∗
∗ < < 3
3 θ θ
θ
Case 4: Comparison welfare effects of the merger between the public firm and the private firm 1, and that the merger between the public firm and the private firm 2
2
The social welfare of the merger between the public firm and the private firm without foreign penetration is large than the social welfare of the merger between the public firm and the private firm with foreign penetration. Due to the foreign penetration 1-α taken away, the public firm choose to merger with the private firm 1, it may be profitable, and that is best strategy.
Proposition 2.9 The merger between the public firm and the private firm without foreign penetration, and is the best strategy of the public firm.
2.9 Concluding Remark
In the chapter, we see that the effects of the post-merger equilibrium. Under the
２４
equilibriums of the post-merger, the public firm decides to merge with another the private firm, the profit after the merger is large than the profit before the merger. The public firm will have incentives to merge, if the profit and social welfare increases after the merger. An increase in the degree of privatization and the proportion of domestic stockholding, the social welfare of post-merger is large than the social welfare of pre-merger, due to the market price decrease, the market quantity increase, and the consumer surplus increase. When the both private firms decide to merge, the profit of the public firm is negative. In the light, the social welfare after merger is lower than the social welfare before merger. There exists a traditional merger paradox in the mixed oligopoly model since the market price increase, the market quantity increase.
２５
CHAPTER THREE: Mixed Oligopoly, Horizontal Merger and Foreign Penetration In a Endogenous Timing Framework
3.1 Introduction
3.1.2 Pre-merger1) There have three firms decide their quantity simultaneously.
2) The public firm as a Stackelberg leader. The public firm decides their quantity in stage 1, two firms decide their quantity in stage 2.
3) The private firm 1 as Stackelberg leader. The private firm 1 decides their quantity in sage 1, the public firm and the private firm 2 decides their quantity in stage2.
4) The private firm 2 as Stackelberg leader. The private firm 2 decides their quantity in sage 1, the public firm and the private firm 1 decides their quantity in stage2.
This literature of endogenous timing in mixed oligopoly, this result from we see Naya (2009), can state that the most existing literature on mixed oligopoly, they
consider that their firms make their decisions simultaneously, such a situation is not the equilibrium. In literature of Naya (2009), for example of simultaneous and sequential equilibrium, Pal (1998), there are two subgame perfect Nash equilibrium, which the private firm decides their quantity simultaneously in stage 1, and the public firm decides their quantity in other stage.
3.1.2 Post-merger
In this chapter, there are three situations in Endogenous Timing of Stackelberg after the merge. In this case, three different alternative scenarios are considered: merger involving public firm and the private firm 1, merger involving public firm and the private firm 2, and merger involving no public firm.
２６
In this context, seven alternatives scenarios should be stated to determine
endogenous timing:1) This simultaneous movement, there have two post-merger firms decide their quantity in the same stage.
2) Merged between public firm and the private firm 1 as Stackelberg leader. In this case, the private firm’s reaction functions (firm 1) are derived in stage 2, and taking into account the said reaction functions, the merged firm optimizes in stage 1.
3) Merged between public firm and the private firm 1 as Stackelberg follower.
4) Merged between public firm and the private firm 2 as Stackelberg leader. In this case, a private firm’s reaction functions (firm 2) are derived in stage 2, and taking into account the said reaction functions, the merged firm optimizes in stage 1.
5) Merged between public firm and a private firm 2 as Stackelberg follower.
6) Merged between both private firms as Stackelberg leader. Both private firms decide their quantity in stage 1, and the public firm makes its decision in stage 2.
7) Merged between both private firms as Stackelberg follower.
Table 1: Endogenous Timing of merged firm and another firm
Leader (L) Follower (F)
Leader (L) Cournot
Case 2 Stackelberg
Follower (F)
Case 1 Stackelberg
Cournot
q
Mqi
２７
Table 1 summarizes three cases situation with simultaneous play (LL and FF), sequential play with merged firm as leadership (LF) and sequential play with other firm as leadership (FL).
In the chapter, there are two variables that play a very important role in determining the endogenous timing of the game in the stated model: the degree of foreign penetration and the degree of privatization of the mixed firm. There are six subgame perfect Nash equilibrium of the game under endogenous timing of post-merger are: the merged firm as a Stackelberg leader, and another firm as Stackelberg follower.
From the analysis of the subgame perfect Nash equilibrium in the seven scenarios, the follow result is obtained:
3.2 Merger Involving Public Firm and a Private Firm 1 of the Perfect Nash Equilibrium
In this case, we assume that the public firm and the private firm 1 without foreign penetration decide to merger in the existing market structure, that it is a duopoly composed of a mixed firm after the merger. We have two alternative scenarios: the merged firm as a Stackelberg leader and another firm as Stackelberg leader, denoted by the superscripts NF, in equilibrium, the output level of the firms, the consumer, the profits of the firms and the social welfare are, respectively:
3.2.1 The merged firm as a Stackelberg leader
θ θ α
θ α θ
9 ) 1 ( 4 31
)]
1 ( 4 ) 5 ( 3 [
1 ,
0
− − +
−
−
=
a−
qLNF
θ θ α
θ θ α
9 ) 1 ( 4 31
] 3 ) 1 )(
( 4 [
2
− − +
+
−
−
=
a+
aqFNF >0
２８
3.2.2 The merged firm as a Stackelberg follower
)