J Econ
DOI10.1007/s00712-011-0254-4
Prence of foreign investors in privatizedfirms
and privatization policy
Ming Hsin Lin·Toshihiro Matsumura
Received:28August2010/Accepted:2November2011
©Springer-Verlag2011
Abstract This paper investigates how the prence of foreign investors in privatized firms affects privatization policy in a mixed oligopoly.Wefind that an increa in the stockholding ratio of foreign investors in a privatizedfirm increas the optimal degree of privatization,whereas an increa in the penetration of foreignfirms in product mar-kets reduces it.The results imply that the degree of openness offinancial markets and that of product markets have contrasting implications for the optimal privatization policy.
Keywords Partial privatization·Foreign investment in privatizedfirms·Foreign private competitors
JEL Classification H42·F13·L13
1Introduction
Privatization,defined as the deliberate sale of a state-owned enterpri to the private ctor,exists in more than100countries.One interesting aspect of privatization is that the sale of a state-owned enterpri is not limited to domestic private investors. Currently,foreign investors are influential buyers of formerly public enterpris.
For example,according to Reuters,the Egyptian government sold80%of its shares in the Bank of Alexandria to the Italian group Sanpaolo IMI in2006and51%of its M.H.Lin(B)
Faculty of Economics,Osaka University of Economics,2-2-8,Osumi,Higashiyodogawa-ku,
Osaka533-8533,Japan
e-mail:linmh@osaka-ue.ac.jp
T.Matsumura
Institute of Social Science,University of Tokyo,Tokyo,Japan
M.H.Lin,T.Matsumura shares in the AlWatany Bank to the National Bank of Kuwait in2007.Egypt also announced a plan to ll up to67%of its shares in the Bank of Cairo,and it will permit foreign banks to bid.According to Nikkei news,the Turkish government sold 55%of its shares in Türk Telekom to Saudi Telecom for$6.5billion,and also sold its public tobacco enterpri in an auction open to both foreign and domestic investors. According to data provided by the Tokyo Stock Exchange,at the end of December 2010,the holdings of foreign investors in NTT(20.2%)and JT(26.2%),both partially held by Japane public ctors,were substantial.Apart from the examples,we can identify foreign investments in formerly publicfirms worldwide.In addition,foreign investors will play important roles as buyers of temporarily nationalizedfirms becau of thefinancial crisis that occurred in2008.
In spite of the importance of foreign investors to privatizedfirms,the relationship between the prence of foreign investors in privatizedfirms and privatization pol-icy is rarely discusd.Numerous studies on mixed oligopoly have already studied competition between domestic publicfirms and foreign privatefirms.1Some adopted a partial privatization approach and discusd how competition with foreign private firms affects the optimal degree of privatization.2However,none of them considered foreign investments in partially privatizedfirms.
This paper considers that buyers of(partially)privatizedfirms can be foreign inves-tors and investigates how the prence of foreign investors in privatizedfirms affects the optimal privatization policy.We adopt a partial privatization approach and inves-tigate the optimal degree of privatization.3Wefind that an increa in the prence of foreign investors in privatizedfirms increas the optimal degree of privatization. This indicates that open policies in capital markets and privatization policies can be complementary,marking a sharp contrast to Han and Ogawa(2007),who suggested that open policies in product markets and privatization policies are substitutes.
The remainder of this paper is organized as follows.Section2prents the model. Section3shows the results.Section4concludes the paper.
2The model
Firms produce perfectly substitutable commodities for which the market demand func-tion is given by p=a−Q(price as a function of quantity).Firm i’s cost function is given
1See Corneo and Jeanne(1994),Fjell and Pal(1996),Pal and White(1998),Fjell and Heywood(2002), Matsumura(2003b),Bárcena-Ruiz and Garzón(2005a,b),Dadpay and Heywood(2006),Matsushima and Matsumura(2006),Heywood and Ye(2009b),Inoue et al.(2009),Long and Stähler(2009),Mukherje
e and Suetrong(2009),Matsumura et al.(2009),and Wang et al.(2009).
2See works cited in footnote3in the context of international trade.
3Partial ownership in privatizedfirms is found worldwide and has become increasingly common.Partial privatization has been extensively discusd in the literature.For a general discussion,e Matsumura (1998).Further,e Chang(2005),Chao and Yu(2006),Fujiwara(2006),and Han and Ogawa(2008)in the context of international trade;Heywood and Ye(2009c)for R&D competition;Kato(2006)and Ohori (2006)for environmental problems;Tomaru(2006)for tax and subsidy policies;Heywood and Ye(2009a) for agency problem;Matsumura and Kanda(2005),Fujiwara(2007),and Wang and Chen(2010)for free entry markets;Lu and Poddar(2007)for product differentiation;and Bárcena-Ruiz and Garzón(2003)and Méndez-Naya(2008)for merger problems.
Prence of foreign investors in privatized firms and privatization policy
by c i (q i )=(1/2)(q i )2,where q i is the output quantity of firm i (i =0,1,...,m ).4Firm 0is a mi-public (partially privatized)firm that competes against γ·m for-eign private firms and (1−γ)·m domestic private firms (m private firms in total)in the domestic product market.γreprents the degree of foreig
n penetration in the domestic product market.In the following paragraph,we will introduce βto denote the prence of foreign investors in the partially privatized firm.We assume that both βand γare exogenous variables and are given before the game.We now formulate a complete information game.Initially,the government holds all the shares in firm 0.5In the first stage,the government lls α∈[0,1]shares in firm 0and foreign investors (respectively domestic investors)buy α−β(respectively α·(1·β))shares in firm 0.We assume that investors are atomistic (i.e.,they have no market power),are rational,and know what happens in the subquent stage (perfect foresight assumption).6The government obtains M (α,β,γ)=α·πe 0in proceeds from the sale of share αof firm 0,where πe 0is the expected profit of firm 0,realized in the subquent stage.7M depends on βand γas well as αbecau βand γaffect the equilibrium value of π0,which is discusd in the next ction.In this stage,the government choos αso as to maximize the domestic social surplus,given βand γ.In the cond stage,after obrving α,βand γ,each firm i choos q i (i =0,1,...,m )independently (Cournot competition).Let m i =0q i be equal to Q.The profit of firm i is given by πi =p (Q )q i −c i (q i )=(a −Q )q i −(1/2)(q i )2.Firm i (i =1,2,...,m )maximizes πi .Firm 0maximizes U 0=α·π0+(1−α)W ,where W is the total domestic social surplus.8Let CS be the domestic consumer surplus,given by CS =(1/2)Q 2.W is given by the following:
W =CS +(1−αβ)π0+(1−γ)m
i =1πi +β·M (α,β,γ)(1)
4This formulation of demand and cost is popular in the mixed oligopoly literature.See De Fraja and Delbono (1989),Fjell and Pal (1996),and Pal and White (1998).Similar results can also be derived in our model by using product-differentiated demand functions like Fujiwara (2007)and Matsumura and Shimizu (2010).Our results are robust to the ca of constant marginal costs wherein the mi-public firm’s cost is higher (but not extremely higher)than that of the private firm.The prentations are not included and are available upon request.
5In this paper,we do not allow the government to nationalize more than one firm.As pointed out by Merrill and Schneider (1966),the most efficient outcome is achieved by the nationalization of all firms in the ca where nationalization does not change firms’costs (i.e.,there is no X-inefficiency in the public firm).The analysis of a mixed oligopoly is required becau it is impossible or undesirable,for political or economic reasons,to nationalize an entire ctor.For example,without competitors,public firms may lo the incentive to reduce their costs,resulting in a loss of social welfare.Thus,we neglect the possibility of nationalizing all firms.Our results hold for the ca of more than one public firm as long as private firms also exist.For a discussion on more than one public firm,e Matsumura and Shimizu (2010).6Our results depend on the assumptions.If the investors are non-atomistic,we
must treat them as active players having market power,and model formulation must be completely changed.If the investors are naïve and consider that the profit of the privatized firm does not depend on αand is given exogenously,the optimal degree of privatization is decreasing in β,the opposite result of Proposition 3(i).
7If we consider multi-stage competition over multiple periods,it must be the discounted sum of profits of firm 0.All of our results hold if we consider multi-stage competition.
8This is a standard formulation of the payoff for a mi-public firm.See the works mentioned in footnote 3.
M.H.Lin,T.Matsumura The government obtains M,while onlyβ·M appears in(1).The remainder(1−β)M is a transfer from domestic investors to the government.Note that the cond term in W includesα(1−β)π0(obtained by domestic stockholders infirm0)as well as (1−α)π0(obtained by the government).
3Equilibrium analysis and results
We u sub-game perfection as the equilibrium concept and solve the game by back-ward induction.
3.1Second stage
In this stage,thefirst-order conditions offirm0andfirm i(i=1,2,...,m)are respectively,
1−αβ+α2β
a−
2+α−3αβ+3α2β
q0−
(1−αβ+α2β)
−γ(1−α)
m
i=1
q i=0,(2)
a−q0−
m
i=1
q i−2q i=0.(3)
The cond-order conditions are satisfied.It should be noted here that investors have already paid M and obtained the stocks of the partially privatizedfirm in thefirst stage; therefore,M must be given exogenously in the cond stage.It is not assumed that M is given exogenously in this stage,but rather,is a basic property derived from the time structure of our model.9
From(3),wefind that all privatefirms choo the same output level in the equilib-rium.Substituting q2=q3=···=q m=q1into(2)–(3)and solving the equations yields the equilibrium outputs offirm0,firm1,and the total market output as follows:
q S0=
2
1−αβ+α2β
+m(1−α)γ
a −1,(4)
q S1=
1+α−2αβ+2α2β
a −1,(5)
Q S=
2
1−αβ+α2β
+m
1+2α2β+γ+α(1−2β−γ)
a −1,(6)
where ≡2(2+α−3αβ+3α2β)+m[1+α−2αβ+2α2β+(1−α)γ].Let the superscript S stands for all corresponding equilibrium values in the cond stage.
9If the government can commit to the output of the partially privatizedfirm before lling its stock, M must be endogenously decided when the output is chon.However,we believe that our time structure is at least as plausible as the alternative where the output offirm0is determined before privatization.
Prence of foreign investors in privatized firms and privatization policy
Proposition 1shows how the equilibrium values change with respect to α,βand γ.
Proposition 1(i):
q S 0d α<0,dq S 1d α>0,d Q S d α<0;(ii):q S 0d β>0,dq S 1d β<0,d Q S d β>0;(iii):q S 0d γ>0,dq S 1d γ<0,d Q S d γ>0.
Proof See Appendix.
Proposition 1(i)is a well-known result in the literature on partial privatization in mixed oligopoly.This property holds regardless of the nationality of private firms (e Matsumura 1998;Matsumura and Kanda 2005;Han and Ogawa 2008;among others).A larger degree of privatization leads the public firm to reduce its output becau it becomes more profit-oriented.This action increas the outputs of private firms through strategic interaction.The total market output decreas under the standard stability condition,which is satisfied in our model.
Proposition 1(iii)has also been investigated by Fjell and Pal (1996),Pal and White (1998),Han and Ogawa (2007),and Matsumura and Tomaru (2011).A greater pen-etration of foreign firms makes the public firm produce more becau its aggressive behavior can reduce the foreign firms’surplus (which will be transferred away from the public firm’s country)and improve the term of trade.This behavior reduces the output of private firms;conquently,the total market output increas for the same reason as in Proposition 1(i).
Proposition 1(ii)is a new result,and it is intuitively nsible.In the public firm’s payoff,a larger βreduces the weight of its own profit,10and this leads the public firm to produce more.This aggressive behavior of the public firm reduces the outputs of private firms,and the total market output increas for the same reasons described above.
3.2First stage
Substituting M =α·πe 0=α·πS 0
into (1),we have W (α,β,γ)=CS S (α,β,γ)+πS 0(α,β,γ)+m (1−γ)πS 1(α,β,γ).(7)
The government maximizes W with respect to α.The first-order condition for the government is
(1+m γ) −1+(1−α)2β m −m γ−m 2γ −G α−2H α2 =0,(8)
where G ≡4(1−β)+m (1+5γ−6βγ)+m 2γand H ≡2β+3m βγ.The cond-order condition is satisfied for α∈[0,1].
10This relation is clear by noting that the public firm’s payoff can be rearranged as U 0=
(1−αβ+α2β)π0+(1−α)CS +(1−α)(1−γ) m i =1πi +(1−α)βM.
