increasing function of the output subsidy.

The welfare benefits from entry equal the external benefits of entry (i.e., B(x‘(c,s))), less the cost
of the subsidy (i.e., sx“(e,s) + 0, plus the entrant’s profits (i.e., x“(c,s,J)) if the entrant is a domestic
firm. The policymaker sets the’ subsidy level to maximize welfare subject to the constraint that the

entrant’s profits are nonnegative,

max, £ = B(x'(c,s)) - (s(x"(c,s)) +) + yx"(s,)) + dx"(c,5,0), 0)

where y = (0) if the entrant is domestic(foreign), \ is the Lagrangean multiplier, and x‘(c,s,l) =
(@(X(x(c,s))) - c)x*(c,s) -f, + (sx*(c,s) + 1). Note that x‘(c,s,l) represents the entrant’s profits inclusive
of any subsidy payments. Recognizing that B,(x‘(c,s)) = E,(x‘(c,s)) (see equation (6)), the first order

conditions are as follows:

Of Al=y+r-1=90, (11a)
OF /as = [E,(x*(c,s)) - 8 + Cy + d)pyx'(e,5)(AX (x (c, 8)/dx JKdx'(c, s)/ds)

+ (7 + A- Dx) = 0, (11b)

where dX,(x‘(c,s))/dx, < 0 represents the total reduction in rival output resulting from an increase in the

entrant's output.” Inserting (11a) into (11b), it holds that the optimal output subsidy, s*, satisfies the

7| As reflected in equation (11b), the effect of the subsidy on the entrant’s profits can be described
as follows: dx‘(c,s,l)/ds = x*(c,s) + [p + pyx‘(c,sdX/dx,) - (c-s)](dx*(c,s)/ds). Noting that dX/dx, =
1 + dX/dx,, the expression in brackets can be expressed alternatively as [p + p,x'(c,s) - (c-s) +
PxX'(c,s)(dX /dx,)]. Since the entrant’s first-order condition for profit maximization satisfies. iP + pxx"(c,s)
-(c-s) = 0, the bracketed expression reduces to p,x“(c,s\(dX/dx,), implying that dx‘(c,s,l)/ds = x‘(c,s)
+ pyx'(c,s)(dX /dx,)(dx‘(c,s)/ds).

18


Proposition 3. When neither of the conditions in Propositions 1 or 2 hold, the optimal policy is
complete deterrence of foreign entry and selective deterrence of domestic entry if B(x,") < 0.
Otherwise, if B(x,") > 0, there exists a threshold output level, x,", which Satisfies B(x,") = 0. Entry
at outputs below this threshold should be completely deterred if the entrant is Soreign and selectively
deterred if the entrant is domestic. Entry at outputs above this threshold should be Sreely permitted

(and promoted in selective cases) regardless whether the entrant is foreign or domestic.

In contrast to Propositions 1 or 2, which describe conditions where entry should be allowed freely
or foreign entry should be deterred completely regardless of the entrant’s output choice, Proposition 3
examines a different situation for the policymaker. In this situation, the optimal policy may depend on
the entrant’s output, with entry being permitted only if the entrant’s scale of operations is sufficiently
large (i.e., greater than x,”). Recognizing that the entrant’s equilibrium output is related endogenously
to the characteristics of its cost function, this implies that the policymaker is actually forced to identify
the entrant’s costs. In essence, there exists a cost threshold which separates entrants that are allowed free
entry from those that are potentially deterred.

For example, assume that the technology used by any potential entrant can be described by a cost
function that is a member of a family of functions, F(n), where this family consists of the cost functions
(x) = g(x) + ah(x,) for 1 € Ltn mas]. We also assume that h(x) > 0 x,, which implies that the
marginal cost of output is increasing in ». Under conditions where individual profit functions are strictly
concave, each entrant’s equilibrium output, x,, is uniquely determined by 9, and ax“(n)/an < 0. Now,
if B(x,") = B(x'(n,)) > 0, it holds from Proposition 3 that there exists a threshold cost level, 9”, where
B(x'(n")) = 0. Entry is freely permitted when 9 < ”, but it may be deterred when 7 > 9”. Note that
a family of linear cost functions can be described by c‘(x,) = a + ax, for 7 € [teas Tmesl, Which implies

that 9” is actually a marginal-cost threshold. Only relatively efficient entrants (i.e., 7 < 9”) are freely

12


setting the welfare-maximizing subsidy that induces the entrant to reveal its true costs. Moreover, rather
than solving for the optimal subsidy expressed as a function of output, this problem can be solved instead
by maximizing welfare with respect to the direct revelation mechanism, (x‘(c,),t(c,)), where x‘(c,) and
4(c,) Tepresent, respectively, the entrant’s output and total subsidy payment as a function of its reported
marginal cost (i.e., ¢,).

To induce truthtelling by the entrant, the following incentive-compatibility constraint must be
satisfied:

a(X'(c),t(c),c) = w(X'(Cp),t(Cy),C)) V Cy (43)

If the social welfare and profit functions are well-behaved, then the solution to the welfare-maximization
problem is continuous with respect to c. Thus, equation (13) cannot be satisfied locally unless the
following condition holds:

w(x*(c), tc), c)xt, + xfx'(c),t(c), ce), = 0. (14)

Since x(x*(c),t(c),¢) = (p(X(x"(c))) - ¢)x*(c) + t(c), it follows that x{x“(c),t(c),¢) = 1 and x,(x"(c), t(c),¢)
= p + p;x‘(c) - c under Cournot behavior. Substituting into equation (14), we obtain:
@ + Pre(c) - c)x*(c) + t(c) = 0. ay

Under complete information, the policymaker acts optimally by subsidizing the entry of any firm
with private losses that are less than the external benefits arising from its entry. On the other hand, the
policymaker does not subsidize any firm with private losses that are greater than the external benefits of
its entry. A policymaker acting under incomplete information can achieve an equally efficient outcome
only by setting the total subsidy payment equal to the external benefits of entry, i.e., t(c)= B(x‘(c)) V c.

Differentiating this expression reveals that the optimal amount of entry is allowed when the following

22


By contrast, our paper is directed specifically toward entry policy. We derive conclusions under
limited cost and demand restrictions in a model where firms are typically heterogeneous. Using a
Cournot oligopoly model, we show that entry brings benefits to domestic consumers and losses to
incumbent domestic producers. The relative strength of these two effects, which is crucial to the
formation of optimal entry policy, depends on the market shares of domestic incumbents and cost and
demand conditions. Consequently, the optimal entry policy derives from the composition of domestic
firms in the market, and it evolves as that composition changes.

We identify conditions where the policy prescription is to unambiguously allow free entry or
unambiguously deter foreign entry regardless of the entrant’s size. Yet other conditions are identified
where the optimal policy rests on the entrant's output level, implying that large entrants are favored over
small entrants. Thus, the policymaker’s decision whether to permit entry requires an assessment of the
entrant’s likely output, or more specifically, the entrant’s costs.

Since welfare can be improved in certain cases by encouraging domestic or foreign entry that is
Privately unprofitable, we also explore the nature of the optimal entry subsidy. This analysis reveals that,
under complete information concerning the entrant’s costs, welfare can attain its maximum level through
the use of a two-part subsidy consisting of a Per-unit output subsidy and a lump-sum subsidy or tax.

Given that the magnitude of the optimal entry subsidy and the entrant’s optimal output varies with
the entrant’s costs, a policymaker with incomplete information concerning the entrant’s marginal and
fixed costs must devise a subsidy mechanism that Provides incentive for the entrant to choose the welfare-
maximizing subsidy and output combination for its cost type. If the entrant continues to act as a Cournot
player, this incentive-compatibility constraint cannot be Satisfied without sustaining welfare losses in
comparison to the complete-information case. With an entry subsidy directed toward domestic firms, the
policymaker may undersubsidize entrants with high marginal costs (i.e., forestalling entry that raises

social welfare) and oversubsidize entrants with low marginal costs (i.e., allowing entry that lowers social


following condition:”

8° = Elx'(c,s*) + pyx'(c,s*HdX (x'(c,s*))/dx,) > 0. (12)

The right-hand side of the equality contains two terms: the first term represents the external
benefits arising from an additional unit of the entrant’s output, and the second term represents the increase
in the entrant’s profits that results from the retrenchment in rival output associated with the entrant’s
output increase (i.e., similar to the profit-shifting effect identified in Brander and Spencer, 1984).2
Additions to the entrant’s output produce positive external benefits at the margin (whenever I(x,) is
monotonically increasing) and increase the entrant’s profits due to rival retrenchment. Thus, it is optimal
to impose a positive per-unit output subsidy, allowing that subsidy to increase to the point where the
benefits from an additional unit of the entrant’s output equal the per-unit subsidy.

Now, consider condition (11a). If the entrant is domestic, then y = 1 (by definition).
Condition (11a) holds only if \ = 0, implying that the entrant’s profit constraint does not affect social
welfare. This occurs because any subsidy payment in excess of the amount required to encourage entry

is merely a domestic transfer payment from the government to the firm. However, if the entrant is

” We assume that the second-order copditions for an internal maximum are satisfied. Moreover,
entry is not permitted unless B(x/) (= § ** E,(x,) dx,) > 0, where E,(x,) = “PyX(dX/dx, I(x). Given
that -p,X(dX/dx,) > 0, and that I(x,) is monotonically increasing, this result requires that I(cJ) > 0,
which implies that E,(x/) > 0 (where xJ = x“(c,s*)). Since PrX“(c,s(aX (x"(c,s*))/dx,) > 0, it follows
that equation (12) is positive in sign.

% In the case of domestic entry, an increase in the entrant’s profits generates direct welfare gains.
In the case of foreign entry, this increase in profits lowers the subsidy payment needed to induce entry.

% If I(x, is instead monotonically decreasing, then it is possible that I(x‘(¢,0)) < 0, which implies
that E,(x*(c,0)) < 0. In this case, the external benefits of entry decline as output increases above x“(c, 0).
If the profit-shifting effect of increasing the entrant’s output is telatively small (i.e.,
PxX‘(c, 0) AX {x"(c,0))/dx,) < -E,{x‘(c,0)), then the optimal entry subsidy requires an output fax in
combination with a lump-sum subsidy. The total subsidy payment would be Positive, however. Under
these conditions, optimal policy may require that low marginal-cost entrants incur an output tax, while
high marginal-cost entrants receive an output subsidy.

19


marginal-cost entrants produce more output and low marginal-cost entrants produce less output than in
the complete-information case.” We now summarize the above discussion:
Proposition 6. In setting the optimal entry subsidy for domestic firms, the presence of incomplete cost
information leads to lower social welfare in comparison to the complete information case. Under
incomplete information, domestic entrants with relatively low marginal costs may be "oversubsidized"
(and produce too little output) while those with relatively high marginal costs may be "undersubsidized"
(and produce too much output) in comparison to the efficient outcome.

An exception to this result occurs if the policymaker induces the domestic entrant to make an
output commitment, subject to the subsidy schedule t(x,) = B(x,), and that commitment induces the
entrant to act as a Stackelberg leader. In this case, the same welfare level is attained under incomplete

information as in the case of complete information.

With respect to promoting the entry of foreign firms, it can be shown that foreign entry is

undersubsidized under incomplete information relative to the efficient outcome attained under complete

% Proof available from the authors. To satisfy the terminal conditions for an optimal solution,
a marginal increase in the subsidy payment to the highest marginal-cost entrant must not affect welfare
after considering the impact of that increase on the subsidy payments received by all other entrant types.
This result implies that some types of entrants are undersubsidized while others are oversubsidized.
Based on the optimality conditions derived from the Hamiltonian, it can be shown that the only feasible
solution requires that high marginal-cost entrants are undersubsidized while low marginal-cost entrants
are oversubsidized.

If an entrant of a given marginal-cost type is undersubsidized (i.e., t(c) < B(x‘(c))), then there
is an incentive to stimulate that entrant’s output beyond the level that satisfies equation (18) in order to
induce further retrenchment of rival output. By itself, this retrenchment increases the profits of that
particular type of entrant, thereby encouraging additional entry that raises social welfare. The opposite
incentive exists when an entrant of a given marginal-cost type is oversubsidized. Of course, the output
choice for any marginal-cost type also depends on how the subsidy paid to that cost type affects the
subsidies received by lower-cost entrants (and the associated welfare implications for those cost types).

25


policymaker cannot observe the entrant’s marginal or fixed costs. Since the decision to enter may depend
on the policymaker having previously committed to an entry subsidy, the policymaker must devise an
output-based subsidy schedule that separates entrants with differing marginal costs, giving each type of
entrant the incentive to choose the output/subsidy combination that corresponds to the policymaker’s
(constrained) optimum for its type. To further complicate matters, the total subsidy payment should
ideally allow the proper amount of entry -- that is, it should induce entry by all firms with private losses
(excluding the subsidy) that are less than the external benefits of entry and deter entry by all other firms.
In other words, the total payment should not be so small that it discourages welfare-increasing entry by
those entrants with relatively low fixed costs, nor so large that it encourages welfare-decreasing entry by
those entrants with relatively high fixed costs.

We now examine the optimal entry subsidy mechanism under incomplete information regarding
the entrant’s marginal and fixed costs, assuming that the subsidy policy applies only to domestic
entrants.” In addition, we continue to assume that the domestic social welfare function assigns equal
weight to consumer surplus, producer surplus, and government revenue. These assumptions are
important because they imply that there is no social loss if the policymaker overpays an entrant (i.e., pays
the entrant more than is needed to encourage entry) as long as the entrant’s private losses (exclusive of
the subsidy) are less than the external benefits of entry. In the case of foreign entry, there is the added
complication that overpayments to foreign entrants reduce social welfare. That would also be the case
with respect to domestic entry if we assumed instead that there is an additional social cost involved in
raising or spending government funds. Later, we discuss the implications of relaxing our assumptions.

By the Revelation Principle (see Myerson, 1979), the policymaker’s problem is equivalent to

% We assume that incumbent firms know the entrant’s true costs prior to choosing output.
Incumbent firms may be better informed than the policymaker concerning the entrant’s costs because the
policymaker may be forced to commit to an entry policy (i.e., an entry subsidy) long before a specific
firm decides to enter the market, and even longer before that entrant reaches the output stage.

21


The above remark is readily explained. When an entrant places output onto the market, domestic
incumbents reduce their own output. This output reduction increases in magnitude as the demand curve
becomes more concave and as marginal cost curves decline in slope. Consequently, entry induces a
greater loss of producer surplus by domestic incumbents. The external benefits from entry are thus
diminished, implying that there is a smaller range of market shares where free entry is optimal.

The results from this section indicate that the optimal policy toward entry evolves in accordance
with dynamic changes in market structure. Starting from a position where no domestic firms serve the
market, free entry (and the selective subsidization of both foreign and domestic entry) is the optimal
policy."® However, as domestic firms obtain an increasing share of the market, the incentives arise for
switching to some form of entry deterrence. Eventually, foreign entry may be discouraged entirely (or
permitted only in the case of large-scale entry'’), and relatively inefficient domestic entrants also may
be deterred. Conversely, starting from a position where only domestic firms serve the market, the

optimal policy is always some form of entry deterrence.

4, Optimal Entry Subsidies Under Complete and Incomplete Information

This section discusses the desirability of subsidizing entry and analyzes the optimal entry subsidy
under complete and incomplete information concerning the entrant’s costs. Our analysis does not
consider whether an entry subsidy is necessarily the best policy for increasing social welfare. Policies

such as domestic production subsidies and import tariffs may frequently lead to higher welfare levels than

'® Note that when the market is inhabited solely by foreign firms, policymakers should promote
domestic entry in order to improve the terms of trade and to transfer rents from foreign firms to domestic
firms. Of course, these objectives can also be attained through import tariffs, which would appear
consistent with some of the arguments for infant-industry protection.

'S The prospect of large-scale foreign entry may arise when a point has been reached where several
foreign firms wish to enter the market.

16


for all feasible levels of the entrant’s output, then privately profitable entry is always socially beneficial.

Consequently, free entry is the optimal Policy. The next section illustrates this reasoning.

3.2 Welfare Analysis of Entry

When the entrant is a foreign firm, the welfare effects of entry for the home country, W(x), are
completely captured by B(x,/) — that is, W(x/) = B(x,). When the entrant is a domestic firm, the home
country’s welfare function also includes the entrant’s profits, implying that W(x) = BR!) + x(xZ).

Let Bax/) = Ofor0 < xf < x,". In this case, it follows that Privately profitable foreign or
domestic entry necessarily raises social welfare. Thus, the home country’s optimal policy is to allow free
entry, and also to promote privately unprofitable domestic or foreign entry whenever B(x/) > -a'(xJ).

Now, let B(x/) < 0 for 0 < xf < x,". In this case, foreign entry into the home country’s
market should be deterred entirely, and domestic entry should be deterred unless the domestic entrant has
relatively high profits (i.., unless x"(x/) > -B(x,)). The optimal entry policy toward domestic firms
is therefore selective, only allowing entry by relatively efficient (i.e., low-cost) competitors."

In all other cases, B(x/) is either positive or negative depending on the entrant’s output level, x/.
Privately profitable entry is socially beneficial in some Cases, but not in others. Thus, entry is permitted

(and possibly promoted) or deterred depending on the entrant's likely output level. We summarize below:

Ina pure export market, the home country’s welfare benefits are based solely on the producer
surplus earned by domestic firms in that market. Accordingly, the external benefits from entry (i.e.,
B(x/)) are represented solely by entry’s impact on the profits of domestic incumbents. Since entry lowers
the profits of existing domestic Producers, the external benefits of entry are negative for all levels of the
entrant’s output (or zero if there are no domestic incumbents). Consequently, B(x/) < 0 for 0 < xfs
x,", implying that domestic entry should be deterred except when x“(x/) > -B(x/) (see Lemma 1). Thus,
selective entry deterrence is always the optimal policy in a pure export market. This result may explain
government attempts to restrain entry or form coalitions of Producers in export-oriented markets. There
are many examples of this behavior (e.g., DeBeers, OPEC).

8


References

Al-Nowaihi, A. and Levine, P.L., “The Stability of the Cournot Oligopoly Model: A Reassessment,"

Journal of Economic Theory, 1985, 35, 307-21.

Amsden, Alice H., Asia’s Next Giant; South Korea and Late Industrialization, New York: Oxford

University Press, 1989.
Brander, James A. and Spencer, Barbara J., "Tariff Protection and Imperfect Competition,” in
H. Kierzkowski, ed., Monopolistic Competition and International Trade, Oxford: Clarendon Press, 1984,

194-206.

Dixit, Avinash, "International Trade Policy for Oligopolistic Industries," Economic Journal Conference

Papers, 1984, 94, 1-16.

Eaton, Jonathan and Grossman, Gene M., “Optimal Trade and Industrial Policy under Oligopoly,"
Quarterly Journal of Economics, 1986, 101, 383-406.

Farrell, Joseph and Shapiro, Carl, "Horizontal Mergers: An Equilibrium Analysis,” American

Economic Review, 1990, 80, 107-26.

Hahn, Frank H., "The Stability of the Cournot Oligopoly Solution," Review of Economic Studies, 1962,
29, 329-31.

28


We consider entry into a Cournot oligopoly where n domestic firms and n* foreign firms produce
perfect substitutes. Demand is represented by p(X), where py < 0. Total market output, X, equals the
sum of the individual firm outputs ~ that is, X = Lier X + Lens” Xp + ,, where x denotes a given
firm’s output, i denotes an incumbent domestic firm, i* denotes an incumbent foreign firm, and e denotes
the entrant.

Profits for firm k (k = i,i*,e) are expressed as

= (Xx, - Ax) - fy @)
where c*(x,) is the production cost function and Si is fixed cost.

The first-order condition for firm k’s optimal output choice is as follows:

m, = PO) + pr, - A (a) = 0. )

Under appropriate assumptions, a Cournot-Nash equilibrium is defined by the simultaneous solution of
equation (2) for all k. To ensure the uniqueness and stability of this equilibrium, we assume that each
firm’s marginal revenue is everywhere declining with respect to rival output, and that marginal costs are
not rapidly decreasing.’ Specifically, we assume that

Px + Pot, < OVE (Al)

CG) > pyrwk. (A2)

Equations (A1) and (A2) are common assumptions. In particular, equation (A1) implies that a given firm
reduces output when a rival firm increases output.
Totally differentiating (2), we obtain the following:

@x + PrrpdX + (py - edz, = 0. @)

7 See Hahn (1962), Rosen (1965), and Al-Nowaihi and Levine (1985).
5


welfare). However, the policymaker can achieve the same welfare level as in the complete-information
case if the policymaker can induce the domestic entrant to act as a Stackelberg leader. We thus provide
a rationale for why policymakers should contract with potential entrants to extract output commitments
in return for specified subsidy payments.

In subsidizing entry by foreign firms, the presence of incomplete cost information implies that
the policymaker may pay the entrant more than is needed to induce entry. Since this overpayment would
result in reduced welfare, the policymaker’s response is to not adequately subsidize certain welfare-
improving entry. Our examination of entry subsidies considers the differences in applying subsidies to
domestic and foreign firms and focuses on the role of fixed costs in determining the optimal subsidy.

The paper is organized as follows. Section 2 develops the model. Section 3 considers the welfare
effects of entry; the analysis highlights how optimal entry policy is affected by the market shares of
domestic incumbents and the entrant's costs. Section 4 examines optimal entry subsidies under complete

and incomplete information concerning the entrant’s costs. Section 5 offers concluding remarks.

2. The Model

Our mode! distinguishes between domestic and foreign firms. The distinction between domestic
and foreign firms depends solely on the location of those individuals that have claim to the firm’s profit
Stream. If we assume that only the capital owners receive any rents (i.e., all other productive factors
Teceive a payment equal to that factor’s opportunity cost‘), then it is immaterial whether the productive
resources of foreign firms reside in the foreign country, the home country, or elsewhere. Thus, our
model can represent foreign entry into the home country’s market through either direct investment or

exports.

* It is also assumed that a given factor’s Opportunity cost is unaffected by changes in industry output.

4


can be achieved by subsidizing entry, particularly if entrants incur substantial fixed costs or face higher
marginal costs than domestic incumbents. Nonetheless, entry subsidies may represent a viable second-
best policy option when subsidies to the domestic industry are precluded by their considerable expense
and increases in import tariffs are restricted by institutional barriers (e.g., GATT).

In general, social welfare can be increased by subsidizing privately unprofitable entry whenever
B(xJ) > -x(x/). Theoretically, the home country is indifferent between subsidizing a foreign or domestic
entrant under these conditions. The home country can induce entry by giving the entrant a lump-sum
payment equal to the private losses from entry, i.e., -“(x/). This subsidy payment directly decreases
social welfare in the case of a foreign entrant. Although this subsidy payment is merely a domestic
transfer payment in the case of a domestic entrant, the home country’s welfare is nonetheless reduced by
the entrant’s private losses, x*(x/). However, these losses are less than the external benefits of entry.

Although we have shown that subsidizing entry can raise social welfare, we have not explored
the optimal form of the entry subsidy. Since the entrant’s output choice determines the social benefits
from entry, the policymaker has incentive to influence that choice through the use of output-related
subsidies (e.g., unit subsidies, capital subsidies, or input subsidies for utilities or materials costs).
However, given that the policymaker must ensure that the entrant earns nonnegative profits, and that the
policymaker does not wish to subsidize a foreign entrant beyond the zero profit level, it may be optimal
to supplement an output-related subsidy with a lump-sum subsidy or tax.

We now consider the policymaker’s welfare-maximization problem in choosing its optimal
subsidy. Let s denote a subsidy applied to each unit of output, and / denote a lump-sum subsidy. Letting
¢ denote the entrant’s marginal costs prior to subsidization,” the entrant’s equilibrium output is a
function of its marginal costs net of the output subsidy, expressed by x“(c,s) = x*(c-s), where dx’/de =

-dx‘/ds < 0. Thus, the entrant’s output is a decreasing function of its actual marginal costs and an

» Purely for expositional convenience, we assume that marginal costs are constant.

17


3. Welfare Analysis and Policy Implications

3.1 External Benefits of Entry

From the standpoint of the home country, the welfare effects of entry depend largely on entry’s
impact on domestic consumer surplus and the producer surplus of domestic incumbents. These sources
of surplus are expressed below:

Btxy = § ¥ 9 pede - pX¢e,) + Sues? KU) ©

In equation (5), consumer surplus is expressed by the first two terms on the right-hand side, while the
producer surplus of domestic incumbents is expressed by the third term. In deciding whether to enter,
a given firm ignores the effect of its entry on the above sources of surplus. These welfare effects, while
critical in determining the social value of entry, are external to the firm’s private entry decision.

Based on the above analysis, the external benefits of entry (i.e., B(xJ)) are represented by the
change in equation (§) as the entrant’s output increases from zero to its equilibrium level. We express
these benefits as

Ber) = Ete/)- BO) = 5 f! Ef,) de, )
where x, is the entrant’s equilibrium output level. Due to technological limitations, we assume that there
is a maximum (equilibrium) scale of entry, x,", that any firm in the set of potential entrants is unable to
exceed. For any potential entrant, it holds that x < x,".°

It is important to consider the external benefits of entry because general policy recommendations

are based on these benefits. For example, if we can show that the external benefits of entry are positive

° One might view this restriction in the following fashion. There is a family of cost functions that
describe the technology used by any potential entrant, and the set of Potential entrants can be described
based on their distribution over this family of functions. Assuming that profit functions are well-behaved,
there is a mapping between an individual cost function and the entrant’s output in a Cournot-Nash
equilibrium. Thus, the distribution over the family of cost functions is equivalent to a distribution over
various equilibrium outputs, where the support of this distribution reaches the maximum value, x",
known as the maximum scale of entry.


condition is satisfied:

BCC)", = Efx"(o)x", = tc). (16)
Combining equations (15) and (16), we obtain:

Elx‘(c)) + p + py(c)~¢ = 0. an

Equation (17) must hold in order to both satisfy incentive compatibility and permit an optimal amount
of entry. Of course, in the complete information case, the entrant’s Output under Cournot behavior,
x“(c,s), satisfied the first-order condition, (p + p,x“(c,s)-c) + s = 0, Substituting this expression into
the optimal output subsidy expressed by equation (12), it holds that the welfare-maximizing output level
for each cost type satisfies the following condition under complete information:

ECs") + (p + pyx“(cs*) - c) + PxX"(c,8*(aX (x'(c,8*)\/dx,) = 0. (18)

Equation (18) differs from equation (17) by the presence of the term, PrX“(c,s* aX (x"(c,s*))/dx,),
which captures the effect on the entrant’s profits due to the retrenchment of rival output. Of course, this
term would be included in equation (15), and Consequently in equation (17), if the entrant acted as a
Stackelberg leader. By committing to an optimal (output-related) subsidy schedule in advance, and
subsequently contracting with any potential entrant so that the entrant commits to a specified output in
Teturn for the payment specified by the subsidy schedule, the Policymaker may Potentially force the
entrant to act as a Stackelberg leader. If this behavior arises, and the policymaker uses the output-related
subsidy schedule, t<"(c)) = B(x*(c)), then the same welfare level is attained as under complete
information (because equations (16) and (18) are both satisfied). Thus, the policymaker should extract
an output commitment from any potential entrant as a condition for making the subsidy payment.

However, if an entrant continues to act as a Cournot player, the Policymaker cannot induce the

welfare-maximizing output choice without tisking entry by firms with excessively high fixed costs.

23


ENTRY POLICY AND ENTRY SUBSIDIES

James D. Reitzes”
Emst & Young LLP

Oliver R. Grawe
Federal Trade Commission

November 3, 1995

JEL Codes: F13, L50, L52, LAO

Abstract: This paper provides a theory that explains why governments allow free entry and selectively
promote entry under certain conditions and deter entry under other conditions. The analysis also
identifies conditions under which optimal policy requires that large-scale entry is freely permitted and
small-scale entry is deterred. In our model, policymakers use entry policy to Strategically shift rents
away from foreign producers toward domestic producers and consumers.

Since it may be socially beneficial to subsidize entry by both domestic and foreign firms, we
explore the optimal means of promoting entry under complete and incomplete information concerning the
entrant's marginal and fixed costs. Under complete information, welfare can be maximized by a two-part
subsidy mechanism consisting of a per-unit output subsidy in combination with a lump-sum subsidy or
tax. Under incomplete information, the policymaker has incentive to treat domestic and foreign entry
differently in setting an optimal entry subsidy. With respect to domestic entry, the policymaker can
eliminate any potential welfare losses due to incomplete information if the entrant can be induced to act
as a Stackelberg leader. Otherwise, the policymaker may undersubsidize domestic entrants with high
marginal costs and oversubsidize entrants with low marginal costs. In the case of foreign entry, the
Presence of incomplete information implies that entry is undersubsidized.

“ Correspondence to: Ernst & Young LLP, 1225 Connecticut Avenue, NW; Washington, DC 20036.
We thank Morris Morkre for useful discussion.


where s{x,) is firm i’s market share (i.e., s{x,) m x(X(x,))/X(x,)). Depending on cost and demand
conditions, 6, may be either a constant or a function of x,.

Referring to equation (9), we define the function, I(x,) = [1 - j2;" s(x, (1 + 0{x,))J. Note that
Efx,) = -pyX(dX/dx,)I(x,), where -p,X(dX/dx,) > 0. Thus, E,(x,) bears the same sign as I(x,).

Since s{x,) is monotonically decreasing, we might expect that I(x,) would be monotonically
increasing in many instances." Although we make this assumption in the following analysis, our
discussion also considers how our results are changed if I(x,) is instead monotonically decreasing.

Let 1(0) = 0. Based on our assumption that J(x,) increases monotonically, it then follows that
I(x) > 0 for 0 < x, < x,". Hence, E,(x,) > 0 for 0 < x, < x,". Condition (a) in Lemma 1 is
therefore satisfied (because, from equation (6), B(x/) > 0 for0 < xf < x,").

Note that 1(0) is merely the value of J under existing market conditions (i.e., prior to entry).
Given that 1(0) = 0 if ¥),2:" s{1 + 8) = 1 under existing conditions (where s, denotes firm i’s market
share), the above discussion leads to the following conclusion:

Proposition 1. Free entry (and selective promotion of entry) is optimal if and only if

Lies” S{1 + 6) S I under existing conditions. Otherwise, some form of entry deterrence is optimal.

Next, let I(x,") S 0. Based on our monotonicity assumption, it follows that I(x) < 0 for
O<x,<x,". Hence, E(x,) < 0 for 0 < x, < x,". Condition (6) in Lemma 1 is thus satisfied
(because B(x/) < 0 for 0 < xJ < x,").

Given that J(x,") < 0 if £2," s{1 + 9) = 1 at the maximum scale of entry, the above

"2 When marginal costs are constant, this condition holds except when pyyy assumes large negative
values. Thus, J(x,) is always increasing under constant marginal costs and a linear or quadratic demand
function. When marginal costs increase or decrease linearly, this condition is satisfied unless pyc’,, or
Pxax assume large negative values (i.e., large relative to the magnitude of (py + pyxJ’ and (pyx)’).
Finally, this condition is less likely to hold if marginal costs increase at a rapidly increasing rate.

10


Lemma 1. The home country’s optimal policy toward entry is:
(a) free entry (and selective promotion of both foreign and domestic entry)
if Bax) = Ofor0 < xf < x,";
(6) complete deterrence of foreign entry and selective deterrence of domestic entry
if Bal) < 0 for0 < xf < x";
(c) deterrence or allowance (and possible promotion) of entry depending on the

entrant’s output level.

Lemma 1 can be expressed alternatively as follows: The home country’s optimal policy is free entry if
condition (a) is satisfied. Otherwise, optimal policy requires some form of entry deterrence.
Conditions (a) or (b) in Lemma 1 may not be difficult to satisfy. For example, if E,(x,) > O for
0 < x, < x,", then condition (a) is satisfied (because, from equation ©), Bix) = Ofor0 < xf 5 x,").
Consequently, the optimal policy toward entry depends on the behavior of E,(x,).
Differentiating E with respect to x, (see equation (5)), we obtain:

Efx,) = -pxX(dX/dx,) + Dini" de/dx, . ”

We obtain an expression for dx'/dx, by differentiating equation (1’):""
dxi/dx, = (p-c)(ax /AXNdX/dx,) + p,x{dX/dx,),

= prtdl + ONdX/dey. ®

Substituting equation (8) into equation (7), it follows that

Ex,) = -pyX(dX/dx,)[1 - Li-7 sfx I + Od), @)

a Since we are examining the equilibrium behavior of the incumbent firms, it necessarily holds that
p-c', = -pzx; (see equation (2)) and that 8x/@X = -,. (see equation (4)). These results are used to derive
the second equality in equation (8).




Horstmann, Ignatius J. and Markusen, James R., "Up the Average Cost Curve: Inefficient Entry and

the New Protectionism,” Journal of International Economics, 1986, 20, 225-47.

Krugman, Paul R., "Import Competition as Export Promotion: International Competition in the Presence
of Oligopoly and Economies of Scale," in H. Kierzkowski, ed., Monopolistic Competition and

International Trade, Oxford: Clarendon Press, 1984, 180-93.

Myerson, Roger B., "Incentive Compatibility and the Bargaining Problem," Econometrica, 1979, 47,

61-73.

Rosen, B., “Existence and Uniqueness of Equilibrium Points for Concave N-Person Games,"

Econometrica, 1965, 33, 520-34.

U.S. International Trade Commission, "Operations of the Trade Agreements Program, 42nd Report -

1990,” Publication 2403, July 1991.

U.S. International Trade Commission, “Certain Flat-Rolled Carbon Steel Products from Argentina,
Australia, Austria, Belgium, Brazil, Canada, Finland, France, Germany, Italy, Japan, Korea, Mexico,
the Netherlands, New Zealand, Poland, Romania, Spain, Sweden, and the United Kingdom - Volume I:

Information Obtained in the Investigations," Publication No. 2664, August 1993.

Venables, Anthony J., "Trade and Trade Policy with Imperfect Competition: The Case of Identical

Products and Free Entry," Journal of International Economics, 1985, 19, 1-19.

29


Based on (A1) and (A2), it then follows that

dx,/dX = 0, where 0, = [(py + Prxt)/(Py - C*,)] > 0. o

Thus, 6, represents the reduction in firm k’s equilibrium output that occurs whenever total market output
increases by one unit in equilibrium. This term is fundamental to the following welfare analysis.®

It is useful for purposes of welfare analysis to treat the entrant’s output exogenously and examine
the resulting Cournot-Nash equilibrium among the incumbent domestic and foreign firms. In this case,
we use the function, X(x,), to describe the relationship between the entrant’s output and the market’s
equilibrium output. Our stability conditions ensure that aX/dx, > 0.

Furthermore, equation (2) describes a functional relationship between an incumbent firm’s
equilibrium output and the market's output. For firm k, we denote this relationship by x,(X), and the
behavior of dx,/dX is described by equation (4). Based on the Previous discussion, we can express the
functional relationship between firm k’s equilibrium output and the entrant’s output as x,(X(x,)) (where
ax/dx, = (0x,/aX)(dX/dx,) = -0,(dX/dx,). Inserting this expression into equation (1), firm k’s
equilibrium profits become a function of the market's equilibrium output X(x,), which, in turn, depends
on the entrant's output level:

XD) = XxX) - He (XD) - fp qa’)

The above expression is important to the following welfare analysis, which considers the effect of entry

on the equilibrium profits of incumbent firms.

* Farrell and Shapiro (1990) use a similar derivation to analyze mergers in a market containing
exclusively domestic firms.


foreign, y = 0. Condition (11a) holds only if A = J, implying that the entrant’s zero-profit constraint
is binding. Since any increase in the subsidy payment transfers income abroad, the home country’s
subsidy payment should only be sufficient to ensure that the entrant earns zero profits. In fact, a lump-
sum fax is appropriate when the optimal per-unit output subsidy is large enough to ensure that the foreign
entrant earns positive profits.*

From the above discussion, it is clear that the structure of a per-unit output subsidy and a
lump-sum subsidy is an efficient mechanism for inducing an entrant to choose the welfare-maximizing
output level under complete information. It can be shown that other more complicated mechanisms,
involving nonlinear output subsidies and lump-sum subsidies or taxes, may be used to attain the same
welfare level. We conclude as follows:

Proposition 5. With respect to entry subsidies under complete information, social welfare can be
maximized through a two-part structure, (s*,1*), consisting of a per-unit output subsidy and a lump-
sum subsidy or tax. The per-unit subsidy, s*, is positive and satisfies equation (12). In the case of
@ foreign(domestic) entrant, the lump-sum subsidy or tax is set to ensure that the entrant’s profits are

zero(nonnegative).

The above proposition assumes that the policymaker has complete information concerning the
entrant’s marginal and fixed costs, so that it can set the optimal output subsidy for the entrant’s cost type

and exactly calculate the private losses from entry (in the absence of a subsidy). Now suppose that the

%5 In fact, a lump-sum tax (in combination with a per-unit output subsidy) is always required when
E,,(x,) > 0. Under this condition, the marginal external benefits from an additional unit of the entrant's
output exceed the average external benefits per unit of the entrant’s output. Since the result in
equation (12) implies that the per-unit output subsidy exceeds the marginal external benefits from the
entrant’s output, it follows that the per-unit output subsidy exceeds the average external benefits per unit
of the entrant’s output. Because optimal policy requires that the toral subsidy payment be no greater than

the roral external benefits from entry, a lump-sum tax must be imposed to offset the excessive payments
made through the output subsidy.

20


information.” Consequently, there is an unavoidable loss of welfare. This result arises because the
policymaker cannot induce additional entry without increasing the overall subsidy payment to a given cost
type, thereby increasing the subsidy paid to entrants with lower fixed costs that would have entered the
market at existing subsidy levels. The increased subsidy payment to these foreign entrants lowers
domestic welfare. This type of information cost is unique to the case of foreign entry. It does not arise
under domestic entry (unless the social value of each unit of government revenue exceeds one) because

the increased subsidy is merely an increased transfer payment from the government to domestic entrants.

5. Concluding Remarks

This paper provides an explanation of government policy toward entry. Based on the unilateral
incentives of policymakers to maximize domestic welfare, we identify conditions where policymakers
should allow free entry and selectively promote entry, and conditions where they should deter entry.
In certain cases, the decision to allow entry depends on the entrant’s expected output level. Lower-cost
firms may be permitted to enter, while higher-cost firms may be deterred from entering the market.

In general, entry policy evolves as market structure changes. As domestic firms become more
prominent in the market, policymakers have stronger incentives to deter further entry.

Our analysis also shows that a policy permitting free entry should be coupled with a policy that
subsidizes entry under appropriate circumstances, regardless whether the entrant is a domestic or foreign
firm. With complete information concerning the entrant’s costs, the optimal subsidy mechanism consists

of a per-unit output subsidy and a lump-sum subsidy or tax, where both domestic and foreign entrants

® Proof available from authors. Output choices are also inefficient. Assuming that the distributions
of marginal and fixed costs are uniformly and independently distributed (and that demand is linear), it
can be shown that foreign entrants with particularly high marginal costs, and those with particularly low
marginal costs, produce more than the “constrained” welfare-maximizing output level for their cost types

(i.e., the output level that satisfies equation (17)). Other entrant types may produce more or less than
this output level.

26


of related infrastructure such as road and rail links, port facilities, and a power-generation plant,
the Korean government also gave Posco discounts of 20 percent for gas usage, 30 percent for water
usage, and 40 percent for usage of rail transportation? Indicative of the broad nature of Airbus’
subsidies is the program intended to protect its sales against adverse exchange rate movements.
This program alone resulted in payments to Airbus of DM390 million in 1990; however, these payments
Tepresent a small portion of the nearly $13.5 billion in government subsidies received by Airbus through
1990.‘ These examples show that entry subsidies may be in the form of output-related payments, such
as discounts on input costs and rebates for adverse exchange rate movements, as well as fixed payments.

Of course, not only do governments promote entry under certain circumstances, but they also
deter entry through such measures as import licenses, quality standards, and domestic-content
requirements. Entry-deterring and entry-promoting measures ultimately alter market structure and the
competitive position of specific firms in the market; thus, these measures may be a prime vehicle for
implementing so-called industrial policy.

This paper provides a theory to explain why governments have varying policies toward entry and
why entry policy differs across sectors. Prior to this paper, little attention has been paid to the strategic
aspects of directly managing competition in a market where both domestic and foreign firms compete.*
Dixit (1984) assessed the welfare impact of mergers, and the associated implications for antitrust policy,
by examining exogenous changes in the number of domestic and foreign firms in an oligopoly model
where all producers in a given country were identical. He drew explicit conclusions only for cases with

restricted demand and cost assumptions.

> For detail, see Amsden (1989), pp. 292 and 297, and USITC (1993), p. E-7.
* See USITC (1991), pp. 102-103.

5 The international trade literature has considered how free entry affects the welfare impact of
various trade policies (see Venables, 1985 and Horstmann and Markusen, 1986). Using a comparative-

Static approach, these papers analyze the effects of trade Policies in an equilibrium with free entry.

2


allowed into the market. Relatively inefficient domestic entrants (i.e., 9 > 1”) are selectively admitted
into the market if they generate sufficient profits to compensate for their negative external benefits.
Consequently, those domestic entrants with relatively high marginal costs, but relatively low fixed costs,
may still gain admittance to the market.

The reasoning behind Proposition 3 is that the market shares of domestic incumbents
Progressively shrink as the entrant increases in size. At the same time, the home country’s welfare
benefits from a given increase in the entrant’s output typically become larger as the market shares of
domestic incumbents shrink. Hence, large-scale (i.e., low-cost) entrants are often capable of providing
more welfare benefits than smaller-scale (i.e., higher-cost) entrants.

More formally, entry creates two key effects: (i) a Price reduction, and, (ii) an output reduction
by domestic incumbents. The price reduction raises consumer surplus but lowers producer surplus;
so, the net gain in social welfare equals the price change multiplied by the amount by which total
domestic sales exceed domestic output (i.e., the term, PrX(aX/dx 1 - L401" sfx] in equation (9)).
Clearly, the net welfare gain from the price reduction becomes larger as the combined market share of
domestic incumbents becomes smaller.

The second effect of entry, the reduction in the output of domestic incumbents, causes a loss of
producer surplus since price exceeds marginal cost. As expected, this loss frequently becomes smaller
as the market share of domestic incumbents declines. This result arises for two reasons. Most simply,
it occurs because the total output reduction by domestic incumbents is smaller when there are fewer
domestic firms in the market. However, it also holds that a domestic firm’s price-cost margin is
Positively related to its (equilibrium) market share, implying that a domestic firm’s output reduction
results in a smaller loss of producer surplus when its market share is relatively small (as expressed by
the term, p,X(dX/dx,)(¥ ;.;" 5{x,)6,), in equation (9)). Entry is thus more likely to increase welfare when

domestic firms occupy a relatively small portion of the market.

13


linear.

Under the conditions described above, the market-share threshold T separates a free-entry policy
from an entry-deterrence policy. All market shares below T are in the free-entry range, while those
above T are in the entry-deterrence range. For example, T = 1/2 when demand is linear and marginal
costs are constant, implying that free entry is optimal if and only if the combined market share of
domestic firms is less than one half.'© Otherwise, when the combined market shares of domestic
incumbents exceeds one half, some form of entry deterrence is optimal.” In examining merger
behavior, Dixit (1984) obtains an analogous result under the same cost and demand restrictions, assuming
that firms are homogeneous. Here, we find that this particular result extends to a model where firms
have varying costs.

As T declines in size, the free-entry range becomes smaller. Given that T and 6 are inversely
related, the free-entry range becomes smaller as @ increases in size. Note from equation (4) that
6 = [Px + Pox )V(Px -'¢',)J, where (py + pyr) and (py - ¢’,,) are both negative in sign (see (A1) and
(A2)). Hence, 6 increases (and T decreases) as pyy and c’,, decline in value. From this, we conclude
as follows:

Remark. The range of market shares where free entry (and selective Promotion of entry) is the optimal
policy shrinks as the demand curve becomes increasingly concave and as domestic incumbents’
marginal cost curves decline in slope.

‘6 Based on these cost and demand assumptions (i.¢., Py» ¢’., = 0) and the definition of 6; from
equation (4), it holds that 6; = J v i. Consequently, T = 1/(1+6) = 1/2.

'" Specifically, if the combined market share of domestic incumbents would still exceed one half at
the maximum scale of entry, then optimal policy recommends that foreign entry be completely deterred
and domestic entry be selectively deterred (see Proposition 2). On the other hand, if this combined
market share currently exceeds one half, but would be substantially less than one half at the maximum
scale of entry, then optimal policy recommends that large-scale entry be permitted and small-scale entry
be completely deterred in the case of a foreign entrant and selectively deterred in the case of a domestic
entrant (see Proposition 3).

15


ENTRY POLICY AND ENTRY SUBSIDIES

1. Introduction

In recent years, the strategic trade policy literature has provided a cogent explanation for
policymakers’ use of various trade policy instruments, such as subsidies, tariffs, and quantitative
restrictions.' Absent from this literature, however, has been an explanation of policies that either
encourage or deter entry. Policies that encourage entry are selectively applied, such as when
governments provide loan guarantees, equity partnerships, and capital subsidies to specific firms in order
to induce them into the market. Incumbent firms, by virtue of their presence in the market, do not obtain
these subsidies. Entry subsidies are attractive policies because they are potentially less costly to the
government than general industry subsidies, which is a particularly important consideration for
policymakers facing tight budget constraints. In general, these subsidies may be a viable second-best
option when budgetary and institutional constraints preclude the use of other trade Policies.

Entry-promoting and entry-deterring policies are both prevalent and substantial on a global scale.
The Korean government’s subsidy package to steel producer, Posco (Pohang Iron and Steel Company),
and the European Community’s support of the aerospace manufacturing consortium, Airbus, are two
Prominent examples of entry promotion.’ Besides the conventional forms of entry subsidies (e.g., loan
guarantees, equity infusions and preferential tax treatment), both cases illustrate the role of nontraditional
subsidies intended to induce entry and influence the entrant’s output choice. The Korean government
targeted Posco as the sole company to receive subsidies for the construction of an integrated steel mill

at Kwangyang Bay. Besides providing the mill site and securing financial assistance for the construction

' Among others, see Brander and Spencer (1984), Dixit (1984), Krugman (1984), and Eaton and
Grossman (1986).

? See USITC (1993), Appendix E, for a detailed account of the subsidies granted to foreign steel
producers.


The entrant will not provide the welfare-maximizing output level under Cournot behavior unless the
subsidy for a marginal output increase equals E,(x'(c)) + prX(chaX(x'(c)/dx,)), which exceeds the
external benefits of that additional output, E,(x‘(c)). Since this relationship must hold with respect to the
optimal output choice of each type of entrant, it is clear that the total subsidy payment would eventually
exceed the external benefits of entry if the policymaker followed this strategy in determining the entrant’s
output.””

To reduce the potential losses from excessive entry, it can be shown that, under an assumption
that marginal and fixed costs are uniformly and independently distributed (and that demand is linear),
the policymaker undersubsidizes domestic entrants with relatively high marginal costs and oversubsidizes
domestic entrants with relatively low marginal costs in comparison to the efficient outcome.
Undersubsidization occurs when firms whose entry would increase social welfare are not subsidized
sufficiently to enter the market. Oversubsidization occurs when firms whose entry would decrease social
welfare are subsidized sufficiently that they enter the market. Under incomplete information (and the

previous assumptions), the optimal subsidy policy toward domestic entrants also implies that high

2 Under Cournot behavior by the entrant, the policymaker wants to induce a domestic entrant to
produce additional output in equilibrium so that the entrant realizes the additional profits that result from
the associated reduction in rival output. To get the entrant to produce this added output, the policymaker
is willing to pay an amount equal to these additional profits, PxX’(c(dX,(x‘(c)/dx,)), plus an amount equal
to the external benefits of the additional output, E,(x“(c)). Consequently, the policymaker is willing to
pay the amount, E,(x‘(c)) + PxX'(c)(dX (x‘(c)/dx,)), to induce the entrant to produce another unit of
output.

However, once the policymaker has induced the entrant to produce additional output and
internalize the additional profits due to rival retrenchment, it would be socially beneficial to have
subsidized entry only if the private losses from entry were less than or equal to the external benefits of
entry. Consequently, to prevent welfare-reducing entry by firms with excessively high fixed costs, the
total subsidy payment should not exceed the external benefits of entry. This implies that the policymaker
would like to use an output-based subsidy to encourage additional output by the entrant, but then reduce
the total subsidy payment through a lump-sum tax. The efficient outcome is unattainable, though, because
setting the optimal subsidy in this manner for each type of entrant would violate incentive compatibility.

If the entrant acts as a Stackelberg player, there is no need to use an output-based subsidy to
induce the entrant to internalize the profit benefits resulting from rival retrenchment. Consequently, the
efficient outcome is attainable by setting the subsidy equal to the external benefits of entry.

24




receive the same output subsidy.

With incomplete cost information, the optimal entry subsidy should treat domestic and foreign
entry differently. Optimizing behavior implies that the policymaker should undersubsidize foreign entry.
Moreover, the policymaker should undersubsidize domestic entrants with relatively high marginal costs
and oversubsidize domestic entrants with relatively low marginal costs. However, in subsidizing domestic
entry, any potential welfare losses under incomplete information can be avoided if the policymaker can

induce the entrant to act as a Stackelberg leader.

27


discussion leads to the following conclusion:

Proposition 2. Complete deterrence of foreign entry (and selective deterrence of domestic entry) is
optimal if ¥;.;" s{1 + 0) = 1 at the maximum scale of entry."

To complete our analysis, another possibility needs to be addressed, i.e., 1(0) < 0 < I(x,").
Since I(x,) is assumed to be monotonically increasing, there exists I(x,’) = 0, where 0 < x,’ < x,".
Moreover, I(x,) <(>) 0 for x, <(>) x,’, which implies that E(x.) <(>) 0 for x, <(>) x,’.
The external benefits from entry, i.e, Bx) = f a E,x,) dx, are therefore negative and
monotonically decreasing for 0 < x/< x,’. After reaching a minimum at x,’, B(x,’) is then
monotonically increasing for x,’ < x/ < x,". Consequently, B(x,’) is negative in sign, but B(x,") may
assume either positive or negative values.

Based on the above reasoning, if B(x,") < 0, it follows immediately that B(x/) < 0 for 0 < xf
 x,". In this case, Lemma 1 indicates that optimal policy requires complete deterrence of foreign entry
and selective deterrence of domestic entry. However, if B(x,") > 0, there exists x,", where x,’ < x,"
<_x,", such that B(x,") = 0. Moreover, B(x/) <(>) 0 for x/ <(>)x,". The external benefits from
entry are positive whenever the entrant’s output exceeds x,”, implying that free entry should be allowed
(and entry should be selectively promoted) at these output levels. However, the external benefits from
entry are negative when the entrant’s output is below x,", implying that foreign entry should be
completely deterred and domestic entry should be selectively deterred at these output levels. In this case,

the output threshold, x,”, separates a free-entry policy from an entry-deterrence policy. We summarize:

‘8 We show in Proposition 3 that this condition, 5,.;" s{x,"\I + Odx,")) = 1 (i.e., I(x,") < 0),
is sufficient, but not necessary, to ensure that foreign entry should be completely deterred (and domestic
entry should be selectively deterred).

11


Finally, assume that the function, J(x,), is monotonically decreasing. Based on reasoning
analogous to that used above, free entry is optimal when the condition identified in Proposition 1 holds
at the maximum scale of entry. Complete deterrence of foreign entry and selective deterrence of domestic
entry is optimal when the condition identified in Proposition 2 holds under existing conditions. The
results in Proposition 3 are changed, however, so that the proper entry policy is either to allow free entry
at all output levels, or to potentially deter large-scale entrants while allowing the free entry of small-scale
entrants. This change occurs because, if I(x,) decreases monotonically, the reduction in the domestic
incumbents’ output in response to a marginal increase in the entrant's output becomes significantly larger
as the entrant’s output increases. This effect swamps the other effects mentioned above, implying that

the welfare benefits from entry may eventually decrease as the entrant’s output increases."*

3.3 Threshold Domestic Market Shares

Based on the prior analysis, the policymaker’s decision to permit or deter entry depends largely
on the combined market share of domestic firms. The following proposition states this relationship
explicitly:
Proposition 4. Let 0, = 6 i. Define T = 1/(1 + 6). Free entry (and selective promotion of entry)
is optimal if and only if the combined market share of domestic firms is less than or equal to T.

Otherwise, some form of entry deterrence is optimal."

Note that 6, = 6 v i when domestic firms are homogeneous or when demand and cost functions are

** It should be noted, though, that J(x,) is not likely to decrease monotonically unless marginal costs
are rapidly increasing or the (inverse) demand curve becomes increasingly concave as output increases
(see footnote 12).

'* The proof follows directly from Proposition 1. If 6, = 6 i, then the condition,

Lies" S41 + 6) < 1, implies that [,.;" s, < 1/(1 + 0), where Liar" 5; is merely the combined market
share of the domestic firms.

14