Quantity Competition; An Example An equilibrium is when each firm's output level is a best response to the other firm's output level for then neither wants to deviate from its output level a pair of output levels(y,*,y2*)is a Cournot-Nash equilibrium(古诺纳什 均衡) yi=R1(2) and y2=R2(yu)
Quantity Competition; An Example An equilibrium is when each firm’s output level is a best response to the other firm’s output level, for then neither wants to deviate from its output level. A pair of output levels (y1 *,y2 *) is a Cournot-Nash equilibrium (古诺-纳什 均衡) if y2 R2 y1 * * y R y = ( ). 1 1 2 * * = ( ) and
Quantity Competition; An Example y=R1(y2)=15-4y2andy=R2(V=45-y1
Quantity Competition; An Example y1 R1 y2 15 y2 1 4 * * * = ( ) = − y R y y 2 2 1 45 1 4 * * * = ( ) = . − and
Quantity Competition; An Example y1=R1(y2)=15-y2andy2)R2(y1) 45-y1 Substitute for y2* to get 1 45-y1 y 15
Quantity Competition; An Example y1 R1 y2 15 y2 1 4 * * * = ( ) = − y R y y 2 2 1 45 1 4 * * * = ( ) = . − and Substitute for y2 * to get y y 1 1 15 1 4 45 4 * * = − −
Quantity Competition; An Example y1=R1(y2)=15-y2andy2)R2(y1) 45-y1 Substitute for y2 to get y1=15 145-y1 →y1=13
Quantity Competition; An Example y1 R1 y2 15 y2 1 4 * * * = ( ) = − y R y y 2 2 1 45 1 4 * * * = ( ) = . − and Substitute for y2 * to get y y 1 y 1 15 1 1 4 45 4 13 * * * = − − =
Quantity Competition; An Example y1=R1(y2)=15-y2andy2)R2(y1) 45-y1 Substitute for y2 to get y1=15 145-y1 →y1=13 Hence 45-13 y2 8
Quantity Competition; An Example y1 R1 y2 15 y2 1 4 * * * = ( ) = − y R y y 2 2 1 45 1 4 * * * = ( ) = . − and Substitute for y2 * to get y y 1 y 1 15 1 1 4 45 4 13 * * * = − − = Hence y2 45 13 4 8 * = . − =