ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E08-1

Partial Privatization, Technology Spillovers,and Foreign Ownership Restriction
byLihua Han
Hikaru Ogawa

July 2008

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Partial Privatization, Technology
Spillovers, and Foreign Ownership
Restriction
Lihua Han
School of Economics, Nagoya University,
Furocho Chikusaku, Nagoya 464-8601, Japan

Hikaru Ogawa
School of Economics, Nagoya University,
Furocho Chikusaku, Nagoya 464-8601, Japan
Tel.:+81-52-789-2379, Fax:+81-52-789-4924,
email: ogawa@soec.nagoya-u.ac.jp

Abstract
This paper examines the interaction between two market-opening
policies; the relaxation of foreign ownership restriction and the privatization of a domestic public firm. Of particular interest are on thetechnology spillovers, which could be one of the prominent motivations
for introducing foreign investment into the domestic market. Our first
result shows that the best response strategy on privatization policy is
not monotonous with the changes in the regulation policy on foreign
ownership, and vice versa. The second result shows that there exist
optimal levels of partial privatization and foreign ownership restriction,
which are strongly aﬀected by the magnitude of technology spillovers.

Key words: regulation on foreign investment, technology spillovers, partial
privatization, mixed oligopoly
JEL Classification: L1, L3, L5, P2

1Introduction

In many countries, governments carry out market-opening policies. Amongothers, the privatization of public-owned firm and the relaxation of regulations on market entry of both domestic and foreign firms are typical agenda.
The main purpose of this paper is to obtain a better grasp of the interaction
between these policies in the framework of an international mixed oligopoly
model.
A notable example is the economic reform in China. Although the paceof market-opening has been quite slow in the initial stages, the Chinese
government has been implementing two main policies as market-opening
strategies since 1978; the privatization and relaxation of foreign investment
regulations. Many foreign firms enter the Chinese market by purchasing
stocks of Chinese domestic firms, so that joint-stock firms owned by domestic and foreign investors become common. Entry into the World Trade
Organization (WTO) in 2001 has sparked further opening of market to foreign investors, and the joint-stock companies are now a crucially importantcomponent of Chinese economy. Recently, however, gradual and partial
privatization and restrictive introduction of foreign investment are moving
into some industries such as banking, insurance, medicine and airlines. The
Chinese government is thus becoming more restrictive towards foreign investment in these fields, and the magnitude of privatization and the level offoreign ownership restriction have become focal issues in policy debates1 .
The present paper attempts to analyze the optimal policy choices ofgovernment on privatization and foreign investment regulations by considering two types of mixed ownership. The first is firms owned in both the
public sector and the domestic private sector. This type of firm is often
called a semi- or partially-privatized public firm. The second is firms owned
1See, for instance, OECD Observer, no.260 (pp.19-20), 2007.

1

by domestic and foreign private investors, which is called an international
corporate joint venture. Mixed ownership of public firm has been a feature of government policy in many developed and developing countries, andintensive studies have been conducted to examine the eﬀects of partial privatization on the economic environment. Matsumura (1998) develops a formal
model for investigating the eﬀect of partial privatization on social welfare ina domestic mixed oligopoly framework and shows that neither full nationalization nor full privatization, but partial privatization is optimal2 . The aimof this paper is to complement and generalize the work of Matsumura (1998)
by incorporating foreign investment and market-opening policy choices in
the international mixed oligopoly framework3 . While Matsumura (1998)
has ignored international aspects of market openings in his domestic mixed
duopoly model, the present paper is now able to highlight the interactionof two market-opening policies; the privatization and relaxation of foreign
ownership restriction.
One of the significant features that makes our model diﬀerent from previous mixed oligopoly studies is that we consider technology spillovers. Muchof the literature has ignored the technology spillovers in the models of international mixed oligopolies. This is somewhat surprising since the governments have a strong interest in attracting foreign firms to benefit technologically ineﬃcient domestic firms. More specifically, one prominent incentive
for the invitation of foreign investment is the presumption that it stimulates
aggregate productivity growth either directly through its own higher productivity growth or though indirect technological spillovers. Recent empirical2

See Fershtman (1990), Maw (2002), Lee and Hwang (2003), Bennett and Maw (2003),
Gupta (2005), Sun, Zhang and Li (2005), Jiang (2006), Chao and Yu (2006), Beladi and
Chao (2006), and Kumar and Saha (2007) for the literature on partial privatization in themixed oligopoly models.
3
A mixed oligopoly analysis in an international context is conducted by Fjell and Pal(1996), Pal and While (1998), Fjell and Heywood (2002), Matsumura (2003), BarcenaRuiz and Garzon (2005), Dadpay and Heywood (2006), among others.

2studies that address the existence of technology spillovers have documented
robust evidence of technology spillovers from foreign direct investment4 . In
this paper, we incorporate productivity spillovers from foreign investment in
the domestic market and examine how the optimal degrees of privatizationand the optimal level of foreign ownership restriction are aﬀected by themagnitude of technology spillovers.
In a simple international mixed oligopoly model with technology spillovers,
we first demonstrate that the best response strategy on privatization is not
monotonous with the changes in the relaxation of foreign investment regulation, and vice versa. For instance, the result would imply that when apublic firm is less privatized, the promoting the privatization program andrelaxation of foreign investment regulations simultaneously improves social
welfare. However, the promotion of privatization and the relaxation of foreign ownership restrictions reduce welfare when privatization is suﬃcient.
Tightening regulations on foreign investment is required as an alternative tofurther privatization in such a case. Second, we derive the optimal level ofpartial privatization and foreign investment ratio, which are strongly aﬀectedby the magnitude of technology spillovers. Encouraging foreign investment
is desirable if technology spillover is significant.
The remainder of the paper is organized as follows. We present the basicmodel in Section 2, and the main results are derived in Section 3. Section 4
concludes the paper.

2

Model

Consider an international mixed oligopoly involving a semi-public firm anda joint-stock private firm, which is owned by domestic and foreign private
4

See Girma and Wakelin (2002, 2007), Griﬃth and Redding, and Simpson (2002),
Sjoholm (1998). See also Blomstrom and Kokko (1998) and Gorg and Greenway (2004)
for extensive reviews of empirical research.

3

firms. Let firm 0 be the semi-public firm and firm 1 be the joint-stock
private firm. Assume that both firms supply homogeneous commodities tothe market, in which the inverse demand function could be expressed as
p = a − Q. We denote a(> 0) as the demand parameter and Q = q0 + q1 ,where Q and qi represent the total output and the output of firm i.
We suppose that foreign firms that invest money in firm 1 have more
eﬃcient technology relative to a domestic firm. For tractability, the cost ofa pure foreign firm is normalized to zero. The cost function of firm i that
operates in the domestic market is defined by ci = Fi + 0.5ki qi2 , where ki
represents the eﬃciency of variable cost and Fi denotes the fixed cost of firmi.
To express the essence of technology improvement brought by the foreign
capital importation, we suppose that when the foreign investment makes anadvance into the market, it brings technology spillovers to the semi-public
firm5 . We also assume that the fixed cost of firm 1, which is partially ownedby the foreign investors, will be reduced when the share of foreign capital infirm 1, 1 − α ∈ [0, 1], increases, i.e., F1 = F1 (α) [dF1 (α)/dα > 0]. α ∈ [0, 1]
represents the share of domestic capital in firm 1. We specify the fixed
cost of firm 1 as F1 (α) = αf . This formulation could be rationalized if we
consider the usage of patented technology. Consider that the foreign firm has
already conducted R&D investment and has patented technology to produce
the product for the market. If firm 1 accepts an investment from a foreign
investor, and is partially owned by the foreign firm, it is allowed to use thepatented technology so that the firm 1’s R&D investment is saved, thougha certain share of profits must be relinquished to foreign investors. In thespecial case that firm 1 is fully owned by the foreign firm, α = 0, it does not
5
There are reasons why foreign investment is an important channel of intra- and interfirm technology transfer. First, the less-eﬃcient domestic firm observes and imitates more
eﬃcient multinational firms. Second, the training of employees by multinational firms andsubsequent turnover of labor is a major source of inter-firm spillovers.

4

have to spend money on R&D and is able to use patented technology fully.
In contrast, if it is a pure domestic firm, α = 1, the fixed cost of firm 1 is f ,which is identical to the domestic public firm, F0 = f .
The technology spillovers are considered in the term ki . Representing
the magnitude of technology spillovers by β, we assume k1 = k1 (α) and k0 =k0 (α, β), where dk1 (α)/dα > 0, ∂k0 (α, β)/∂α > 0, and ∂k0 (α, β)/∂β < 0.
In the following analysis, we specify the eﬃciency of variable costs as k0 =1 − β(1 − α) and k1 = α, where β ∈ [0, 1] represents the technology spillovers
emerging from foreign capital inflow. The latter expression indicates thatas the share of foreign investments increase in firm 1, the lower firm 1’svariable cost. The former formulation shows that if there exists an intrafirm technology spillover, β > 0, the share of foreign investment in firm 1
aﬀects the variable cost of firm 0. The larger value of β means a larger
magnitude of technology spillovers. Specifically, β = 0 implies no spillovers
while β = 1 implies full spillovers. If no spillovers exist, the variable cost
structure of two firms is identical when the foreign investment is not allowed,
α = 1.
Given the formulation of the cost function, the profit function of firm 0,
π0 , can be expressed as

π0 = (a − q0 − q1 )q0 − 0.5k0 q02 − F0 ,= (a − q0 − q1 )q0 − 0.5[1 − β(1 − α)]q02 − f.

(1)

Similaly, the profit of firm 1 is given by
π1 = (a − q0 − q1 )q1 − 0.5k1 q12 − F1 ,= (a − q0 − q1 )q0 − 0.5αq12 − αf.
The social surplus in the country can be defined as
5(2)W = π0 + απ1 + CS,(3)

where CS ≡ 0.5Q2 is the consumer surplus. In (3), α (0 ≤ α ≤ 1) represents
the extent of domestic ownership of a private firm 1. In this paper, therestrictions on foreign investment are represented by α. When α = 1, foreign
investments are not allowed so that private firms are owned by domestic
residents/consumers. α = 0 corresponds to the case in which firm i isa foreign enterprise which is completely owned by foreign investors. If α
is positive (but not equal to one), private firms are considered as a joint
ownership enterprise. In this case, it is natural to consider that 100α percent
of firm 1’s profit should be attributed to domestic residents6 .
The government owns a share of (1 − θ) ∈ [0, 1] of the public firm.
Conversely speaking, θ measures the degree of privatization. The managerof this firm will maximize the weighted average of social welfare and the
profit. Following Matsumura (1998), we define the objective function offirm 0 as

V = θπ0 + (1 − θ)W .

(4)

Note that the manager of a fully privatized firm (θ = 1) seeks the firm’s
profit, while the manager of a fully nationalized firm (θ = 0) maximizessocial welfare.

3

Equilibrium

The game is constructed by two-stage decision-making. The government
chooses θ and α, to maximize (3) in the first-stage. Observing θ and α, thefirms choose the quantity supplied in the second stage. The private firm 1
maximizes (2) and the manager of firm 0 maximizes (4).
6This formulation follows Ogawa and Sanjo (2007).

6

3.1

Second StageFor given θ and α, the standard Cournot-Nash equilibrium in the second
stage can be derived as

q0 = a(2 − θ + αθ)/Λ,(5)

q1 = a[1 + θ + β(α − 1)]/Λ,(6)

p = a(1 + α)[1 + θ + β(α − 1)]/Λ,(7)

where Λ ≡ 2αθ + α + θ + 4 + β(α + 2)(α − 1) > 0. Using (5)-(7), the profits
of two firms and the consumer surplus can be derived as

π0 =
πi =
CS =

a2 (2 − θ + αθ)[αθ + 2α + 3θ + β(α − 1)(2α + θ − αθ)]− f, (8)2Λ2a2 (α + 2)[(α − 1)β + 1 + θ]2
− αf
(9)
2Λ2
a2 [3 + αθ + β(α − 1)]2
.
(10)
2Λ2

Substitution of (8)-(10) into (3) yields

W =

a2 Ω
− f (1 + α2 ),
2Λ2

(11)

where Ω = (2 − θ + αθ)[αθ + 2α + 3θ + β(α − 1)(2α + θ − αθ)] + α(α + 2)[(α −1)β + 1 + θ]2 + [3 + αθ + β(α − 1)]2 .

3.2

First Stage

The maximization of (11) with respect to θ yields the optimal strategy on
the level of privatization as θ = θ(α; β). Similarly, the maximization of(11) with respect to α gives us the optimal strategy on the level of foreign
investment regulation as α = α(θ; β, f ). We notice here that while the levelof foreign investment regulation depends on the endogenous variable of θ
7with given parameters of β and f , the optimal strategy of privatization
depends on the endogenous variable of α and given parameters of β, and it
does not depend on f .
Owing to the complexity, however, the further analytical comparisons of
the optimal policy choices are not feasible even in our simple model settings.
In the following analysis, therefore, we employ simulation analyses to obtaincomparative reaction of the optimal levels of privatization and the restriction
on foreign investment.
By setting a = 1, β = 0.2 and f = 0.02, Figure 1 depicts the optimal
strategy on α as α(θ). The strategy on θ is drawn as θ(α) in this figure. The
shapes of the reaction curves do not change drastically even if we take othervalues of β and f , as long as β > 0 and f > 0. From this simulation result, weobserve that the optimal reaction of θ to a change in α is not monotonous. In
addition, the reaction of θ to a change in α is not monotonous, either. Thatis, the optimal reaction to an increase in θ from the low level is to reduce α,
and to increase α when θ increases from the high level. The optimal reactionof θ to a change in α is the same as with that of α, but it is less subject
to a change in α since it is in the shape of a rod around θ = 0.2. This
indicates that the level of foreign investment regulation is strongly aﬀectedby the magnitude of domestic privatization, while the domestic privatization
is aﬀected less by the magnitude of foreign investment regulation.
We summarize the property of reaction curves as follows:

Proposition 1. The reaction curves, α(θ) and θ(α), are not monotonous.
The optimal strategy of α has a large variation with θ, while that of θ hasjust a slight variation with α. θ(α) is nearly vertical on θ = 0.2.

Figure 1. HERE
8

In figure 1, the two curves intersect on the point C, and the optimal levelof privatization, θ, and foreign investment regulation, α, are 0.175 and 0.360
in this case.
We can provide an intuitive reason that explains the non-monotonousshape of θ(α) and α(θ). An increase in the share of foreign investment
reduces the cost of the semi-public firm 0 and the firm 1, but a greater
share of firm 1’s profits outflows from domestic market. These factors are in
conflict in increasing social welfare. An increase in the degree of privatization
boosts the profit of firm 1, but it reduces the consumer surplus. These two
factors also conflict to increase the social welfare. Where the degree ofprivatization is very low or when the share of foreign investment is large, anincrease in the degree of privatization and an increase in the share of foreign
investment produces an additional surplus that is greater than the surplus
loss. In contrast, when the degree of privatization is high or when the shareof foreign investment is small, an increase in the degree of privatization andan increase in the share of foreign investment cause the surplus loss that isgreater than the increase in the social surplus.

3.3

Comparative Statics

This subsection presents a numerical comparative statics to show how the
optimal policy choices on α and θ are impacted on changes in parameters,
β and f . This exercise is quite useful for clarifying the forces required toachieve certain policy choices.

Eﬀects of changes in β. To examine the eﬀects of an increase in β,a stable equilibrium is illustrated in Figure 2 by assuming the following
set of parameters: a = 1 and f = 0.02. From computing the optimal
degree of privatization and the level of restriction on foreign investment,
we find that they both decrease with an increase in β. We notice that θ
9slightly changes in β, but α changes to a large degree, implying that thelevel of foreign investment regulation is quite sensitive to the magnitude oftechnology spillovers, β. We summarize the results as follows:

Proposition 2. α(θ), representing the optimal strategy of foreign investment regulation, shifts down to a large extent with an increase in β.
θ(α), representing the optimal strategy of privatization, shifts slightly to theleft with an increase in β. The optimal values of α and θ are monotonously
decreased with an increase in β.

An intuition that explains why the government reduces α(θ) when β
becomes large can be given as follows. An increase in β may lead to cost
reduction of a semi-public firm, but the impacts of the change in β dependon the value of α. When α = 1, an increase in β has no impact on the cost
structure of the semi-public firm. In contrast, when α is small, an increasein β reduces the cost to a large extent. Hence, the welfare-maximizing
government has more incentive to reduce α to receive a significant benefitof technology spillovers the larger that β is. The government also reducesθ as β increases because an increase in β improves the semi-public firm’s
cost eﬃciency. As the semi-public firm can produce more eﬃciently, thegovernment reduces θ to shift the production from the private firm to thesemi-public firm.
Figure 2. HERE
Eﬀects of changes in f . Figure 3 is drawn to examine the eﬀects ofchanges in f on the optimal policy choices. To examine the eﬀects of anincrease in f from 0.02 to 0.06, we take a = 1 and β = 0.2. α decreases
monotonously when f increases, irrespective of the magnitude of f . Interestingly, however, the change in f aﬀects the policy choice on θ in a diﬀerent
10way. Whereas an increase in f from 0.02 to 0.04 slightly decreases θ, θ increases from 0.170 to 0.172 as f increases from 0.04 to 0.06. Summarizing
the above, we have the following result.

Proposition 3. α(θ), representing the optimal strategy of foreign investment regulation, shifts down with an increase in f . θ(α), representing
the optimal strategy of privatization, does not shift with any change in f .
The optimal value of θ is not a monotonous function of f , while the optimalvalues of α is monotonously decreased with an increase in f .

We here give an intuitive explanation for this result. An increase in the
fixed cost, f , causes a cost increase in a domestic firm. In order to oﬀset thiscost increase by reducing the variable cost, the government relaxes restraints
on foreign investment to benefit the technology spillovers. Thus, the reaction
curve of α(θ) shifts down as f increases. The reaction curve of θ(α) is not
monotonous, so the impacts of a change in f on the optimal choices of θ andα are ambiguous.
Figure 3. HERE

Eﬀects of changes in a. No graphic illustration is provided for this parameter variation since no essential eﬀects emerge in our model.

The comparative statics results under the simulation method seem remarkably clear-cut, although the analytical solution does not appear practicable. In a wide-ranging simulation exercise, no dramatic changes of theproperties of optimal strategy emerge. Neither were there completely diﬀerent eﬀects of changes in spillovers on the optimal policy choices.

11

4Concluding Remarks

Using a simple international mixed oligopoly model with the technology
spillovers, this paper has examined the interaction of two market-opening
policies; the privatization and relaxation of foreign investment regulations.
This paper also analyzes the impacts of technology spillovers on the government’s policy choices. We first find that the best response strategy for
privatization policy is not monotonous with the changes in the relaxationof foreign investment regulations, and vice versa. This result implies that
we cannot simply evaluate the welfare impact of market-openings throughpromotion of privatization and the relaxation of foreign investment regulations. Second, we derive the optimal level of partial privatization andforeign investment regulations and show that they are strongly aﬀected by
the magnitude of technology spillovers. The result indicates that the active
market-openings are good choices if the magnitude of technology spillovers
is significant.
Finally, we point out some problems that remain unsolved. First, we have
only considered a case of mixed duopoly. The extension to include multiple
private firms allows us to examine the eﬀects of a change in the number offirms on the optimal choices for market-opening policies. Second, one could
easily imagine that the diﬀerent ways of technology spillover specification
should be investigated to check the robustness of the results. These issues
are potential topics that will be investigated in future research.

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12

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15

α
θ(α)
1.00
α(θ)

0.96

0.50
0.45
C
(θ, α) = (0.175, 0.360)

0.00
0.000

θ
0.500
0.175

0.200

Figure 1. Reaction curves (β = 0.2 and f = 0.02).

16

1.000

α

1.00

(θ, α) = (0.195, 0.800)
Aα(θ)|β=0.0(θ, α) = (0.185, 0.610)
α(θ)|β=0.1B0.50(θ, α) = (0.175, 0.360)

α(θ)|β=0.2

C

θ(α)|β=0.2
0.00
0.150

θ(α)|β=0.1

θ(α)|β=0.0
θ

0.175

0.185

Figure 2. Eﬀects of changes in β (f = 0.02).

17

0.200

α
θ(α)|∀f

1.00

0.50(θ, α) = (0.175, 0.360)
α(θ)|f =0.02

C(θ, α) = (0.170, 0.150)
α(θ)|f =0.04

B

α(θ)|f =0.06
A
0.00
0.150

(θ, α) = (0.172, 0.090)
θ

0.175

0.185

Figure 3. Eﬀects of changes in f (β = 0.02).

18

0.200