Download PDF - Ivie

( )= (3 − )
; =1 2 6= (8)
9 −
Solving the above equations gives the subgame perfect equilibrium (SPE)
levels of qualities, advertising, market shares and profits:
= 3 ; = ; = 1 2 ; (9 − )
= , =1 2 (9)
18
As can be seen from (9), in equilibrium both platforms choose the same
quality and ads, so that they obtain the same demand and profit. We also
find that profits are increasing in . This is because platforms’ profitability
of quality improvement positively depends on , whichisreflectedinthefact
that equilibrium qualities are increasing in . Finally,wefind that the level
of quality does not depend on the degree of substitutability.
Consumer surplus () is calculated as: 5
Z 1
Z 1
= 1 1 − 1 1 −
0
+ 2 (1− 1 )− 2 (1− 1 )− (1−) (10)
1
We now calculate social welfare ( ), defined as the sum of platforms’
profits ( = 1 + 2 ) and consumer surplus (),
=( − ) 2 +( 1 − 2 + +( − )( 1 − 2 )) 1 − 2 1 + 2 − +2 1 +2 2
2
(11)
By using (9) in (11), we obtain the social welfare at the SPE in the private
duopoly, which is given by:
= (36 − 45) − 4(2 − 3)
(12)
36
3 The mixed duopoly model
In this section, we will assume that platform 1 is a publicly-owned firm that
maximizes social welfare, while platform 2 is a private firm that maximizes its
profit. Substituting (2) in (11) and maximizing the resulting welfare function
5 Recall that 2 =1− 1 .
6
8