WPS3950
Infrastructure and Public Utilities Privatization
in Developing Countries
Emmanuelle Auriol*
University of Toulouse I
Pierre M. Picard
University of Manchester
Abstract
The paper analyzes governments' tradeoff between fiscal benefits and consumer surplus
in privatization reforms of noncompetitive industries in developing countries. Under
privatization, the control rights are transferred to private interests so that public subsidies
decline. This benefit for tax-payers comes at the cost of price increases for consumers.
In developing countries, tight budget constraints imply that privatization may be optimal
for low profitability segments. For highly profitable public utilities, the combination of
allocative inefficiency and critical budgetary conditions may favor public ownership.
Finally, once a market segment gives room for more than one firm, governments prefer
to regulate the industry. In the absence of a credible regulatory agency, regulation is
achieved through public ownership.
World Bank Policy Research Working Paper 3950, June 2006
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the
exchange of ideas about development issues. An objective of the series is to get the findings out quickly,
even if the presentations are less than fully polished. The papers carry the names of the authors and should
be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely
those of the authors. They do not necessarily represent the view of the World Bank, its Executive Directors,
or the countries they represent. Policy Research Working Papers are available online at
http://econ.worldbank.org.
*Emmanuelle Auriol: ARQADE and IDEI Universit� de Toulouse I, France. Email: eauriol@cict.fr.
Pierre Picard, University of Manchester and University of Louvain. Email:
Pierre.Picard@man.ac.uk.
1 Introduction
Over the last 25 years low-income countries have reduced their share of state ownership
by more than half.1 In most cases, governments have privatized public assets because of
critical budgetary conditions.2 While international donors and creditors, like the World
Bank or the IMF, made privatization programs a condition for economic assistance during
the 1980s debt crisis, governments have been keen on using privatization proceeds to relax
their budget constraints.3 Privatization yielded about $50 billion per year in non-OECD
countries, no less than one-third of the worldwide proceeds of privatization (Mahboobi,
2000; Gibbon, 1998, 2000). The fiscal benefits of privatization are not limited to the
divesture proceeds of state owned enterprises (S0E). They also encompass the possible
termination of recurrent, inefficient subsidies to the latter. In particular, when govern-
ments hardly discriminate between good and bad projects and/or management teams,
they are likely to transfer too many resources to public firms. Privatization eliminates
governments' legal obligations to subsidize unprofitable firms. In practice, privatization
reforms have resulted in substantial decreases of government subsidies to former SOEs.4
The present paper aims to study the impact of poor fiscal conditions on the privatization
decision in regard to infrastructure and public utilities in low-income countries.
Privatization brings well-known economic costs when industries are characterized by
strong economies of scale. By giving up the direct control of firms' operations, govern-
ments lose control over prices to the disadvantage of consumers. Private firms benefit
from large market power and have large incentives to enter. In practice price increases
1 According to a study by Megginson and Netter (2001) between 1980 and 1996 alone it went from
16% to 8% of GDP.
2 This has also been the case in rich countries. For instance, the first Japanese privatizations were
initiated in 1982 when the Japanese public deficit reached 41.2% of GDP. Similarly in the U.S. Lopez-
de-Silanes et al. (1997) show that privatizations have been more likely in states where fiscal constraints
were more binding.
3 Using a panel of 18 developing countries, Davis et al. (2000) show that budgetary privatization
proceeds have been used to reduce domestic financing on a roughly one-for-one basis.
4 For instance, the privatisation commission of Burkina Faso reports that government subsidies to
SOEs went from 1.42 percent of GDP in 1991 to 0.08 percent of GDP in 1999 as a result of privatisation
(AfDB-OECD 2003).
2
are often organized by the governments. Indeed, they have the choice between auctioning
off markets on the basis of either the highest fee payment or the lowest product/service
price (see Estache, Foster and Wodon 2002). Guasch (2003) shows in a survey of 600
concession contracts from around the world that in most cases contracts are tendered for
the highest transfer or annual fee. Because fee payments rise with the profitability of
the privatized firms, many governments choose policies that increase the firms' profitabil-
ity such as exclusivity periods and price liberalization.5 Prices are sometimes increased
ahead of privatization in order to reduce the SOE financing gaps and attract buyers. This
has been for instance the case in Zimbabwe, Kenya and Senegal, where governments in-
creased electricity prices by 10 % after reaching an agreement with Vivendi Universal (see
AfDB-OECD 2003). An unaccounted part of price increases stems from the termination
of illegal electricity connections (Birdsall and Nellis 2002, Estache, Foster and Wodon
2002, AfDB-OECD 2003).
The present paper studies the privatization decision as the result of the government's
cost-benefit analysis where the social benefit obtained from the termination of subsidies to
unprofitable public firms and the fiscal benefit from the cash-flows generated by the public
firms' divesture are balanced against the loss in consumer surplus induced by the higher
prices in privatized industries and to the social cost of the foregone taxable revenues that
are available in profitable public firms. To get clear cut results privatization is treated as
the move from public ownership with entry and price regulation to private ownership with
price liberalization.6 Privatization is close but not equivalent to laissez-faire because entry
remains regulated (i.e. through license and entry fees). If, as we show, privatization with
5Wallsten (2000) studies the impact of the exclusivity period on the privatization price of twenty
telecommunication firms in fifteen developing countries. In his sample, two thirds of the countries chose
to allocate exclusivity periods for an average of 7.42 years. They apparently had a very good reason for
doing so. According to the author's computations, granting a monopoly in fixed local services would
more than double the price private investors pay for the firm. This comes at the cost of high prices and
lower network growth relative to privatization without exclusivity periods.
6Under the complete contract approach adopted in the paper there exists no difference between public
and private ownerships under entry and price regulation. We thus model the difference between the two
ownership structures as the choice between regulated public firms and unregulated private ones. This
assumption is consistent with empirical evidence.
3
such price liberalization dominates state ownership with full price regulation, privatization
also dominates in more realistic situations where prices are liberalized to a lesser extent
and are kept under some governmental control.
The present paper shows that a main factor in privatization decisions is the opportunity
cost of public funds, which captures the tightness of government budget constraints.7 The
role of budget constraints in the privatization decision is not obvious because, under
perfect information, governments should be able, at worst, to mimic the outcomes of
private monopolies. However, under asymmetric information between governments and
firms, public finance matters and privatization may dominate public ownership because
subsidies are socially costly. To illustrate this result consider the specific case where
the government cannot finance an infrastructure project (e.g. a road). Privatization is an
appealing alternative as it is better to have a privately owned and operated infrastructure,
even with monopoly distortion (e.g. a toll), than no infrastructure at all. By continuity
the result still holds when the government is able to finance the infrastructure. We hence
show that when the profitability of the industry is low, as it is for instance in the case
of transport or the water industry, the privatization decision is a monotone function of
the opportunity cost of public funds.8 That is, for low opportunity costs (i.e. for wealthy
governments) public ownership dominates privatization, whereas the reverse holds for
large opportunity costs (i.e. for financially strapped governments).
Nevertheless, the above monotonic relationship between privatization and tightness of
budget constraints breaks down when natural monopolies are sufficiently profitable and
when governments are not able to recoup large enough franchise fees or divesture proceeds.
In that case, we show that privatization is optimal only for intermediate opportunity costs
of public funds. Such situations often stem from the difficulty met by developing coun-
tries to attract investors when they auction off profitable SOEs.9 Indeed, according to
7The opportunity cost of public funds is the Lagrange multiplier of the government budget constraint.
It captures the tightness of this constraint. It is different from the marginal cost of public funds which is
the dead weight loss created by a marginal increase of a specific tax (see Auriol and Warlters 2005).
8Trujillo et al. (2003) show that transport privatization leads to a reduced need for public investment.
9Country risk analysis is very important in today's global investment strategies because it is the basis
of determining future expected returns on investment. Since the perception of business risk tends to be
4
Trujillo, Quinet and Estache (2002), there exist rarely more than two bidders who partic-
ipate in developing countries' auctions for major concession contracts. Therefore, SOEs
are often sold at a discount (see Birdsall and Nellis 2002).10 Hence, with underpriced
public assets, privatization decisions are non-monotone functions of the opportunity cost
of public funds. The intuition goes as it follows: as before, when opportunity costs of
public funds are small, the bailouts of firms by governments are cheap and it is opti-
mal to keep regulated publicly owned firms, to set prices close to marginal costs and to
subsidize the firms to guarantee a break-even situation. For higher intermediate oppor-
tunity costs of public funds, bailout becomes costly and governments prefer to privatize
the public firms, cash the divesture proceeds and let private entrepreneurs manage firms.
Yet, for high enough opportunity costs of public funds, the privatization decisions differ
as governments may find it valuable to `hold-up' on profitable industries. Governments
then prefer not to privatize profitable public firms; they operate the firms by themselves
and they possibly set prices close to private monopoly prices to reap the maximal rev-
enues. This non-monotonicity result has potentially important policy implications. That
is, while divestiture of profitable public firms may be optimal in developed countries, it is
not necessarily so in developing countries where budget constraints are tight and market
institutions are weak.
Finally, when firms' profitability substantially rises, the market leaves room for more
than one firm. Market liberalization then corresponds to the divestiture of a historical
monopoly and the introduction of new entrants. In the framework of the model the di-
vestiture of the historical monopoly is motivated by smaller fixed costs and/or by larger
product demand. The mobile and internet segment of the telecommunication industry
provides a good illustration of such technical and demand changes. The paper then shows
that privatization with price liberalization is no longer optimal. Indeed, when a second
higher in poor countries (see for instance the International Country Risk Guide), this affects negatively
the supply and cost of international capital flows for these countries.
10For political reasons some public utilities have been sold at a mark up. This is typically achieved
by an over-optimistic forecast of future demand (see Trujillo, Quinet and Estache (2002). However these
sales have led to rapid renegotiation of the contract terms. It turns out to be a bad deal for the taxpayers
because subsidies have been re-introduced.
5
firm is introduced, the information costs in regulated firms diminish more than the so-
cial costs induced by excessive prices and entry prevailing in private Cournot oligopolies.
The advantage of private unregulated structures disappears for large, profitable markets.
For instance the experience in industrialized countries shows that regulation of access
pricing to bottleneck facilities (e.g. fixed-line network) is a key component of successful
market liberalization. As illustrated by the empirical evidence, price and entry regula-
tion is a problem in developing countries which usually lack the human resources and the
institutions to enforce effective regulation. Since privatization reforms cannot be success-
ful without effective regulation of entry and prices, developing countries are better off at
keeping their profitable utilities public as long as they cannot establish credible regulatory
bodies.11
1.1 Relationship with the literature
It is well-known that public ownership generates inefficiencies because it encourages gov-
ernments to bail out or subsidize money-losing firms. Such inefficiencies were first coined
by Kornai (1980) as the `soft budget constraint' problem:12 "The softening of the budget
constraint appears when the strict relationship between expenditure and earnings of an
economic unit (firm, household, etc) has been relaxed, because expenditure will be paid by
some other institution, typically the paternalistic state." (Kornai 1980). The author shows
that soft-budget constraints explain many inefficiencies occurring in socialist economies
such as shortages or low price responsiveness. Since less efficient firms are allowed to
rely on government funding, they lack the financial discipline required for efficient man-
agement. For instance, under contract incompleteness, soft-budget constraints affect the
level of investments made by public managers. The transfer of public to private owner-
ship is therefore often advocated as a remedy for the poor economic performance of public
11A major concern with privatization reforms in developing countries is the lack of governments' ability
to commit to the concession contracts. For instance, according to a World Bank database on Latin
America, the concessions that were granted to private operators following the divestiture of public firms
have been renegotiated after an average 2.1 years only (see Laffont 2001).
12Interesting surveys are available in Kornai (2000) and Kornai, Maskin and Roland (2002).
6
enterprises (see for instance Dewatripont and Maskin (1995), Schmidt (1996a, 1996b) and
Maskin (1999)). By hardening the firm's budget constraint, privatization helps restore
investment incentives.13 Another concern about public ownership is the governments' lack
of economic orientation. For instance in Kornai and Weibull (1983), Shleifer and Vishny
(1997), Debande and Friebel (2003), governments demonstrate `parternalistic' or political
behaviors as they seek to protect or increase employment; in Shapiro and Willig (1990),
governments are malevolent. The main conclusion of the above two strands of literature is
that privatization improves the internal efficiency of firms. Empirical evidence supports
this result. Megginston and Netter (2001) in a literature review covering 65 empirical
studies (some at national level and some across countries) at the firm level conclude that
private firms are more productive and more profitable than their public counterparts. The
result, which is robust theoretically and validated empirically, is consensual. However,
efficiency gains are not automatically passed along to consumers. This is particularly
true in increasing returns to scale industries where market power generates significant
allocative inefficiency. The deadweight loss created by monopoly pricing is the rationale
for setting up public ownership in the first place.14
The present paper discusses the privatization decision on infrastructure and public
utilities with a special focus on the allocative efficiency issue. For this reason, the paper
ignores the moral hazard issue that is discussed at length in the aforementioned papers
about soft budget constraints. In contrast the paper belongs to the traditional literature
on regulation with adverse selection (see Laffont and Tirole 1993). A utilitarian govern-
ment maximizes a weighted sum of consumer surplus and transfers from/to firms. To
overcome the information asymmetry on the firm's cost parameters the government must
offer a menu of incentive contracts. Since the government is residual claimant of the
public firms' profit and loss, and since it wants to avoid the threat of service interruption,
13On the other hand when governments are able to offer the same contracts to public and to private
firms, for instance in the form of bribes to private firms as in Kornai (2001), both structures have the
same degree of contract completeness and private or public ownership is irrelevant.
14Empirical studies reveal that privatization results in lower prices and higher output in competitive
industries. In increasing returns to scale industries changing the ownership structure does not solve the
problem of lack of competitive pressure (see Nellis (1999)).
7
contracts entice the least productive firm to break even. This implies that the more pro-
ductive firms earn informational rents and that government subsidizes firms losing money.
Production is distorted to reduce information costs which in turn diminishes consumer
surplus. Privatization reduces the need to subsidize firms losing money.
The paper is organized as follows. Section 2 presents the model and the main as-
sumptions. Section 3 compares the performance of private and regulated monopolies
while Section 4 studies the duopoly case. Section 5 derives the optimal industrial policy.
Section 6 summarizes our results and offers some concluding remarks.
2 The model
We consider a problem of industrial policy setting. The government has to decide whether
an industry characterized by increasing returns to scale should be under public or private
control. In line with Laffont and Tirole (1993), we call regulation regime the regime in
which the government controls the production of a public firm. The government's control
rights are associated with accountability on profits and losses. That is, it must subsidize
the firm in case of losses whereas it taxes the firm in case of profits.
In contrast, we call private regime the regime in which the government imposes no
control on the operations of a private firm, and it takes no responsibility for the firm's
profits or losses. That is, no transfer is possible between the government and the private
firm once production has begun.15 Private firms do not pay tax on profit but they pay an
entry fee. This is an artifact of the formalization. In the static model below it is optimal
for the government to sell the firm ex-ante (i.e. while it is in a position of symmetric
information vis `a vis the firm) rather than to tax its profit ex-post (i.e. once the firm
has learned its cost parameter and has an informational advantage). Empirical evidence
shows that developing countries rely on entry fees to raise revenues from firms (see Auriol
and Warlters (2005)). Entry fees are paid up front and do not require follow up. They
15This is of course a simplification. In practice government might transfer some funds to the private
sector. However subsidies are lower under privatization than under public ownership which is what
matters for the results.
8
hence fill two purposes: as a tax instrument they have low administrative costs, as a
barrier to market entry they are a convenient tool of government's industrial policy.
To keep the analysis simple we consider a linear product demand. However the results
are robust to more general demand function.16 The inverse demand function for Q 0
units of the commodity is given by
P(Q) = a - bQ
where a > 0 and b > 0 are common knowledge. The gross consumer surplus is therefore
Q b
S(Q) = P(x)dx = aQ - Q2.
0 2
On the production side there are N firms in the industry. Firm i {1,...,N} produces
output qi. The total production in the industry is Q = N
i=1 qi. Firm i {1,...,N} has
the following cost function:
C(i,qi,K) = K + iqi,
As in Baron and Myerson (1982), the cost function includes a fixed cost K > 0, and an
idiosyncratic marginal cost i. Firm i must make the investment K before discovering
i. Neither the government nor the competitors of firm i observe this firm-specific cost
parameter. The parameter i is independently drawn from the support [,�] according
to the density and cumulative distribution functions g(�) and G(�). This law is common
knowledge. We denote the expectation operator by E, the average marginal cost by E,
and the variance of marginal cost by 2 =var().
We focus on increasing returns to scale industries. The fixed cost K is large so that
the maximal number of firms N that can survive under laissez-faire is small. To be more
specific we make the following assumption:
(a - E)2 2
A0 K + .
16b 4b
Assumption A0 implies that N {0,1,2}.17
16This model with linear demands is analytically tractable. Models with iso-elastic demand functions
require numerical simulations but yield similar results. Computations are available on request.
17To find out how condition A0 is computed see section 4.1 footnote 25.
9
The firms are profit maximizer. The profit of firm i is
i = P(Q)qi - C(i,qi,K) + ti (1)
where ti is the net transfer that the firm gets from the government (subsidy minus tax
and franchise fee).
The government is utilitarian and maximizes the sum of consumer and producer sur-
pluses minus the social cost of transferring public funds to the firm(s). The transfer to the
firm(s) can either be positive (i.e. a subsidy), or negative (i.e. a tax). The government's
objective function is
N N
W = S(Q) - C(i,qi,K) - ti (2)
i=1 i=1
where is the opportunity cost of public funds.18
The opportunity cost of public funds, , drives the results of the paper. This opportu-
nity cost, which can be interpreted as the Lagrange multiplier of the government budget
constraint, measures the social cost of a transfer from the government to the firm. For
close to 0, the government maximizes the net consumer surplus; for larger , the gov-
ernment puts more weight on transfers. The opportunity cost of public funds is positive
because transfers to regulated firms imply either a decrease in the production of public
goods, such as schooling and health care, or an increase in distortionary taxation. Each
dollar that is transferred to the regulated firm costs 1+ dollars to society. In developed
economies, is mainly equal to the deadweight loss accrued to imperfect income taxa-
tion. It is assessed to be around 0.3 (Snower and Warren, 1996). In developing countries,
low income levels and difficulties in implementing effective taxation programs are strong
constraints on the government budget, which leads to higher values of . As a benchmark
case the World Bank (1998) suggests an opportunity cost of 0.9. The value is much higher
in countries that are heavily indebted.
18The analysis and the results of the paper are consistent with a less optimistic view of government
objectives. It is just a matter of interpretation of . With a non benevolent government, is the weight
the government puts on the transfers it can get out of the firms (e.g., bribes).
10
3 Private versus regulated monopoly
When K is large, a natural monopoly emerges: N {0,1}. Since there is at most one
firm, the firm index can be temporarily dropped. The production of the monopoly is equal
to the total production Q. Regulation aims at correcting the distortion associated with
monopoly pricing in the laissez-faire situation. Regulation theory suggests that, at worse,
a benevolent regulator should be able to mimic the choice of a private firm. Hence, welfare
should never be smaller under regulation than under laissez-faire. Although regulation
always dominates laissez-faire under complete information, we show that it is not always
the case under asymmetric information.
3.1 Private monopoly
The production levels of private monopolies (henceforth PM) are not controlled by the
government. The government can nevertheless control the entry of private monopolies by
auctioning the right to operate. Let F() 0 be the franchise fee that the private firm
pays to the government in order to operate in the product market. The private monopoly
contemplates the following sequential choices. First, the monopoly chooses to enter the
market by paying the franchise fee F() and by making the investment K. If it enters,
then nature chooses the marginal cost according to the distribution G(�). The private
firm learns and chooses a production level Q. After the realization of the private firm
never pays or receives a transfer from the government.
The profit of the private monopoly is
PM = maxP(Q)Q - C(,Q,K) - F().
Q
The optimal production is independent of K and F():
QPM = a - . (3)
2b
If a is smaller than the firm's marginal cost , the production level falls to 0. In order to
rule out corner solution in the sequel of the paper, we assume that a is not too small:
A1 a max 2, + G() .
g()
11
Substituting QPM in equations (1) and (2), we get the ex-ante profit and welfare of a
private monopoly,
1
EPM = V - K - F(), (4)
2
3
EWPM() = V - K + F() (5)
4
where
E(a - )2
V = (6)
2b
The value of operating the firm after the investment is made is measured by V .19 A
monopoly is privately feasible if it is ex-ante profitable, i.e. if EPM 0. This requires
1V K and F() [0, V -K]. Similarly a monopoly is socially valuable if it brings ex-
1
2 2
ante positive welfare, i.e. if EWPM 0. It is easy to check that monopolies are socially
valuable but privately infeasible if 3V > K > V . The ex-ante welfare EWPM()
1
4 2
increases linearly with F(). The maximal entry fee that the government can collect
is the maximum price a risk neutral entrepreneur would agree to pay for the monopoly
concession:
1
F max{0, V - K}.
2
In practice international capital flows depend on country risk ratings so that developing
countries'government do not collect the maximal fee F (see Brewer and Rivoli 1990).
Because of the service of their debt, the perception of corruption in the administration
and the social instability, the lack of transparency and predictability of their political and
judicial institutions, developing countries get bad risk ratings.20 A consequence of the
bad ratings is that private investors, especially foreign ones, are very reluctant to invest
in these countries. For instance in 1999 foreign direct investment (FDI) inflows to the
19One can check that V = (a-E)2 + 2 . It can be separated into two components: the value at the
2b 2b
average cost, (a - E)2/2b, and the value of the cost spread, 2/2b.
20The ratings combine a range of qualitative and quantitative information. They reflect the ability and
willingness of a country to service its financial obligation. There are five different measures of country
risk: political risk, financial risk, economic risk, composite risk indices and institutional investor's country
credit ratings. The leading rating agencies are Standard and Poor's, Moody's, Euromoney, Institutional
Investor, Economist Intelligence Unit, International Country Risk Guide. See for instance Global Risk
Assessments web site, www.grai.com/links.htm.
12
49 least developed countries (10% of the world population) was 0.5% of total world FDI
flows. Since less than 10% of this investment was cross-border merger and acquisition
(including privatization), privatization proceeds are lower in poor countries than in rich
ones, despite sometimes a large number of privatizations.21 In the context of our model a
bad rating translates into a large . That is, countries characterized by a large are also
countries that get low privatization proceeds. To capture this idea we make the following
assumption.
A2 F() [0,F] is non-increasing and weakly convex in 0.
3.2 Regulated monopoly
Under public ownership, the government, which is accountable for the profits and losses
of the firm, monitors the production of the regulated monopoly (RM hereafter). The
timing is as follows: The government first decides to make the investment K. Second,
nature chooses the marginal cost according to the distribution function G(�). Third,
the regulated firm's manager learns , but the government does not. The government
proposes a production and transfer scheme (Q(�),t(�)). Finally the regulated firm reveals
the information and production takes place according to the contract (Q(),t()). We
first study the benchmark case of regulation under symmetric information.
3.2.1 Symmetric information
When the realization of is publicly observed the government solves max{Q,t W s.t. }
0 with W and defined in (2) and (1). Since is positive, transfers to the regulated
firm are costly and must be reduced down to the break-even point = 0. That is,
tRM = -P(Q)Q + K + Q. Substituting this expression in W and maximizing W with
respect to Q yields
QRM () =
1 + a - . (7)
1 + 2 b
21See http://www.ncpa.org/pd/private/oct98ab.html 'Privatization: Privatization Trends in Develop-
ing Countries' 1997.
13
Inserting QRM in (2) gives the ex-ante welfare under symmetric information
1 +
EWRM () = (1 + )
V - K (8)
1 + 2
where V is defined in equation (6). The government invests K in a regulated firm only if
(8) is positive. The ex-ante welfare increases in V . It is non-monotonic in if V > K.
1
2
That is, it decreases for small and increases for large . This deserves a comment.
For small , the government incurs small social costs of transferring money to the
regulated firm. It then chooses quantities that are close to the first best level which
means a price that is close to marginal cost. Indeed, lim QRM = (a - )/b and
0
therefore P [(a - )/b] = . At this price, the regulated monopoly cannot recover its
fixed cost. The loss is compensated by a transfer to the firm t = K > 0. By continuity,
the government will subsidize the regulated firm as long as remains small enough. In
contrast, for large , the government is more interested in receiving transfers from the
firm than in maximizing consumer surplus. It chooses production to induce a positive
profit which is confiscated through taxes. As becomes very large, the government seeks
the maximal revenue from the state-owned firm. In the limit it chooses the production
level of a private monopoly (i.e. lim QRM = QPM = (a - )/2b).
3.2.2 Asymmetric information
Under asymmetric information, is not observed by the government. The government
must design the contracts such that the regulated firm reveals its private information.
Incentive compatibility constraints are added to the previous problem. By virtue of the
revelation principle, the analysis is restricted to a direct truthful revelation mechanism
( = ). To avoid the technicalities of `bunching' we make the classical monotone hazard
rate assumption:
A3 G()/g() is non decreasing.
We define the virtual cost as
G()
v(,) = + . (9)
1 + g()
14
The virtual cost includes the marginal cost of production, , and the marginal cost of
information acquisition, G() . We deduce that v(,) , and by A3, that v(,)
1+ g()
increases in and . Let
E(a - v(,))2
VRM () = (10)
2b
This implies that V RM () decreases in . Following the Baron and Myerson's (1982)
approach, we deduce the following lemma, which proof is standard.
Lemma 1 Under asymmetric information, the optimal production and the ex-ante wel-
fare of a regulated monopoly are those of the symmetric information case evaluated at
the virtual cost v(,) . That is,
QRM() = QRM (v(,))
(11)
1 +
EWRM() = (1 + ) V RM () - K (12)
1 + 2
The quantity produced by a regulated monopoly under asymmetric information is the
quantity of a regulated monopoly under symmetric information valued at the virtual cost.
Since v(,) , we deduce that QRM() QRM () for any . Moreover, since v(,)
increases in , the distortion is higher at larger marginal costs. Indeed by lowering the
production of inefficient firms, the government reduces the overall incentive to inflate cost
report. Comparing (6) and (10) it is easy to verify that VRM () V for all 0. Hence,
the ex-ante welfare of a regulated monopoly is lower under asymmetric information than
under symmetric information: EWRM() WRM (). In the next section we compare
the welfare levels generated by a private monopoly with those of a regulated monopoly.
3.3 Regulation versus privatization
As a benchmark case we first consider the symmetric information case.
Proposition 2 Under symmetric information, regulated monopoly dominates privately
feasible monopoly, whether the latter is franchised or not.
15
Proof: See Appendix 1.
Proposition 2 is very intuitive. Under symmetric information a benevolent government
cannot do worse than a private monopoly because, for any realization of , it can always
replicate the outcome of the private firm. However, it is easy to show that, for large
opportunity costs of public funds, a regulated monopoly under symmetric information
does not bring much more welfare than a private monopoly when the latter pays the
maximal franchise fee, F. The welfare function under regulated monopoly then is equal
to EWRM () = ((1 + )/(1 + 2))V/2 +(1+)(V/2-K), whereas the welfare function
under private monopoly is equal to EWF () = V/4+(1+)(V/2-K). One can check
PM
that the two welfare functions have a common asymptote with slope V/2 - K (see figure
1). The welfare of a regulated monopoly coincides with the welfare of a private monopoly
for large . From this argument, we can infer that the additional cost introduced by
the asymmetry of information in the regulated monopoly gives a welfare advantage to
the private monopoly for large . That is, under asymmetric information, the welfare
function of the regulated monopoly has an asymptote with (negative or positive) slope
R lim + EWRM()/. It is easy to check that
VRM
R = ()
- K (13)
2
is smaller than V - K. We deduce that privately feasible monopolies can dominate
2
regulated monopolies. Let the fixed cost K satisfy the following condition.
1 2B+VRM
C0 V K V () - 1 -B with B = E a- G() .
2 V 2 b g()
Condition C0 firstly implies that the fixed cost is small enough so that a monopoly is
privately feasible (see equation 4). It secondly implies that the fixed cost is large enough
to make the government prefer privatization for at least some value of opportunity cost of
public funds. The interval defined in condition C0 is non empty. Indeed, it is equivalent
to (V )2 +
B V -VRM () > 0 which is always true since V > V RM (). Appendix 2 shows
V
how the right hand side of condition C0 is derived.
Proposition 3 Suppose that assumptions A0 to A3 and C0 hold. Two cases are possible.
(i) If lim+ F() R then there exists a unique threshold, , such that privatization
16
dominates regulation if and only if > .
(ii) If lim + F() < R then there are two thresholds and , < , such that
privatization dominates regulation if and only if [,].
Proof: See Appendix 2.
EW
T
V - K
3V - K @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
EWRM EWPM(F = F)
4
EWPM(F = 0)
EWRM
E
0
^ 0
~
Figure 1: Welfare for Private and Regulated Monopoly
Figure 1 illustrates Proposition 3. The bold solid curve represents the ex-ante welfare
of regulated monopoly under symmetric information (RM) and the bold dashed curve
displays ex-ante welfare under asymmetric information (RM). The ex-ante welfare of
regulated monopoly is non-monotone in . It is higher for low or high values of than
for intermediate ones. The thin solid lines represent two boundaries (i.e. F() F and
F() 0) of ex-ante welfare of a private monopoly (PM). Depending on the franchise
fee function, F(), the welfare function associated to a private monopoly varies between
these two bounds.
17
Proposition 3 establishes that privatization with price liberalization dominates a benev-
olent regulation under public ownership for (at least) intermediate value of the opportunity
cost of the public fund. This result is very robust. As shown in Appendix 2, even with
F() 0, the interval [0 ] where privatization dominates regulation is non empty (see
, 0
figure 1). In other words, positive franchise fee does not explain the preference for private
feasible monopolies even if it fosters it. The intuition for this result is as follows. A
private entrepreneur enters the business if his/her firm is ex-ante profitable. After the
investment, the private firm makes a large or a low operating profit depending on the
realization of technical/demand uncertainties. A private entrepreneur, who bets her own
assets (or the shareholders' ones) in the firm, is accountable for these profits and losses.
In contrast, under regulation, accountability lies on the government side; the business
risk is borne by the government that has to grant ex-post subsidies to unprofitable firms.
Under symmetric information, the tightness of government budget plays no role because
the government perfectly controls the firm's cost and profit. This is illustrated in figure
1 by the fact that, even for F() F, EWRM () is always above EWF () 0.
PM
However, under asymmetric information, the regulated firm uses the possibility of trans-
fers from the government to acquire a positive informational rent. The government prefers
that the private sector takes over when the social cost associated with the rent outweighs
the social benefit of controlling the firm's operation. As shown section 5 this ultimately
depends on the profitability of the industry.
Positive franchise fees increase the preference for private monopoly. On the one hand,
when the franchise fee F() is large (i.e. F() R 0), the opportunity costs
supporting privatization belong to an unbounded range [,+). The optimal industrial
policy is monotone in . Regulation is preferred to privatization for whereas
the reverse holds for > . On the other hand, when the franchise fee falls below
the threshold R, regulation re-dominates privatization for large value of . The optimal
industrial policy then is non monotone in . For intermediate value of privatization with
price liberalization dominates regulation under public ownership. The opposite conclusion
holds for lower and larger value of . The intuition for this result is as follow. Because
many developing countries' governments are constrained by tight budgetary conditions,
18
they have a weak bargaining position during privatization processes. They sell their
public assets at a discount to avoid the embarrassment of unsuccessful sales (see Birdsall
and Nellis 2002). In contrast under public ownership they legally seize the firms' profit
which provides regular revenue inflows. For instance over the period 1990-95, revenue
collected from public firms amounted to 8% of GDP in Bolivia, 2.2% in Brazil, 5% in
Chile, 1% in India, 3% in Mexico, 3% in Peru (World Bank 1998). "On the whole this
non-tax revenue is more important for developing than opposed to industrial countries,
comprising about 21 percent compared to 10 percent of total revenue." (Burgess and
Stern (1993) page 782). More recently Trujillo et al. (2003) have shown that utilities
privatization results in additional public investment. The authors explain the negative
impact of utilities privatization on public finances, by the fact that the reduction in
current public expenditure plus the tax revenue from the new private firms is not enough
to compensate for the loss in non-tax income from public firms. Since in most of the cases
utilities privatization also leads to price rises, it hurts both consumers and taxpayers.
Governments of developing countries should resist the privatization of their profitable state
owned enterprises, which in practice they do. For instance one-third of the privatizations
to end 1996 in Africa were liquidations or asset sales of unprofitable firms (Sarbib 1997).
Similarly Namibia is one of the few countries in the world without a privatization plan,
mainly because its public enterprises are operating at a profit (Harsch 2002).
3.4 Numerical Assessment for
Proposition 3 shows that independently of the privatization proceeds, privatization with
prices liberalization dominates a benevolent regulation under public ownership for inter-
mediate value of . The relevance of this result depends on what 'intermediate' value
means. If it is very high, in practice privatization will never be optimal. In what follows
we assess the lowest value of the opportunity cost, , for which privatization becomes
attractive. By definition is obtained when the highest franchise fee F applied (see
figure 1). It solves EWRM() = EWF (). This equation is equivalent to
PM
4(1 + )2V RM () = (3 + 2)(1 + 2)V. (14)
19
Using (9) and (10), we observe that this expression defines a second degree equation in
. In order to get explicit value for , we make the assumption of a uniform distribution
of over [,]. Still, the conclusions of the simulation are robust to other statistical
specifications (e.g. normal distribution). Under the uniform distribution, equation (14)
is equivalent to: 4E((1 + 2)(a - ) - (a - ))2 = (3 + 2)(1 + 2)E(a - )2. Divide
the right hand side and the left hand side by a2. One can then check that depends on
/a and /a only. Since under the uniform specification the demand intercept a satisfies
A1 if and only if a 2, we get that 0 /a < /a 0.5. Table 1 displays for the
various admissible values of /a and /a.
/a = 0.0 0.1 0.2 0.3 0.4
/a = 0.1
� 1.14 - - - -
0.2 0.71 1.07 - - -
0.3 0.52 0.66 0.99 - -
0.4 0.42 0.48 0.60 0.90 -
0.5 0.35 0.38 0.44 0.54 0.81
Table 1: Minimal opportunity costs above which privatisation can be preferred
The opportunity cost of public funds is generally assessed to be around 0.3 in industrial
countries (see for instance Snower and Warren (1996)) and higher in developing countries.
We conclude from the simulation that if demand and cost functions are reasonably ap-
proximated by linear functions and satisfy assumption A1, which is an empirical issue,
lies below the range of the opportunity costs prevailing in developing countries. The re-
sults in Table 1 also highlight that privatisation is more likely as technological uncertainty
rises (i.e. decreases with ( - )/a). Indeed larger cost uncertainty implies stronger
information asymmetry between firms and governments and hence larger information cost
in the regulated structures.
20
4 Private and regulated duopoly
We next explore the optimal industrial organization when the fixed cost K becomes
smaller or equivalently, when the value of operating the firm after investment, V , be-
comes larger.22 This is relevant because in the last two decades some industries such
as telecommunication have experienced dramatic technological and/or demand changes
resulting both in a decrease in fixed costs and an increase in demand. Moreover, for a
given industry the demand is generally weaker in developing countries than in industrial-
ized countries, resulting in lower V . That is, for the same population size, the number of
consumers and their propensity to pay are higher in rich countries. This difference might
again imply different industrial policy. We first study the case of a private duopoly.
4.1 Private duopoly
To simplify the exposition, we rule out franchising in the sequel. The results are never-
theless robust to more favorable specifications of the franchise fee.23
A4 F() 0 .
Private duopoly (PD here after) is modeled as Cournot duopoly with asymmetric
information between firms. Each firm gets private information on its own marginal cost
but it is not informed about the competitor's marginal cost. As in any Cournot game,
each firm maximizes its profit taking the other firm's output as given. The timing of the
game is as follows: First both firms simultaneously make the investments K. Second,
each firm i {1,2} learns the realization of its own marginal cost i and chooses its
22From figure 1, we see that a private monopoly is less likely to be preferred to a regulated monopoly
as K/V diminishes. However this result is incomplete. For lower K/V more than one firm may enter the
market.
23Considering F > 0 would reinforce the bias in favor of the private monopoly in Lemma 6 because
franchise fees are higher with a private monopoly than with a private duopoly. Empirically Wallsten
(2000) finds using panel data of 17 developing countries that exclusivity periods (i.e., temporary monopoly
position) can double the firm's sale price (i.e., F) in telecommunication industry.
21
production level qi. The equilibrium concept is Bayesian Nash equilibrium:
qi arg maxEj (a - b(qi + qj))qi - iqi
i = 1,2,j = i.
qi
Due to the linear shapes of the demand and cost functions, firm i's optimal strategy is
equal to qi (i) = (2a + E - 3i)/6b.24 The existence of a duopoly with both firms pro-
ducing at the equilibrium requires that a 3� - E /2, which is true under assumption
A1. Substituting (q1(1),q2(2)) in (1) and (2), we compute the ex-ante firm profit and
the industry welfare of the Cournot duopoly
2 5 2
EPD = V + - K, (15)
9 18 2b
8 11 2
EWPD = V + - 2K. (16)
9 18 2b
A duopoly is privately feasible if the two firms are ex-ante profitable. It means that
expression (15) should be positive.25 A private duopoly is socially desirable if it brings
more welfare than a private monopoly. That is, if EWPD EWPM. Let KPD/PM be the
level of fixed cost such that the government is indifferent between a private duopoly and
a private monopoly, i.e. EWPD = EWPM. From (5) and (16), we compute
5 11 2
KPD/PM = V + . (17)
36 18 2b
Walras (1936) and Spence (1976) have shown in a context of symmetric information
that industries with increasing returns to scale were characterized by excess entry. The
next result shows that the presence of asymmetric information does not alter this result
of wasteful competition.
Lemma 4 Under asymmetric information there is excessive entry. Privately feasible
duopolies are socially undesirable whenever 5 V + 11 2 K V + 2 5 2 .
36 18 2b 9 18 2b
24For more on Cournot competition under asymmetric information see Sakai (1985), Shapiro (1986)
and Raith (1996).
25More generally the expected profit of N firms playing a generalized Cournot competition is ENi =
2V + (N-1)(N+3) 2 V + 3 2 2V + 5 2
(N+1)2 2(N+1)2 -K with N 1. We deduce that if K then N {0,1,2}.
2b 8 8 2b 9 18 2b
This yields assumption A0.
22
The set of values of fixed costs defined by the condition in Lemma 4 is not empty.
One can indeed show that that condition is equivalent to a > E + 3 which is true
under A1. Therefore, the ex-ante welfare is higher if a private monopoly is legally set and
if entry is prevented. Indeed, firms do not internalize the social cost of the investment
duplication in their entry decision. As a result they enter too often in the industry.
4.2 Regulated duopoly
Many contributions in procurement and regulation theory emphasize the idea that despite
sub-additive cost functions, it can be optimal to have several producers in a regulatory
setting. A regulated duopoly can be better than a regulated monopoly because it increases
the variety of products, lowers transportation costs, or because it reduces prices through
(yardstick) competition. In the present model, the firms' marginal cost are independent
and identically distributed. The benefit of choosing a regulated duopoly originates from
the sampling gain as first analyzed by Auriol and Laffont (1993).
4.2.1 The sampling effect under symmetric information
The timing is the same as for a regulated monopoly with the following differences: the
investment K is made in the two regulated firms (henceforth RD) and the marginal cost
parameters i with i {1,2} are independently drawn. Under symmetric information
the transfers ti to the regulated firms i {1,2} which are socially costly, are reduced
until firms break even: ti = -(a-bQ)qi +iqi +K. Substituting this expression into the
welfare function yields
WRD = S(Q) + P(Q)Q - (1 + )(1q1 + 2q2 + 2K).
The welfare function is linear in q1 and q2. Optimizing it with respect to qi we deduce
that qi = QRD > 0 if i = min{1,2} and qi = 0 otherwise. The optimal produc-
tion level coincides with the level of the regulated monopoly defined in equation (7):
QRD (1,2) = QRM (min{1,2}). Monitoring a regulated duopoly is equivalent to
monitoring a regulated monopoly for which the investment level is 2K and the marginal
23
cost is distributed as min = min{1,2}, that is, with the law:
gmin() = 2(1 - G())g(). (18)
The ex-ante welfare of the regulated duopoly under symmetric information is
1 +
EWRD () = (1 + )
V min - 2K (19)
1 + 2
where
�
Vmin = (a - )2gmin( )d. (20)
2b
The facts that gmin(�) stochastically dominates g(�) and that (a - )2/2b decreases in
imply that V min > V . Then comparing (8) and (19), the ex-ante welfare is larger under
a regulated duopoly than under a regulated monopoly if the sampling gain, measured by
(V min - V ) (1 + )/(1 + 2), is larger than K, the duplicated investment.26
4.2.2 Asymmetric information
Under asymmetric information, the two regulated firms must be enticed to reveal their pri-
vate information to the government. By the revelation principle, the analysis is restricted
to direct revelation mechanisms. The equilibrium is defined as truthful Bayesian Nash
equilibrium. Each firm i {1,2} sets its revelation strategy i such that it maximizes
the expected profit given the cost distribution of the competitor j = i. Let
�
V RD () = (a - v(,))2gmin( )d. (21)
2b
The following lemma presents the structure of production and the welfare level of the
duopoly under asymmetric information.
26Only one firm produces at the equilibrium. This is an artifact of the assumption of constant marginal
costs which is used to isolate the sampling effect. Models with non-constant marginal costs yield qualita-
tively similar results (see Auriol and Laffont 1993). Finally we assume that the government shuts down
the least efficient regulated firm for the sake of readability. It could instead transfer the best technol-
ogy to all regulated firms and share the optimal production QRD among them. The analysis would be
unaltered.
24
Lemma 5 Under asymmetric information, only the firm with the lowest marginal cost
produces. Output and welfare levels are the levels obtained under symmetric information
evaluated at the virtual cost:
QRD(1,2) = QRM v(min,) , (22)
1 +
EWRD() = (1 + ) VRD() - 2K . (23)
1 + 2
Proof: The proof is similar as in Auriol and Laffont (1993) Proposition 2.
Monitoring a regulated duopoly is equivalent to monitoring a regulated monopoly for
which the investment level is 2K, the marginal cost is v(min,) and min is distributed
according to gmin(�). Let K RM/RD
() be the value of the fixed cost such that the govern-
ment is indifferent between a regulated monopoly and a regulated duopoly, i.e. such that
EWRM() = EWRD() :
RM/RD 1 +
K () = VRD () - V RM () (24)
1 + 2
RM/RD
Under asymmetric information, the sampling gain is measured by K (). Since the
distribution function gmin() stochastically dominates g() and since (a - v(,))2/2b
decreases in we deduce that V RD () V RM (). However the larger is, the lower
is the impact of the sampling gain and the smaller is the government's preference for
regulated duopoly.
4.3 Private versus regulated duopoly
We have seen in Section 3 that private monopoly can be preferred to regulated monopoly.
By extension, private duopoly could also be preferred to monopoly or regulated duopoly.
However, excess entry and weak competition in private Cournot duopolies will generally
RD/PD
preclude this structure from being socially desirable. To be more specific let K ()
be the value of the fixed cost such that regulated duopoly is equivalent to private duopoly,
i.e. such that EWRD() = EWPD. The government prefers a regulated duopoly to a
RD/PD PD/PM
private duopoly if and only if K K (). On the other hand, if K K
defined in equation (17), the government prefers a private monopoly to a private duopoly.
25
We deduce that if
RD/PD PD/PM
C1 K () K
a private duopoly is never preferred by the government. Appendix 3 shows that assump-
tion C1 holds if the demand parameter a is not too small. For instance if i is uniformly
distributed over [0,] then assumption A1 implies condition C1.
Lemma 6 Under assumption C1 a private duopoly is never optimal.
We now turn to the study the optimal industrial policy.
5 Optimal industrial policy
Under complete information, the government can always replicate the production decisions
of private firms so that privatization is never optimal. The optimal industrial policy varies
from no production, regulated monopoly to regulated duopoly according to whether the
investment cost K is large, medium or small. Under asymmetric information, information
RM
costs alter this result. That is, let K () be the value of the fixed cost such that the
government is indifferent between a regulated monopoly and no production (i.e. such that
EWRM() = 0). It is easy to check that
RM 1 +
K () = VRM (). (25)
1 + 2
RM/PM
Similarly let K () be the value of the fixed cost such that the government is indif-
ferent between a regulated monopoly and a private monopoly (i.e. such that EWRM() =
EWPM). It is easy to check that
RM/PM (1 + )2 3V
K () = VRM () - . (26)
(1 + 2) 4
We deduce the next result.
Proposition 7 Suppose that assumptions A0 to A4 hold. Under condition C1, the op-
timal industrial policy under asymmetric information is to set:
26
V RM
� no production if K > max ,K () ;
2
RM/PM
� a private monopoly if K () < K ; V
2
RM/RD RM/PM
� a regulated monopoly if K () < K min K (), V or if V K <
2 2
RM
K ();
RM/RD
� a regulated duopoly if K K ().
Proof. See Appendix 4
K
T
V
KRM
3V
4
1V
2
D
D
PM
RM
min
V - V
KRM/PM
l
l
l
KRM/RD
l
l
d
d
d
l
l
l
d
d
d
l
l
RD
d
l
d
l
d
l
l
l
d
l
d
l l
l l
l
d
l
d
l l
l
l
l
d
l l d
l
E
Figure 2: Optimal Industrial Policy
Figure 2 illustrates Proposition 7 in (,K) space. It allows to consider three types of
market organization in function of the profitability of the infrastructure project or of the
utility.
27
The first case occurs when the ex-ante profitability of the infrastructure project or
RM
of the industry is low (i.e. for K K (+)). When K is large there is room for at
most one firm. The optimal industrial policy then is monotone in the opportunity cost
of public funds. We distinguish two cases. First when K is larger than V/2 the project
is not privately feasible. Depending on being either low or high the optimal industrial
policy is public ownership (in wealthy countries) or no production (in poor countries).
In figure 2 public, regulated monopolies that are desirable under asymmetric information
are depicted by the white area denoted RM, no production corresponds to the area
denoted . Second when K falls below V/2, the project becomes privately feasible for
one firm. Regulation is preferred to privatization if and it is the reverse otherwise.
When K is close to V/2 private monopoly is preferred for large simply because it is
feasible whereas regulated monopoly is not. By continuity private monopoly dominates
regulated monopoly for lower values of the fixed cost. This situation is denoted PM and
RM/PM
is represented by the hatched area above the curve K .
Because developing countries have large opportunity costs of public funds, they may
implement industrial policies that strongly differ from those implemented in advanced
economies. There are for instance a public good aspect and externalities associated to
sunk cost investment such as infrastructure (e.g., a road). As recommended by standard
economic theory wealthy nations subsidize the construction of the infrastructure and let
people use it at marginal cost (e.g., for free). With a low opportunity cost of public funds
this policy maximizes welfare. On the other hand many developing countries plagued by
financial problems have started build-operate-and-transfer (BOT) programs. In such pro-
grams, a private firm finances the sunk cost of an infrastructure, for instance a highway, in
exchange for a 10-30 years licence to exploit it in a monopoly position. Clearly, a privately
owned and operated infrastructure, even with the monopoly distortion (e.g., a toll), is a
better solution than no infrastructure at all, which is, in the absence of public financ-
ing, the alternative to privatization. Water supply, which typically is provided worldwide
through public ownership, could be a good candidate for such type of privatization. This
is at least what is advocated by Brook Cowen and Cowen (1998). In developing countries
tariffs are so low that on average they do not cover half of the total cost (World Bank
28
1994). This precludes public investment, and large fraction of the population in cities has
no formal water hook-up. To increase access some countries have chosen to implement
BOT contracts. China, Malaysia, Thailand implemented it in water, and Chile, Mexico,
in sanitation (World Bank 1997). The drawback of such privatization policy is that it
increases inequality. That is, rise in public utility tariffs (to reach costs recovery level),
recovery of unpaid bills and termination of illegal connexion hurt the poor. On the other
hand, extension of the network favor those who are wealthy enough to access the new
infrastructure. Empirical studies hence suggest that the reforms have worsened wealth
and income distribution (see for instance Chisari, Estache and Romero 1999, Birdsall
and Nellis 2002, Estache, Foster and Wodon 2002, Estache 2003). This in turn might
explain why privatizations are so unpopular.27 Privatization is a good alternative to the
absence of public funds if it leads to an increase of available infrastructure such as roads,
railroads, or distribution networks. Nevertheless the reforms have to be accompanied by
subsidies in direction of the poor (either directly from government, or international insti-
tutions, or from the wealthy part of the consumers through cross-subsidies) to constitue
genuine Pareto improvement. Last, but not least, governments with bad country risk rat-
ings might find impossible to attract international investors on low profitability projects.
They should rather target national private investors or national NGOs which are better
informed on local profitability and risk.
RM
The second case occurs when K belongs to [V min- V,K (+)]. When K lies in
this interval the market offers good ex-ante prospects to one firm. Production (with a
monopoly) is always optimal. However, contrary to the low profitability case, the optimal
industrial policy is non monotone in . This is illustrated Figure 2 by the fact that the
RM/PM RM/PM
curve denoted K () is non monotone in . Let K denote the minimum of
RM/PM RM/PM RM
K (). For K K K (+), as increases, the optimal industrial policy
successively becomes public ownership, then privatization and finally public ownership.
Indeed when is very large the government seeks the maximal revenue from the firm.
27For instance 63% of people surveyed in 2001 in 17 countries of Latin America disagreed or strongly
disagreed with the statement "The privatization of state companies has been beneficial" (The Economist
July 28-August 3 2001, p38). There is a widespread perception that they have been hurting the poor,
notably through increase in tariff and unemployment, while benefiting the powerful and wealthy.
29
Privatization which generates low proceeds (because of the high ) is not appealing.
It is better to keep the profitable firm public while fixing its price close to monopoly
level. This generates more revenue. The traditional fixed-line and long distant segment
of the telecommunication industry illustrates this non monotonicity result: "A PTT[Post
and Telecommunication Company]'s yearly revenues (especially charges from international
call) were used by governments to subsidize mail service, or to ease yearly budget deficits.
Given this public convenience and necessity, the interests of third world governments are
often diametrically opposed to telecom policies of privatization and network deregulation
favored by wealthy nations." (Anania 1992).
Finally, when V/2 is much larger than K (i.e. when K Vmin - V ), markets offer
good ex-ante prospects to more than one firm. Lemma 6 then shows that a private
Cournot duopoly is never optimal. The negative impact of market power and excessive
entry are too strong compared to the positive effects (here the `sampling gains') of a
regulated duopoly. In other words, the advantage of private structures with liberalized
prices disappears once the market allows the entry of more than one firm (i.e. when it
is very profitable). This result may look at odds with theories where private structures
perform better with larger number of entrants (see for instance Vickers and Yarrow (1991)
and Segal (1998)). A basic difference in our model lies in the intensity of competition
that exists within private and regulated structures. Under privatization, private firms
compete in quantities so that the addition of a firm does not fully eliminate market power
and profits. In contrast, under the regulation regime, information costs dramatically fall
when a second firm is added in the regulated market. Regulation is then more attractive.
This result is congruent with the theory of adverse selection in which a rise in the number
of agents reduces the cost of information revelation (see Auriol and Laffont (1993)).28
The case where regulated duopoly is preferred to regulated monopoly is depicted by the
RM/RD
hatched area below the curve K denoted RD.
28If we had considered that firms operating in the same industry have correlated costs, we would
have used this correlation to implement yardstick competition, reducing further the cost of information
revelation (see Auriol and Laffont 1993).
30
This last result sheds light on the link between market liberalization, on the one
hand, and technological and/or product demand changes, on the other hand. Market
liberalization, often referred to as `deregulation', corresponds to the divestiture of the
historical monopoly and the introduction of new entrants. As shown in Proposition 7 this
is not equivalent to laissez-faire. In practice prices and entry remain regulated to protect
consumers against collusion and predatory behavior (through licences and price caps for
instance). This is important because in profitable industry the consumer surplus is high.
Monopoly pricing then has more impact on welfare than it has on low profitability indus-
try. In the framework of our model the divestiture of the historical monopoly is motivated
by a drop of the ratio K/V . That is, by smaller fixed costs and/or by larger product de-
mand. In figure 2 this corresponds to a downward shift, where industry structures move
from regulated monopoly to regulated duopoly. The mobile and internet segment of the
telecommunication industry provides an example of such a drop. Introduction of wireless
technologies has significantly reduced the fixed costs to operate networks whereas the
demand for communication has steadily increased. Consistently with our model, many
developed and developing countries have deregulated their domestic telecommunication
industry. Wallsten (2000), who studied telecom reforms in Africa and Latin America,
found that privatization by itself does not yield improvements but that privatization
combined with an independent regulator does.29 Similarly Estache (2002), shows that
technical/productive efficiency gains generated by Argentina's 1990s utilities privatiza-
tion have not been transmitted to consumers. According to the author the benefits were
captured by the industry because of inefficient regulation. The lesson to be drawn here is
that privatization, being defined as a move from regulation to laissez-faire, is not optimal.
When the ratio K/V is low, the consumer surplus is large.30 Regulation then is a key
component of successful privatization reforms.
To conclude we need to assess the empirical relevance of the arguments developed
in the paper. The first argument that can be tested concerns the reasons that trigger
29For more on the telecommunications reforms in developing countries see Auriol (2005).
30For instance Fuss, Meschi and Waverman (2005) estimates that in a typical developing country,
an increase of ten mobile phones per 100 people boosts growth by 0.6 percentage points. The growth
dividend is similar to that of fixed-lines phones in developed countries in the 1970s.
31
privatization. On the one hand privatization increases productive efficiency. This provides
a first rationale for privatizing, the efficiency argument. On the other hand in profitable
increasing returns to scale industries allocative inefficiency combined with the critical
budgetary conditions found in most developing countries favor public ownership. It is an
effective way to combine the regulation of the industry with a maximal level of taxation. In
contrast when profitability is low privatization is a better option. This is the public revenue
rationale of privatization which is explored in the present paper. Li, Li, Lui and Wang
(2001) based on a data set from privatizations in China test whether government privatizes
in order to enhance production efficiency, the `efficiency' argument, or to increase its
revenue, the `revenue' argument. They conclude "our tests based on the data set from
China reject the efficiency theory and yield support for the revenue theory." Warlters
(2004) and Auriol and Tuske (2005) also find that macro economic variables, such as the
introduction of a VAT system, country risk ratings, or the level of public debt significantly
influence the probability of infrastructure privatization. The macro economic rationale
works also for developed countries. Bortolotti, Fantini and Siniscalco (2003) analyze
panel data for privatization around the world. They consider any type of industry (i.e.
competitive and oligopolistic ones) and any type of countries (i.e. rich and poor). They
find that privatization is more likely in wealthy democracies with right-wing governments,
high debt, liquid stock markets and a legal system that protects shareholders.
A more subtle implication of the model arises while focusing on profitable infrastruc-
ture and public utilities. Depending on the value of privatization might be the optimal
policy in a rich country while it is not necessarily the same in a poor one. Under the
paper assumptions the critical value lies in the range of the opportunity cost of public
funds generally retained for developed economies (i.e. [0.35,1.10] table 1).31 If the
model assumptions are empirically relevant we should observe that the probability to pri-
vatize profitable infrastructure and public utilities in developing countries decreases with
the opportunity cost of public funds.32 Warlters (2004) was the first to check empirically
31 The critical value is the same in figure 1 and 2. Indeed in figure 2 is such that KRM/PM() = V.
2
It is easy to check that this equation is equivalent to equation (14).
32 The prediction is reversed for advanced economies (see figure 2) as suggested by Bortolotti, Fantini
and Siniscalco (2003) where the probability of privatization increases with the level of debt.
32
this result. He studied the determinants of infrastructure privatization using probit re-
gressions with panel data covering 155 developing countries for the years 1984-1998. He
concludes that `infrastructure privatization is more likely when the shadow cost of public
funds falls.' Auriol and Tuske (2005) find similar results while focusing on the telecommu-
nication industry. The probability of privatization of the fixed access and long distance
segment decreases with country risk rating. When controlling for firms' characteristics,
the privatization probability increases with the level of total telephone subscribers, the
number of main telephone lines in the largest city, the percentage of digital main lines,
and the level of annual telecom investment. This suggests that efficient firms are sold
more often than less efficient ones which contradicts the idea that governments use priva-
tization to improve firms' efficiency.33 On the other hand the macro-economic argument
seems empirically supported. Developing countries' governments that are concerned with
solving critical financial problems regard privatization as a useful fiscal instrument.
6 Conclusion
The present paper shows that countries' privatization decisions non-trivially depend on
their development stages. Such an argument is particularly decisive in developing economies
constrained by bad macro-economic conditions and poorly performing tax systems. On
the one hand, for low-profit natural monopolies, privatization always dominates regula-
tion for intermediate and large values of opportunity costs of public funds. Privatization
is indeed Pareto improving when it leads to the creation of an infrastructure that would
otherwise not have existed. Numerical simulations suggest that the `intermediate' values
compatible with the model, are in the range of those of developing countries. On the other
hand, for more profitable natural monopolies, the privatization decision is a non monotone
function of the opportunity costs of public funds. Indeed developing countries plagued
with financial problems are tagged with bad country risk ratings and are unable to attract
international capital flows. Privatization does not yield large divesture proceeds. Since
public firms are sold at a discount, governments in need of cash should preferably keep
33On the other hand it is consistent with the idea of maximizing the sale revenue.
33
profitable public firms under their direct control. They can then choose monopoly prices
and legally capture firms' profits. Such a policy maximizes their revenues. Finally, the
advantage of private structures with liberalized prices disappears once the market offers
room for more than one firm. Technological and demand changes explain the destitution
of historically regulated monopolies and the creation of oligopolies. They induce some
form of competition which still requires efficient regulation.
34
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Appendix 1: Proof of Proposition 2
We have to show that (1 + ) 1+ V - K V - K + F()
1 0 The maximal
1+2 2
franchise fee, denoted F, is equal to the firm's ex-ante profit, i.e. F = V -K. Therefore
1
2
the above inequality is satisfied if 0 (1+) 1+ V - K V -K +3 1 V - K ,
1+2 4 2
or equivalently if 4(1 + )2 (3 + 2)(1 + 2) which is always true 0.
Appendix 2: Proof of Proposition 3
RM PM
Step 1: Regulation is preferred to privatization if and only if EW () EW ().
By virtue of equation (12) this inequality is equivalent to
(1 + )2 3
V RM () - (1 + )K V - K + F(). (27)
1 + 2 4
RM
Developing V () defined in equation (10) one can check that:
RM 1 + 2 2 RM
V () = V + V () - B (28)
(1 + )2 (1 + )2 (1 + )2
where terms V = E [(a - )2/(2b)], and V RM () = E (a - - G() 2
) /(2b) , and B =
g()
E [G()(a - )/(g()b)] are all positive by virtue of assumption A1. Substituting (28)
in (27) and dividing the right and left hand side by , we get after some straightforward
computations:
V B
- V RM () + K + F(). (29)
4 1 + 2 1 + 2
It is easy to check that the left hand side of (29), denoted LHS(), is a decreasing and
convex function of . Similarly, under the assumption A2 the right hand side of (29),
denoted RHS(), is decreasing and convex. The following proof relies on the property
that two decreasing and convex functions can intersect only once, twice or none.
Step 2: For = 0, expression (29) is equivalent to V 0 which is always true. We
deduce that for small enough regulation dominates privatization.
For + two cases hold: either lim + LHS() > lim + RHS(), which is
equivalent to F(+) < R, or lim + LHS() lim + RHS(), which is equiva-
lent to R F(+) where R = V RM() - K.
2
39
Consider first the case R F(+). This condition implies that for large enough
privatization is preferred to regulation. Since it is the reverse for low enough, we deduce
that LHS() and RHS() cross once and only once. This proves part (i) of proposition
3.
Step 3: Consider next the case R > F(). This condition implies that for large
enough , regulation is preferred to privatization. Since this is also true for low enough
, we deduce the following possibilities: first, LHS() and RHS() never cross, in which
case regulation is always preferred to privatization, second, they cross twice which yields
part (ii) of proposition 3. This ultimately depends on K.
Step 4: To complete the proof of proposition 3 we need to show that there are at
least some values of the parameters such that LHS() and RHS() cross twice. Since
privatization is less attractive for smaller franchise fees, a sufficient condition is that
LHS() and RHS() crossing twice for F = 0. Simplifying expression (29) and using
F = 0, we get that privatization is preferred to oublic ownership if and only if
P() = (V RM () - 2K)2 + (V/2 - B - K) + V/4 < 0. (30)
Inequality (30) is satisfied for ((K),(K)) with 0 < (K) < (K) under three
conditions:
(a) (V/2 - B - K)2 > V (V RM () - 2K).
(b) V/2 - B - K < 0
(c) V RM () - 2K > 0
Condition (a) yields a positive discriminant for P() = 0 and thus implies the existence
of two roots (K) and (K); condition (b) and (c) imply positivity for both roots of
P() = 0; finally since P(0) > 0 and lim + P() > 0 under (c), we have that P() < 0
for ((K),(K)).
Conditions (b) and (c) are satisfied if and only if K (V/2 - B,V RM ()/2). This
interval is not empty since V RM () = V - B + E [(G()/g())2/(2b)]. Then, observe
that the left hand side of condition (a) is equal to zero at K = V- B and increases for
2
larger K. Similarly the right hand side of condition (a) decreases with K and is equal to
40
zero at K = V RM ()/2. Hence there exists a unique K (V/2 - B,V RM ()/2) such
that (V/2 - B - K)2 = V (V RM () - 2K). Solving this equation one can check that
1
2B+V RM
K = V () - - B.
V 2
To conclude we have just shown that conditions (a), (b) and (c) are satisfied for any
RM
K (K, V () ), which is a non empty set. Finally note that, because F() 0,
2
RM
K V () (i.e., condition (c)) is implied by the condition R > F() (i.e., condition
2
(ii) in Proposition 3).
This complete the proof of proposition 3. It is independent of the cost distribution.
Appendix 3: Condition C1
RDI/PD PD/PM
Lemma 6 is true as soon as K () K . This is equivalent to
18(1 + )2 1 + 2 112
V RDI () V + .
(1 + 2)(16 + 5) 16 + 5 2b
Let v(,) be the virtual cost + G() . Simplifying by 2b, C1 is equivalent to:
1+ g()
18(1 + )2 (1 + 2)112
Emin (a - v(,))2 E (a - )2 + .
(1 + 2)(16 + 5) 16 + 5
Let h() = 18(1+)2 -1 = 2-+82 > 0 0. Let also () = Emin [v(,)2]+
(1+2)(16+5) (1+2)(16+5)
Emin (v(,)2 -E 2
[ ] [ ]
- (1+2)112 . The condition C1 is equivalent to:
h() (16+5)h()
E [v(,)] - E
a2 - 2a Emin [v(,)] + min + () 0.
h()
This condition, which requires that a is large enough, is not very strong. For instance,
one can check that with an uniform distribution over [0,], and with the convention that
a = A, condition C1 is equivalent to: H(A) = 12A2(82-+2)+12A(4-7)(1+2)+
(1+2)(44-59) 0. Under the assumption A1 (i.e. A 2), it is easy to check that H(A)
is increasing in A for all 0. We deduce that H(A) H(2) = 1362 - 98 + 133 > 0
0. So, for a uniform distribution, assumption A1 is a sufficient condition to get C1.
More generally, let
E [v(,)] - E
al Emin [v(,)] + min
h()
41
+ E 2
E
[v(,)] - E
[v(,)] + min - K()1 . /2
min
h()
If a is larger than al condition C1 is satisfied.
Appendix 4: Proof of Proposition 7
RM/RD
First of all recall that K (), defined equation (24), is the value of the fixed cost
such that the government is indifferent between a regulated monopoly and a regulated
duopoly (i.e. such that EWRM() = EWRD()). A regulated monopoly is preferred
RM/RD
to a regulated duopoly if and only if K K () defined equation (24). Similarly
RM
a regulated monopoly is preferred to no production whenever K K (), defined
RM/PM
equation (25). It is preferred to privatisation whenever K K (), defined equation
RM/PM
RM
(26). Comparing equations (25) and (26) one can check that K () > K ().
Moreover using the fact that gmin() 2g(), one can check that V RD () < 2V RM () so
RM RM/RD RM
that K () > K (). We deduce that if K > K () regulation is never optimal.
On the other hand if K > V privatisation is not possible. Putting all the pieces together
2
yields the result.
7 Acknowledgement
Pierre Picard's work has been supported by a grant "Actions de Recherche Concert�ees"
n 93/98-162 of the Ministry of Scientific Research of the Belgian French Speaking Com-
munity. We are grateful to Amir R. and Michael Warlters for improvements of the paper.
We are especially indebted to Antonio Estache for detailed, insightful comments and very
helpful references. Any remaining errors are our own.
42