Download PDF - Ivie

1 = − 2 1
2
; 2 = 2
2 − 1 +− 2
2
− 2 2
2
(17)
From maximizing the private platform’s profit,wecanobtaintheprivate
platform 2’s advertising level, so:
2 = 2 − 1 +
(18)
2
By substituting the level of advertising (18) in the profit functions (17)
we obtain the profits:
1 = − 2 1
2
; 2 = ( 2− 1 +) 2
− 2 2
8 2
We now consider the platforms’ quality choices, so the publicly-owned
platformmaximizesthesocialwelfareandtheprivateonemaximizesher/his
profit. Taking into account that platform 1 does not obtain any revenue from
advertising, the social welfare ( )atthefirst stage is now given by:
= 2 − 2 + ( 1− 2 +3)(3( 1 − 2 )+)
16
+ (−1)( 2− 1 +) 2
8
− 2 1
2
− 2 2
2
(19)
where the platforms’ profits () and consumer surplus ()aregivenby:
= 1 + 2 = ( 2 − 1 + ) 2
8
− 2 1
2 − 2 2
2
(20)
= 2 − 2 + ( 1 − 2 +3)(3( 1 − 2 )+)
16
− ( 2 − 1 + ) 2
8
From the first order conditions in the first stage of the game, we can
obtain the reaction function of each platform:
1 ( 2 )= (2−7)+(2+1) 2
;
2−8+1 2 ( 1 )= (− 1)
4+
From the intersection of platforms’ quality reaction functions, we obtain
the levels of advertising, market shares and profits at the SPE of this game:
9
11