4.2 Merger Profitability and Partial Privatization
4.2.4 Incentives for Mergers
In an international mixed oligopoly market, there exist one domestic public firm with partial privatization, one domestic private firm and several private foreign firms. Public firm has more incentives to merge because of social welfare improving, namely, social welfare
after merging is better than both the social welfare of pre-merger and of direct privatization.
Lemma 4.2: Post-merger social welfare is the best; the social welfare of no privatization is worst.
Therefore, public firm have to please to merge and when domestic firm’s readiness to merge.
For domestic private owner who would like to merge with the public firm, only if, the fraction of that private owner owns profits of the mixed firm after merging, ( )
a b
M M
δ π +π , is higher enough than the profit obtained by domestic private firm before merging, πb. Therefore, for any m∈N there exist δΓ∈(0,1)which denotes the value of the degree of privatization such that ( )
a b
With the proceeding of privatization, domestic private owner choose to merge with public firm when δ δ> Γ.18
18 See the proof of proposition 2 in Méndez-Naya (2008).
Proposition 4.2: In an international differentiated mixed oligopoly, domestic private firm decide to merge with public firm when ( )
a b
The ambiguous comparison is subject to both the differentiated degree of commodity and numbers of foreign private firm.
Proposition 4.2 is illustrated in Fig 4.2.
-1
Fig 4.2. Private Firm’s Incentives to Merge Region I and III represent δ δ− Γ >0, that is, ( )
a
M M
b b
δ π +π >π . In other words, the nature of commodity and number of foreign firm could influence private owner’s incentives to merge. When products are substitutes, the private owner chooses to merge in region I.
Identically, when products are complementary, the private owner chooses to merge in region III. In general, more foreign private firms competing in the domestic market will promote private owner’s merging decision. The degree of substitution of commodity which is too higher or lower would not influence private owner’s decision. Higher degree of complement
γ II I m
III
δ δ− Γ=0
δ δ− Γ =0
of commodity promotes private owner’s merging decision.
Proposition 4.3: In general, more foreign private firms and higher degree of complement of commodity will promote private owner’s merging decision. The degree of substitution of commodity which is too higher or lower cannot be incentives for private owner to merge.
4.3 Concluding Remarks
This chapter considered that there exist one domestic public firm, one domestic private firm and several private foreign firms in an international mixed oligopoly market. To be more efficient, the public firm allowed for partial privatization and through a program with two distinct measures, privatizing directly, or deciding to merge with domestic private firm.
Under the utility assumption of differentiated commodity in Häckner (2000), we found whether public firm merger with domestic private firm or not, the optimal privatization policy is monotonic in the differentiated degree of character of commodities; the degree of privatization is monotonically increasing with the more the number of foreign private firm entry.
Moreover, there exist some incentives for domestic firm to choose to merge. For public firm, the incentives are explicit because of welfare improving. For private owner, generally, more foreign private firms and higher degree of complement of commodity will promote private owner’s merging decision. The degree of substitution of commodity which is too higher or lower cannot be incentives for private owner to merge.
CHAPTER FIVE: CONCLUSIONS
The government has more policy choices. We considered the issues of public policy-environmental taxation, equity control on foreign competitors, and merger for partial privatization-in an international mixed oligopoly. Based on the studies of environmental taxation in Lai (2004) and Ohori (2006), welfare model in Fjell and Pal (1996), partial privatization with differentiated commodity in Fujiwara (2007) and merger profitability in Méndez-Naya (2008), we extended the past results to be more completed by apt models.
For environmental taxation, using the simple linear demand model, part of our findings are consistent with what has been shown in Lai (2004) and Ohori (2006), even though they considered all firms producing homogeneous goods. In an international oligopoly market wherein the environmental damage is associated with consumption, the order of optimal environmental tax parallels the results of the duopoly model irrespective of the properties of the goods. In addition, we have shown that when the domestic market increases its openings, the tariff reduction does not always bring positive effects on the environment in mixed oligopoly; but, in pure oligopoly with homogeneous goods, the tariff reduction is bad for the environment.
For equity control, we considered in an international oligopoly market with a homogeneous good, one partially privatized domestic public firm competes with n domestic private firms and m foreign private firms. To protect domestic firms in this single market, the government determines the proportion of domestic equity on foreign competitors.
We have shown that stringent control of domestic equity on foreign firms increases private firms’ outputs, profits, market price and social welfare, but decreases public firm’s output.
Furthermore, along with the stringent control on the domestic equity of foreign firms, the government should increase the degree of privatization. In an opening market, intensive competition from private firms in general will enhance the degree of privatization.
Comparing our results with the result in Fjell and Pal (1996), we found that the effect of the number of foreign firms on public firm’s profit is ambiguous. Public firm’s profit increases if and only if the number of foreign private firms is small relative to the number of domestic private firms; social welfare increases if and only if the number of foreign private firms is large relative to the number of domestic private firms.
For merger for partial privatization, we considered that there exist one domestic public firm, one domestic private firm and several private foreign firms in an international mixed oligopoly market. To be more efficient, the public firm allowed for partial privatization and through a program with two distinct measures, privatizing directly, or deciding to merge with domestic private firm. Under the utility assumption of differentiated commodity in Häckner (2000), we found whether public firm merger with domestic private firm or not, the optimal privatization policy is monotonic in the differentiated degree of character of commodities; the degree of privatization is monotonically increasing with the more the number of foreign private firm entry.
Moreover, there exist some incentives for domestic firm to choose to merge. For public firm, the incentives are explicit because of welfare improving. For private owner, generally, more foreign private firms and higher degree of complement of commodity will promote private owner’s merging decision. The degree of substitution of commodity which is too higher or lower cannot be incentives for private owner to merge.
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APPENDIX A
A.1 Pure Oligopoly with Homogeneous Goods
Under the Cournot-Nash assumption, we obtain the following first-order conditions,
0 0 0
p c− − +t p q′ = , and (A.1.1)
f i 0
p c− − − +t τ p q′ = , 1, 2,...,i= n. (A.1.2)
Having obtained the results, we then differentiate social welfare equation with respect to t ,
The optimal environmental tax,
*
A.2 Mixed Oligopoly with Homogeneous Goods
Under the Cournot-Nash assumption, we obtain the following first-order conditions,
0
Then differentiating social welfare equation with respect to t , it yields
0
The optimal environmental tax,
( 0 )
1
M n c cf r
t = +θ n− −
+ . (A.2.4)
APPENDIX B
We follow Lai’s (2004) basic set-up but assume the linear inverse demand function is
0
= − −
∑
. Differentiating domestic and foreign firms’ total profits with respect to their own output, we obtain the following first-order conditions,0 0
Then, the outputs are given by
0 0
The optimal environmental tax is
If all firms produce homogeneous goods, letτ =1, the optimal output and environmental tax are
APPENDIX C
Consider in an international oligopoly market, one domestic public firm (firm 0), n private firms (firm i ; i=1, 2,...,n) and m foreign private firm (firm j ; j=1, 2,...,m) compete. The public firm does not proceed to privatize, e.g. θ =0. All private firms simultaneously maximize their own profits to choose their quantity, while the privatized public firm maximizes social welfare, equation (1), to choose its quantity. We then obtain
* Then the effects of equity control,
*
The effects of an open-door policy
If the public firm competes only with foreign private firms (n=0), then entry by a new foreign firm always increases welfare,
* 2