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 y1, firm 2's profit function is I(y2;y1)=(60-y1-y2)y2-15y2-y2
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
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
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
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 = = − ( )
Quantity Competition; An Example y2 Firm 2s reaction curve y2=R,(V._45-y1 45/4 45 y1
Quantity Competition; An Example y2 y1 Firm 2’s “reaction curve” y R y y 2 2 1 45 1 4 = = − ( ) . 45/4 45