit function is So, given y2 , firm 1’s profit-maximizing output level solves    y y y y 1 = 60 − 2 1 − 2 − 2 1 = 0. I.e. firm 1’s best response to y2 is y1 R1 y2 15 y2 1 4 = ( ) = −

Quantity Competition; An Example y2 Firm 1s reaction curve 60 y1=R1(y2)=15-y2 15 y1

Quantity Competition; An Example y2 y1 60 15 Firm 1’s “reaction curve” y1 R1 y2 15 y2 1 4 = ( ) = −

Quantity Competition; An Example Similarly, given 1, firm 2's profit function is I(y2:y1)=(60-y1-y2)y2-15y2-y2 So, given y1, firm 2s profit-maximizing output level solves =60-y1-2y2-15-2y2=0 dy2 I. e firm 1's best response to y2 Is y2=R2(y1)= 45-y

Quantity Competition; An Example (y ;y ) ( y y )y y y . 2 1 1 2 2 2 2 2 = 60 − − − 15 − Similarly, given y1 , firm 2’s profit function is So, given y1 , firm 2’s profit-maximizing output level solves    y y y y 2 = 60 − 1 − 2 2 − 15 − 2 2 = 0. I.e. firm 1’s best response to y2 is y R y y 2 2 1 45 1 4 = = − ( )