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Strategic trade policy
Journal of International
Economics 35 (1993) 169-183. North-Holland
Strategic trade policy Choosing between export subsidies and export quotas under uncertainty Ram Shivakumar” Department of Economics, Indiana University, Bloomington, IN 47405, USA
Received July 1991, revised version received January 1993
I consider a trade policy game in which the choice of policy (subsidy or quota) and time of implementation mfore (commit) or after (delay) observing the random demand intercept] is endogenously determined. Each country has four possible options: CQ, CS, DS and DQ, where CQ denotes a commitment to a quota and the other options are similarly labeled. For the special case of an international duopoly, countries prefer quotas to subsidies: CQ is chosen if noise is ‘small’ and DQ if noise is ‘large’. Also interesting is that quotas in the DQ regime coincide with firms’ desired exports.
1. Introduction I consider a trade policy game between two countries in which each country makes two strategic decisions. First, each can choose a type of policy, either an export subsidy or a strict quantity control. Second, each has the prerogative of implementing policy before observing the random demand intercept (commitment) or delaying the implementation of policy till after observing the random demand intercept (delay). Thus each country has four possible policy options: CS, CQ, DQ and DS, where CS stands for a commitment to a subsidy and the other policy options are similarly labelled. Depending on the option chosen and the realization of the uncertain demand parameter, firms may want to produce less than, more than, or possibly exactly the required quantity. Thus, the quantity control may or may not have the ‘normal’ interpretation of an export quota as a restraint on exports. However, in the paper, I will often refer to the policy as a ‘quota’ for expositional convenience. Correspondence to: Ram Shivakumar, Department of Economics, Indiana University, Bloomington, IN 47405, USA. *An earlier version of this paper was presented at the Spring 1991 Mid-West International Economics Meetings in Evanston. I thank John Wilson, David Besanko, Roy Gardner, Raymond Riezman, Arindam Bandopadhyay, Krishna Srinivasan and two anonymous referees for their helpful comments. The usual disclaimer applies.
0022-1996/93/%06.00 0
1993-Elsevier
Science Publishers B.V. All rights reserved
170
R. Shivakumar,
Strategic trade policy
How can these four policy options be ranked in the flexibility-commitment spectrum? Intuitively, CQ represents maximum commitment and DS and DQ represent maximum flexibility. Furthermore, ranking these instruments is simplified by recognizing that countries choosing between DS and DQ will choose DQ because it is preferable to opt for the policy option that makes one’s own output reaction function less elastic, since this weakens the rival’s ability to shift profits. Amongst the remaining three policies, CQ represents maximum commitment, DQ represents maximum flexibility and CS represents intermediate flexibility. Therefore, one might conjecture that CQ is the best policy under ‘small’ noise, CS the best policy under ‘intermediate’ noise and DQ the best policy under ‘large’ noise. Results, for the special case of an international duopoly,’ show that countries choose CQ in the ‘small’ noise case and DQ in the ‘large’ noise case. There are also three ‘intermediate’ noise cases. In the first ‘intermediate’ case, one country chooses CQ and the other chooses DQ. In the second ‘intermediate’ case, both countries choose DQ while in the third ‘intermediate’ case, there are two equilibria. In one equilibrium, both countries choose CS, and in the other, both countries choose DQ. However, DQ payoff dominates CS. That is, the payoffs for both countries under DQ are higher than under CS2 These results suggest that countries will prefer export quotas to export subsidies. What is also interesting is that with the DQ policy, the export quotas coincide with firms’ desired exports. That is, the de facto policy of each country is free trade. This result is noteworthy because it contrasts with a widely held view that Nash equilibria in models of imperfect competition typically call for interventionist trade policy. These results on the choice of timing and policy are in contrast to existing results in the strategic trade policy literature. The seminal paper on strategic trade policy is by Brander and Spencer (1985) who explain the role of an export subsidy in terms of a profit-shifting effect. Using a Cournot duopoly model, they show that each country subsidizes its firms exports even though such a policy leaves both firms and countries worse off than they were before the intervention.3 Cooper and Riezman (1989) argue that constraining each country’s policy choice to export subsidies is unrealistic. They consider a model in which countries choose a type of policy (an export subsidy or a strict quantity control) in the first stage and a level for policy in the second stage. The random intercept of demand is then revealed after which firms in each country compete. The ‘In Shivakumar (1992a), I use simulation methods to examine how departures from the duopoly framework affect results. ‘A formal definition of payoff dominance is given in Harsanyi and Selten (1988). ‘Eaton and Grossman (1986) point out that the form of policy (export subsidy vs. export tax vs. free trade) is sensitive to assumptions about the type of conjectures firms make (Cournot vs. Bertrand vs. conjectural variations).
R. Shivakumar, Strategic trade policy
171
subgame perfect equilibrium depends on the noise. With small noise, countries choose quantity controls because each country is able to immunize its firms from the profit-shifting policies of rivals. With large noise, countries choose export subsidies because firms are given the flexibility to respond to the environment. Arvan (1991) considers a similar model but restricts the countries’ options to CS and DS. He shows that the subgame perfect equilibrium frequently involves asymmetric timing, i.e. the country with the relatively small number of firms acts like a Stackelberg leader while the country with the relatively large number of firms acts like a Stackelberg follower. In contrast to the above papers, the present paper allows countries the option of choosing both a type of policy and a time to implement the policy. That is, countries choose between CS, CQ and DQ. The equilibrium choice of timing and policy is characterized by examining three separate games, each of which has only two policy options. In the first game (the CS-CQ game), the countries choose between CS and CQ. In the second game (the CQ-DQ game), the countries choose between CQ and DQ, while in the third game (the CS-DQ game), the countries choose between CS and DQ. Each of these games has the property that one of the policy options is more flexible and hence performs better when there is large noise, while the other policy option performs at least as well when there is small noise. Section 2 describes the basic model and the structure of the trade policy game. Section 3 characterizes equilibria in the CS-CQ game, section 4 characterizes equilibria in the CQ-DQ game and section 5 characterizes equilibria in the CS-DQ game. Section 6 characterizes subgame perfect equilibria when countries can choose between CS, CQ and DQ. Section 7 concludes. 2. The model Ni firms from country i and Nj firms from country j produce a homogeneous commodity and compete as quantity-setters in a third market. Each firm is identical and incurs a constant marginal cost of production, c > 0. The inverse demand function is given by
P(Xi +Xj)=U-b(Xi
+Xj)+8,
i#j,
(I)
where Xi = Nixi [i, j = 1,2] and Xi represents the quantities exported by each firm in country i. The parameters a and b are positive and it is assumed that a is strictly greater than c. 13is a random disturbance term with mean zero and a variance denoted by 0’. Each firm chooses output, xi, to maximize profits given by ni=[P(Xi+Xj)-C]Xi,
i#j=1,2.
(2)
R. Shivakumar,
172
Strategic trade policy
From the first-order conditions for this problem, it is possible to show that Xi(Xj)
=
a-c+O--bNjxj b(Ni+l)
It is straightforward firm profits equal
’
i#j=
1,2.
to establish that equilibrium exports and expected per
(a-c+@ xi = b(N, + Nj + 1)’
EZIi =
(a--)‘+a2 b(N, + Nj + 1)2’
i#j=
1,2.
(4)
The presence of supranormal profits may provide each country with the incentive to intervene. But the policy chosen by each country will depend on the variability of demand and the policy of its rival. Trade policy may thus be seen as the outcome of a game between countries. The structure of the game considered here is as follows. In the first stage of the game, each country makes two decisions simultaneously. Each chooses a type of policy (an export subsidy or a strict quantity control) and a time to implement the policy (commit or delay). In the second stage, countries choose a level for their policy instrument. If a country commits to policy, then the level of the policy instrument is chosen before the random demand intercept is revealed.4 If, on the other hand, a country chooses to delay implementation, the level of its policy instrument is chosen after observing the random demand intercept. In the third stage of the game, firms choose their output to maximize profits contingent on the policies chosen. If a country chooses a quantity control policy, then it is assumed that firms in this country export exactly the quantity chosen. Thus each country has three possible policy options: CS, CQ or DQ.5 The equilibrium choice of policy is characterized by studying three games, each of which allows only two policy options. In the first game (the C!S--CQ game), each country chooses a level for its subsidy/quota before observing the random demand intercept. In the second game (the CQ-DQ game), the countries choose between implementing a quota before and after observing the random demand intercept. In the third game (the CS-DQ game), the countries choose between implementing a subsidy before observing the random demand intercept and implementing a quota after observing the random demand intercept. A comparison of expected payoffs in each game determines which policy is chosen. The solution concept adopted is the subgame perfect equilibrium: that is, non-credible threats are excluded.
“The distribution of the random demand intercept is common knowledge. It is assumed the countries cannot design policies so as to induce firms to reveal the true state of nature. 5The fourth option, DS, is eliminated because DQ dominates it.
that
R. Shivakumar,
3. The CS-CQ
173
Strategic trade policy
game
In this game, each country chooses the level of its policy variable before intercept is revealed. This is identical to the game the random demand considered by Cooper and Riezman (1989) and hence only the essentials of the analysis are repeated here. Suppose that each country provies a per-unit export subsidy, Si, to each of its firms. Each country chooses a value for the subsidy (prior to the resolution of uncertainty and before the firms decide their outputs) to maximize expected per-firm profits, net of subsidies. Such a specification is appropriate since it is assumed that there is no domestic consumption, countries are risk neutral and income distributional issues are not relevant. Country i’s maximization problem is given by i#j=
maxEHi(xi(Si,Sj),xj(Si,Sj)), 6%
1,2,
(5)
where E denotes the expectation operator. Substituting the equilibrium value of the export subsidy [obtained by solving the pair of first-order conditions to eq. (5)] in eq. (5) it is possible to show that Encs/cs
I
G2 l)(a-c)2 bNi(Ni + Nj + 3)‘+b(fi_T~l)”
=
(Nj
+
i#j=
(6)
1,2,
where the superscripts denote the policies chosen by each country.6 Suppose that each country chooses an export quota. Then each country chooses its export quota to maximize expected per-firm profits, given by EHi =[P(X,
+Xj)-c]xi,
i#j=
1,2.
(7)
Substituting the equilibrium value of the export quota (obtained by solving the pair of first-order conditions for the above equation) in eq. (7) it is easy to show that E@Q/CQ
=
b$,
i = 1,2. I
Now suppose that country i subsidizes its firms’ exports chooses an export quota.’ Country j’s problem is given by max Eflj(xj, xj
Xi(Si, xj)),
and
country
i #j,
6That is, EI$siCS represents the equilibrium value of expected commit to subsidies. ‘The reverse case is obtained by altering subscripts.
j
(9)
net profits
when country
i and j
R. Shivakumar, Strategic trade policy
174
Table 1 The CS-CQ
game: Expected per-firm profits in country i. Country j CS
CQ I
CQ
(a-c)’ 8b
I
(a-c)’ 9b
and country i’s problem by max Eni(xi(Si, xj(Sr), xj(ST)), si
i #j,
(10)
where SF is the equilibrium value of the export subsidy. By substituting the equilibrium value of the export quota and export subsidy (obtained by solving the pair of first-order conditions to the above problems simultaneously) in eqs. (9) and (lo), it is possible to show that E~CS/CQ = I
~fl$?Q/CS=t~j
J
(a-c)’
Is2
bNi(Ni + 3)2 +b(Ni + 1)2’
+
l)(a-~)~
bNj(Ni + 3)2 ’
izj-
(11)
(12)
Table 1 summarizes the analysis of this game by listing the expected payoffs for country i for the special case of an international duopoly (one firm in each country). In order to characterize equilibria in this game, define the following functions: VC(S) =
81(a-c)‘. 2oo ,
VC(Q) =v.
VC(S) is the unique level of noise which leaves country i indifferent between CS and CQ given that country j chooses CS and VC(Q) is the unique level of noise which leaves country i indifferent between CS and CQ given that country j chooses CQ.
R. Shivakumar, Strategic trade policy
175
The next three lemmas characterize equilibria in this game.8 Lemma 1. Proof
If o2 < VC(Q), both countries choose CQ.
By inspection of payoffs in table 1.
As Cooper and Riezman point out, this result calls into question the relevance of the Brander and Spencer model which excludes quotas as a policy option. Lemma 2.
Proof:
If CT’> I/C(S), both countries choose CS.
By inspection of payoffs in table 1.
When o2 >VC(S), countries are willing to trade the inflexibility export quota for the flexibility of an export subsidy. Lemma 3. If VC(Q)5a2 chooses CQ. Proof.
2 VC(S),
of an
one country chooses CS and the other
By inspection of payoffs in table 1.
Symmetric equilibria with both countries choosing CS or both countries choosing CQ arise if VC(Q) > VC(S).’ 4. The CQ-DQ
game
Now consider the CQ-DQ game. Here, the countries choose between implementing quantity controls before and after observing the random demand intercept. When both countries choose CQ, expected per-firm profits are given by eq. (8). When both countries choose DQ, each chooses the export quota to maximize per-firm profits after observing the random demand intercept. Substituting the equilibrium value of the export quota” in eq. (2), it is possible to show that
~~~PIDQ=(a-c)2’a2,7 i=l
I
9bNi
2
*
(13)
8See Cooper and Riezman (1989) for equilibria in the oligopoly case. ‘When Ni = Nj = N, it is possible to show that VC(Q) > VC(S) if N is large while the opposite is true if N is small. “Given by +=(a-c+6’)/3bNi.
R. Shiuakumar, Strategic trade policy
176
Table 2 The
CQ-DQ
game:
Expected per-firm country i.
Country
profits
in
j
CQ
DQ
CQ Country
i
DQ
When country i chooses CQ and country j chooses DQ, country j maximizes per-firm profits [given by (2)] and country i maximizes expected per-firm profits give by” max Eni(Xi, Xj(Xi)), i #j. XI
(14)
Substituting the solution for this problem12 in eqs. (2) and (14), it is possible to show that
~fl~Q’W=(a_ i+j,
(15)
8bN,
E~~~,c&-C)2+402 J
-
16bNj
’
’
’
“”
Table 2 summarizes the analysis of this game by listing the payoffs for country i for the special case of international duopoly. In order to identify equilibria in this game, define the following functions: VC(F)
=
=$;
VC(G)
A!$.
VC(F) denotes the unique level of noise at which country i is indifferent between CQ and DQ given that country j chooses CQ and VC(G) denotes the unique level of noise at which country i is indifferent between CQ and DQ given that country j chooses DQ. “Since country i chooses a level for its export quota before country j its, country country j’s best response function, xj, (xi) =(a -c + (3- bN,xi)/2bNj, into account. “Given by xi =(a-c)/2bNj.
i takes
177
R. Shivakumar, Strategic trade policy
The next three lemmas
characterize
equilibria
in this game.r3
Lemma 4. For all o2 < VC(G), both countries choose CQ. Pro05
By inspection
of payoffs in table 2.
When e2 V/C(F), both countries choose DQ, Proof.
By inspection
of payoffs in table 2.
When o2 >VC(F), countries prefer DQ more than offsets the disadvantage Lemma 6. For chooses DQ. Proof:
VC(G) so2 5 I/C(F),
By inspection
DQ to CQ because the flexibility of being a Stackelberg follower.
of
one country chooses CQ and the other
of payoffs in table 2.
The country choosing to commit is the Stackelberg leader and the country choosing to delay is the Stackelberg follower. The follower’s policy allows for flexibility while the leader’s does not.
5. The CS-DQ
game
Now consider the CS-DQ game. Here, countries choose between implementing an export subsidy before observing the random demand intercept and implementing a quantity control after observing the random demand intercept. When both countries choose CS, expected per-firm profits (net of subsidies) are given by eq. (6) and when both countries choose DQ, expected per-firm profits are given by eq. (13). If country i chooses CS while country j chooses DQ, country j maximizes per-firm profits [given by eq. (2)] an d country i maximizes expected per firm profits (net of subsidies) given by r4
max Eni(xi(Si,
xj(Si)), xj(Si)),
i #j.
(17)
Si 131n fact, the lemmas are true regardless of the number of firms in each country. ‘%ince country i chooses a level for its subsidy before country j chooses its export country i takes country j’s response, x,(S{)=(a-c+B-N,S,)/2bN,, into account.
quota,
R. Shivakumar,
178
Strategic trade policy Table 3
The
CS-DQ
game:
Expected per-firm country i.
cs
Country
DQ
~?&+++&
j
DQ
(a-c)’ 18b
u2 +%I
Substituting the solution for this problem” to show that
- 4bNj(2 + Ni)2
I
_
(a-c)*+o’ 9b
in eqs. (2) and (17), it is possible
fJ2
EnDQ,CS_(a-c)2(Ni-11)+ J
E~CW’Q
in
i
Country
cs
profits
(a-c)’
. .
4bNj(Ni + 1)2’ ‘#j’
o2
-4bNi(2+Ni)+4b(Ni+1)2’
. . ‘#j’
(18)
(19)
Table 3 lists the payoffs for country i for the special case of an international duopoly. In order to characterize equilibria in this game, define the following function:
VC(H) denotes the unique level of noise which leaves country between CS and DQ, given that country j chooses CS. The next two lemmas characterize equilibria in this game.
i indifferent
Lemma 7. Zf f125 VC(H), there are two equilibria. In one equilibrium, both countries choose CS, and in the other, both countries choose DQ. Proof
By inspection of payoffs from table 3.
When country j chooses CS, country i finds it optimal to choose CS rather than DQ because the greater flexibility of DQ is not sufficient to offset the disadvantage of being a Stackelberg follower. When country j chooses DQ, ‘%iven
by Si =(a-c)/N,(2+Ni).
179
R. Shivakumar, Strategic trade policy
country i finds it optimal to choose DQ rather than CS. Although deviating to CS makes country i a Stackelberg leader vis-&vis country j, country j obtains a Stackelberg leadership advantage vis-$-vis firm i. Lemma 8. Proofi
Zf o2 > I/C(H), both countries choose DQ.
By inspection
When n2 >VC(H), flexible than CS.
of payoffs in table 3. both
countries
prefer DQ
to CS because
DQ is more
6. Subgame perfect equilibria
Now suppose that the countries have the option of choosing between CS, CQ and DQ. Each country’s equilibrium choice of policy will depend on the noise and the number of firms in each country. The next two propositions address the special case of an international duopoly. In characterizing subgame perfect equilibria, it is useful to note that VC(H)>VC(S)>VC(Q)=VC(F)>VC(G). The first proposition
characterizes
the equilibrium
choice of policy.
Proposition 1. (a) For o2 < I/C(G), both countries choose CQ. (b) For VC(G)~CT~ < VC(Q)= I/C(F), one country chooses CQ and the other chooses DQ. (c) For VC(Q) = VC(F) sa2 < I/C(S), both countries choose DQ. (d) For I/C(S) so’< I/C(H), there are two subgame perfect equilibria. In one equilibrium, both countries choose CS and in the other, both countries choose DQ. (e) For a2 2 I/C(H), both countries choose DQ. Proof.
See the appendix.
To understand Proposition 1, first consider the case where there is no noise. Each country prefers CQ to CS and DQ because, with no noise, commitment is valued more than flexibility and CQ represents maximum commitment. Because the payoffs are continuous, CQ remains a dominant policy for ‘small’ noise, i.e. a2 < VC(G). In the range, VC(G) 5 a2 < VC(Q) = VC(F), countries prefer CQ to CS and in the CS-DQ game, DQ is an equilibrium. However, in the CQ-DQ game, one country chooses CQ while the other chooses DQ. Thus, the subgame perfect equilibrium is asymmetric with one country choosing CQ and the other choosing DQ.16 As the noise 16Note that this asymmetric choice of timing is endowed with a first mover advantage.
arises endogenously
even though
neither
country
180
R. Shivakumar, Strategic trade policy
increases, CQ becomes less desirable relative to CS and DQ because the countries begin to value flexibility. For this reason, countries prefer DQ to CQ in the range VC(Q) = VC(F) 5 g2 s VC(S). Since DQ is an equilibrium in the CS-DQ game and since asymmetric equilibria are the only equilibria in the CS-CQ game in this range (see Lemma 3), the unique subgame perfect equilibrium is DQ. As the noise increases further, i.e. VC(S) za2< VC(H), CS is preferred to CQ and DQ to CQ. And since both CS and DQ are equilibria in the CSDQ game, both are subgame perfect equilibria. Thus, it would appear that either policy could be chosen. However, the principle of payoff dominance allows us to eliminate CS as an equilibrium. That is, DQ payoff dominates CS because the payoffs for both countries under DQ are greater than under The payoff dominance principle expresses the idea that equilibrium cs.” points with greater payoffs for all players should be given preference in problems of equilibrium point selection. What this principle implies is that the two countries should not have trouble coordinating their expectations at the preferred equilibrium, DQ. When c? > VC(H) (call this ‘large’ noise), both countries prefer DQ to CS and CQ, This is not surprising since DQ allows for maximum flexibility. Proposition 1 is an interesting result because is suggests that countries will prefer quantity controls to exports subsidies. This is in contrast to Cooper and Riezman’s results which suggest that export subsidies will be preferred to quantity controls in volatile environments. It is also in contrast to Brander and Spencer’s and Arvan’s results which preclude countries from choosing 1 raises questions concerning the quantity controls. Thus, Proposition positive role ascribed to export subsidies in the profit-shifting literature. Proposition 1 has had to rely on the extreme assumption that countries can, by delaying the implementation of policy, observe the random demand intercept perfectly. Suppose instead that countries observe only a component of the random demand intercept. For instance, suppose that the demand intercept is given by a + Q+ E, where 8 and E are independent zero mean random variables and countries observe 0 but not E if they choose delay. When the noise in E, a:, equals zero (as is implicitly assumed in this paper), export quotas will be preferred to export subsidies. For CJ~ ‘small’, it is plausible that export quotas will continue to dominate export subsidies. But as the size of of increases, CS will be more attractive than DQ because it allows for a potential Stackelberg leader’s role and provides firms with flexibility. The implication is that some form of residual uncertainty is neccessary in order to rationalize the reliance on export subsidies. An implication of the countries choosing export quotas is that total output “Note also that since the payolls in the game are symmetry invariant, the DQ equilibrium is also payoff effkient. See Harsanyi and Selten (1988) for a formal definition of payoff dominance and payoff efficiency.
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Strategic
trade policy
181
is lower and prices higher than when the countries choose subsidies. For instance, in the CQ regime, total output equals 2(a-c)/3b whereas total output in the CS regime, is, on average (0=0), equal to 4(a-c)/5b. Since total output in the CS regime exceeds total output under free trade, consumers are better off when countries attempt profit-shifting policies.” The following proposition shows that exports in the DQ regime are identical to exports under free trade. Furthermore, countries choosing DQ commonly associated with designing policy do not incur the menu costs” for different environments. Proposition 2. desired exports. Proof:
In
the
DQ
regime,
the
export
quotas
coincide
with firms
See the appendix.
Proposition 2 states that the de facto policy of each country is free trade. The reason the export quota coincides with the firm’s desired exports is that the firm’s problem and the country’s problem coincide when both have the same information set. This is an interesting result because it is in contrast to the widely held view that a role for activist trade policy generally emerges in models of imperfect competition. That free trade is the de facto outcome is crucially dependent on the assumption of a single firm in each country. When the number of firms in each country exceeds one, the export quota will bind since each country now has an incentive to limit excess competition between its firms.
7. Conclusion This paper considers a stylized model in which countries choose a type of policy (an export subsidy or a strict quantity control) and a time to implement policy (commit or delay). The choice between the four possible options, CS, CQ, DS and DQ, depends on the noise and the number of firms in each country. Results are presented for the special case of an international duopoly. When noise in demand is ‘small’, countries choose CQ and when noise in demand is ‘large’, countries choose DQ. There is an ‘intermediate’ range in which countries choose CS and DQ. However, DQ payoff dominates CS. That is, the payoffs for both players under DQ are higher than “These results suggest that the importing country may take steps to prevent its consumers from being exploited. Shivakumar (1992b) shows that the importing country can, by choosing trade policy strategically (an import tariff or an import quota), induce an exporting country to choose free trade. “Mankiw (1990) defines menu costs as ‘. the resource costs of posting new price lists. These include the time taken to inform customers, the customer annoyance caused by price changes and the effort required to even think about a price change .‘.
R. Shivakumar,
182
Strategic trade policy
under free trade. These results show that countries will prefer export quotas to export subsidies. What is also interesting is that in the DQ regime, the export quotas coincide with the firms’ desired exports. That is, the de facto policy of each country is free trade. This result is in contrast to the prevailing view that Nash equilibria in models of imperfect competition typically call for intervention. Many special assumptions have been used to obtain these results. Hence, it is not clear whether the superiority of quantity controls to export subsidies demonstrated here is robust to changes in the assumptions of the model. For instance, changes in the specification of the form of uncertainty (additive vs. multiplicative),20 different types of uncertainty (cost vs. demand uncertainty), general formulations of demand and cost, the potential for countries to design policies that induce firms to reveal the state of nature, the presence of residual uncertainty, etc. may provide a rationale for export subsidies. Appendix 1 Proof of Proposition 1. (a) Lemma 1 shows that CQ is preferred to CS for c2 < VC(Q) and Lemma 4 shows that CQ is preferred to DQ for a2 < VC(G). Since VC(G)
DQ. (c) Let VC(F) = VC(Q) 5 0’ < VC(S) be called ‘intermediate 2’ noise. When o2 is in this range, Lemma 5 shows that DQ is preferred to CQ and Lemma 7 shows that DQ is an equilibrium in the CS-DQ game. Thus, DQ is a subgame perfect equilibrium. (d) Let VC(S) sa2
of Proposition
2.
Observe
that the optimization
problem
for the
20Klemperer and Meyer (1986) show that the form of uncertainty combines with the slope of marginal cost and the curvature of the demand function to influence firms’ choice of strategic variables: price or quantity.
R. Shivakumar,
Strategic
trade policy
183
country is identical to the optimization problem for the firm [see eq. (2)] Q.E.D. when there is only one firm in each country. References Arvan, L., 1991, Flexibility versus commitment in strategic trade policy under uncertainty: A model of endogenous policy leadership, Journal of International Economics 31, 341-355. Brander, J.A. and B.J. Spencer, 1985, Export subsidies and international market share rivalry, Journal of International Economics 18, 83-100. Cooper, R. and R. Riezman, 1989, Uncertainty and the choice of trade policy in oligopolistic industries, Review of Economic Studies 56, 129-140. Dixit, A., 1984, International trade policy for oligopolistic industries, Economic Journal 94, 1-16. Eaton, J. and G. Grossman, 1986, Optimal trade and industrial policy under oligopoly, Quarterly Journal of Economics 101, 383406. Harsanyi, J.C. and R. Selten, 1988, A general theory of equilibrium selection in games (MIT Press, Cambridge, MA). Klemperer, P. and M. Meyer, 1986, Price competition versus quantity competition: The role of uncertainty, Rand Journal of Economics 17, 618-638. Mankiw, G., 1990, A quick refresher course in macroeconomics, Journal of Economic Literature 28, 1645-l 660. Shivakumar, R., 1992a, Strategic trade policy: Choosing between export subsidies and export quotas under uncertainty, Working paper (Department of Economics, Indiana University). Shivakumar, R., 1992b, The efficacy of export promotion, Working paper (Department of Economics, Indiana University).
Economics 35 (1993) 169-183. North-Holland
Strategic trade policy Choosing between export subsidies and export quotas under uncertainty Ram Shivakumar” Department of Economics, Indiana University, Bloomington, IN 47405, USA
Received July 1991, revised version received January 1993
I consider a trade policy game in which the choice of policy (subsidy or quota) and time of implementation mfore (commit) or after (delay) observing the random demand intercept] is endogenously determined. Each country has four possible options: CQ, CS, DS and DQ, where CQ denotes a commitment to a quota and the other options are similarly labeled. For the special case of an international duopoly, countries prefer quotas to subsidies: CQ is chosen if noise is ‘small’ and DQ if noise is ‘large’. Also interesting is that quotas in the DQ regime coincide with firms’ desired exports.
1. Introduction I consider a trade policy game between two countries in which each country makes two strategic decisions. First, each can choose a type of policy, either an export subsidy or a strict quantity control. Second, each has the prerogative of implementing policy before observing the random demand intercept (commitment) or delaying the implementation of policy till after observing the random demand intercept (delay). Thus each country has four possible policy options: CS, CQ, DQ and DS, where CS stands for a commitment to a subsidy and the other policy options are similarly labelled. Depending on the option chosen and the realization of the uncertain demand parameter, firms may want to produce less than, more than, or possibly exactly the required quantity. Thus, the quantity control may or may not have the ‘normal’ interpretation of an export quota as a restraint on exports. However, in the paper, I will often refer to the policy as a ‘quota’ for expositional convenience. Correspondence to: Ram Shivakumar, Department of Economics, Indiana University, Bloomington, IN 47405, USA. *An earlier version of this paper was presented at the Spring 1991 Mid-West International Economics Meetings in Evanston. I thank John Wilson, David Besanko, Roy Gardner, Raymond Riezman, Arindam Bandopadhyay, Krishna Srinivasan and two anonymous referees for their helpful comments. The usual disclaimer applies.
0022-1996/93/%06.00 0
1993-Elsevier
Science Publishers B.V. All rights reserved
170
R. Shivakumar,
Strategic trade policy
How can these four policy options be ranked in the flexibility-commitment spectrum? Intuitively, CQ represents maximum commitment and DS and DQ represent maximum flexibility. Furthermore, ranking these instruments is simplified by recognizing that countries choosing between DS and DQ will choose DQ because it is preferable to opt for the policy option that makes one’s own output reaction function less elastic, since this weakens the rival’s ability to shift profits. Amongst the remaining three policies, CQ represents maximum commitment, DQ represents maximum flexibility and CS represents intermediate flexibility. Therefore, one might conjecture that CQ is the best policy under ‘small’ noise, CS the best policy under ‘intermediate’ noise and DQ the best policy under ‘large’ noise. Results, for the special case of an international duopoly,’ show that countries choose CQ in the ‘small’ noise case and DQ in the ‘large’ noise case. There are also three ‘intermediate’ noise cases. In the first ‘intermediate’ case, one country chooses CQ and the other chooses DQ. In the second ‘intermediate’ case, both countries choose DQ while in the third ‘intermediate’ case, there are two equilibria. In one equilibrium, both countries choose CS, and in the other, both countries choose DQ. However, DQ payoff dominates CS. That is, the payoffs for both countries under DQ are higher than under CS2 These results suggest that countries will prefer export quotas to export subsidies. What is also interesting is that with the DQ policy, the export quotas coincide with firms’ desired exports. That is, the de facto policy of each country is free trade. This result is noteworthy because it contrasts with a widely held view that Nash equilibria in models of imperfect competition typically call for interventionist trade policy. These results on the choice of timing and policy are in contrast to existing results in the strategic trade policy literature. The seminal paper on strategic trade policy is by Brander and Spencer (1985) who explain the role of an export subsidy in terms of a profit-shifting effect. Using a Cournot duopoly model, they show that each country subsidizes its firms exports even though such a policy leaves both firms and countries worse off than they were before the intervention.3 Cooper and Riezman (1989) argue that constraining each country’s policy choice to export subsidies is unrealistic. They consider a model in which countries choose a type of policy (an export subsidy or a strict quantity control) in the first stage and a level for policy in the second stage. The random intercept of demand is then revealed after which firms in each country compete. The ‘In Shivakumar (1992a), I use simulation methods to examine how departures from the duopoly framework affect results. ‘A formal definition of payoff dominance is given in Harsanyi and Selten (1988). ‘Eaton and Grossman (1986) point out that the form of policy (export subsidy vs. export tax vs. free trade) is sensitive to assumptions about the type of conjectures firms make (Cournot vs. Bertrand vs. conjectural variations).
R. Shivakumar, Strategic trade policy
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subgame perfect equilibrium depends on the noise. With small noise, countries choose quantity controls because each country is able to immunize its firms from the profit-shifting policies of rivals. With large noise, countries choose export subsidies because firms are given the flexibility to respond to the environment. Arvan (1991) considers a similar model but restricts the countries’ options to CS and DS. He shows that the subgame perfect equilibrium frequently involves asymmetric timing, i.e. the country with the relatively small number of firms acts like a Stackelberg leader while the country with the relatively large number of firms acts like a Stackelberg follower. In contrast to the above papers, the present paper allows countries the option of choosing both a type of policy and a time to implement the policy. That is, countries choose between CS, CQ and DQ. The equilibrium choice of timing and policy is characterized by examining three separate games, each of which has only two policy options. In the first game (the CS-CQ game), the countries choose between CS and CQ. In the second game (the CQ-DQ game), the countries choose between CQ and DQ, while in the third game (the CS-DQ game), the countries choose between CS and DQ. Each of these games has the property that one of the policy options is more flexible and hence performs better when there is large noise, while the other policy option performs at least as well when there is small noise. Section 2 describes the basic model and the structure of the trade policy game. Section 3 characterizes equilibria in the CS-CQ game, section 4 characterizes equilibria in the CQ-DQ game and section 5 characterizes equilibria in the CS-DQ game. Section 6 characterizes subgame perfect equilibria when countries can choose between CS, CQ and DQ. Section 7 concludes. 2. The model Ni firms from country i and Nj firms from country j produce a homogeneous commodity and compete as quantity-setters in a third market. Each firm is identical and incurs a constant marginal cost of production, c > 0. The inverse demand function is given by
P(Xi +Xj)=U-b(Xi
+Xj)+8,
i#j,
(I)
where Xi = Nixi [i, j = 1,2] and Xi represents the quantities exported by each firm in country i. The parameters a and b are positive and it is assumed that a is strictly greater than c. 13is a random disturbance term with mean zero and a variance denoted by 0’. Each firm chooses output, xi, to maximize profits given by ni=[P(Xi+Xj)-C]Xi,
i#j=1,2.
(2)
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172
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From the first-order conditions for this problem, it is possible to show that Xi(Xj)
=
a-c+O--bNjxj b(Ni+l)
It is straightforward firm profits equal
’
i#j=
1,2.
to establish that equilibrium exports and expected per
(a-c+@ xi = b(N, + Nj + 1)’
EZIi =
(a--)‘+a2 b(N, + Nj + 1)2’
i#j=
1,2.
(4)
The presence of supranormal profits may provide each country with the incentive to intervene. But the policy chosen by each country will depend on the variability of demand and the policy of its rival. Trade policy may thus be seen as the outcome of a game between countries. The structure of the game considered here is as follows. In the first stage of the game, each country makes two decisions simultaneously. Each chooses a type of policy (an export subsidy or a strict quantity control) and a time to implement the policy (commit or delay). In the second stage, countries choose a level for their policy instrument. If a country commits to policy, then the level of the policy instrument is chosen before the random demand intercept is revealed.4 If, on the other hand, a country chooses to delay implementation, the level of its policy instrument is chosen after observing the random demand intercept. In the third stage of the game, firms choose their output to maximize profits contingent on the policies chosen. If a country chooses a quantity control policy, then it is assumed that firms in this country export exactly the quantity chosen. Thus each country has three possible policy options: CS, CQ or DQ.5 The equilibrium choice of policy is characterized by studying three games, each of which allows only two policy options. In the first game (the C!S--CQ game), each country chooses a level for its subsidy/quota before observing the random demand intercept. In the second game (the CQ-DQ game), the countries choose between implementing a quota before and after observing the random demand intercept. In the third game (the CS-DQ game), the countries choose between implementing a subsidy before observing the random demand intercept and implementing a quota after observing the random demand intercept. A comparison of expected payoffs in each game determines which policy is chosen. The solution concept adopted is the subgame perfect equilibrium: that is, non-credible threats are excluded.
“The distribution of the random demand intercept is common knowledge. It is assumed the countries cannot design policies so as to induce firms to reveal the true state of nature. 5The fourth option, DS, is eliminated because DQ dominates it.
that
R. Shivakumar,
3. The CS-CQ
173
Strategic trade policy
game
In this game, each country chooses the level of its policy variable before intercept is revealed. This is identical to the game the random demand considered by Cooper and Riezman (1989) and hence only the essentials of the analysis are repeated here. Suppose that each country provies a per-unit export subsidy, Si, to each of its firms. Each country chooses a value for the subsidy (prior to the resolution of uncertainty and before the firms decide their outputs) to maximize expected per-firm profits, net of subsidies. Such a specification is appropriate since it is assumed that there is no domestic consumption, countries are risk neutral and income distributional issues are not relevant. Country i’s maximization problem is given by i#j=
maxEHi(xi(Si,Sj),xj(Si,Sj)), 6%
1,2,
(5)
where E denotes the expectation operator. Substituting the equilibrium value of the export subsidy [obtained by solving the pair of first-order conditions to eq. (5)] in eq. (5) it is possible to show that Encs/cs
I
G2 l)(a-c)2 bNi(Ni + Nj + 3)‘+b(fi_T~l)”
=
(Nj
+
i#j=
(6)
1,2,
where the superscripts denote the policies chosen by each country.6 Suppose that each country chooses an export quota. Then each country chooses its export quota to maximize expected per-firm profits, given by EHi =[P(X,
+Xj)-c]xi,
i#j=
1,2.
(7)
Substituting the equilibrium value of the export quota (obtained by solving the pair of first-order conditions for the above equation) in eq. (7) it is easy to show that E@Q/CQ
=
b$,
i = 1,2. I
Now suppose that country i subsidizes its firms’ exports chooses an export quota.’ Country j’s problem is given by max Eflj(xj, xj
Xi(Si, xj)),
and
country
i #j,
6That is, EI$siCS represents the equilibrium value of expected commit to subsidies. ‘The reverse case is obtained by altering subscripts.
j
(9)
net profits
when country
i and j
R. Shivakumar, Strategic trade policy
174
Table 1 The CS-CQ
game: Expected per-firm profits in country i. Country j CS
CQ I
CQ
(a-c)’ 8b
I
(a-c)’ 9b
and country i’s problem by max Eni(xi(Si, xj(Sr), xj(ST)), si
i #j,
(10)
where SF is the equilibrium value of the export subsidy. By substituting the equilibrium value of the export quota and export subsidy (obtained by solving the pair of first-order conditions to the above problems simultaneously) in eqs. (9) and (lo), it is possible to show that E~CS/CQ = I
~fl$?Q/CS=t~j
J
(a-c)’
Is2
bNi(Ni + 3)2 +b(Ni + 1)2’
+
l)(a-~)~
bNj(Ni + 3)2 ’
izj-
(11)
(12)
Table 1 summarizes the analysis of this game by listing the expected payoffs for country i for the special case of an international duopoly (one firm in each country). In order to characterize equilibria in this game, define the following functions: VC(S) =
81(a-c)‘. 2oo ,
VC(Q) =v.
VC(S) is the unique level of noise which leaves country i indifferent between CS and CQ given that country j chooses CS and VC(Q) is the unique level of noise which leaves country i indifferent between CS and CQ given that country j chooses CQ.
R. Shivakumar, Strategic trade policy
175
The next three lemmas characterize equilibria in this game.8 Lemma 1. Proof
If o2 < VC(Q), both countries choose CQ.
By inspection of payoffs in table 1.
As Cooper and Riezman point out, this result calls into question the relevance of the Brander and Spencer model which excludes quotas as a policy option. Lemma 2.
Proof:
If CT’> I/C(S), both countries choose CS.
By inspection of payoffs in table 1.
When o2 >VC(S), countries are willing to trade the inflexibility export quota for the flexibility of an export subsidy. Lemma 3. If VC(Q)5a2 chooses CQ. Proof.
2 VC(S),
of an
one country chooses CS and the other
By inspection of payoffs in table 1.
Symmetric equilibria with both countries choosing CS or both countries choosing CQ arise if VC(Q) > VC(S).’ 4. The CQ-DQ
game
Now consider the CQ-DQ game. Here, the countries choose between implementing quantity controls before and after observing the random demand intercept. When both countries choose CQ, expected per-firm profits are given by eq. (8). When both countries choose DQ, each chooses the export quota to maximize per-firm profits after observing the random demand intercept. Substituting the equilibrium value of the export quota” in eq. (2), it is possible to show that
~~~PIDQ=(a-c)2’a2,7 i=l
I
9bNi
2
*
(13)
8See Cooper and Riezman (1989) for equilibria in the oligopoly case. ‘When Ni = Nj = N, it is possible to show that VC(Q) > VC(S) if N is large while the opposite is true if N is small. “Given by +=(a-c+6’)/3bNi.
R. Shiuakumar, Strategic trade policy
176
Table 2 The
CQ-DQ
game:
Expected per-firm country i.
Country
profits
in
j
CQ
DQ
CQ Country
i
DQ
When country i chooses CQ and country j chooses DQ, country j maximizes per-firm profits [given by (2)] and country i maximizes expected per-firm profits give by” max Eni(Xi, Xj(Xi)), i #j. XI
(14)
Substituting the solution for this problem12 in eqs. (2) and (14), it is possible to show that
~fl~Q’W=(a_ i+j,
(15)
8bN,
E~~~,c&-C)2+402 J
-
16bNj
’
’
’
“”
Table 2 summarizes the analysis of this game by listing the payoffs for country i for the special case of international duopoly. In order to identify equilibria in this game, define the following functions: VC(F)
=
=$;
VC(G)
A!$.
VC(F) denotes the unique level of noise at which country i is indifferent between CQ and DQ given that country j chooses CQ and VC(G) denotes the unique level of noise at which country i is indifferent between CQ and DQ given that country j chooses DQ. “Since country i chooses a level for its export quota before country j its, country country j’s best response function, xj, (xi) =(a -c + (3- bN,xi)/2bNj, into account. “Given by xi =(a-c)/2bNj.
i takes
177
R. Shivakumar, Strategic trade policy
The next three lemmas
characterize
equilibria
in this game.r3
Lemma 4. For all o2 < VC(G), both countries choose CQ. Pro05
By inspection
of payoffs in table 2.
When e2
By inspection
of payoffs in table 2.
When o2 >VC(F), countries prefer DQ more than offsets the disadvantage Lemma 6. For chooses DQ. Proof:
VC(G) so2 5 I/C(F),
By inspection
DQ to CQ because the flexibility of being a Stackelberg follower.
of
one country chooses CQ and the other
of payoffs in table 2.
The country choosing to commit is the Stackelberg leader and the country choosing to delay is the Stackelberg follower. The follower’s policy allows for flexibility while the leader’s does not.
5. The CS-DQ
game
Now consider the CS-DQ game. Here, countries choose between implementing an export subsidy before observing the random demand intercept and implementing a quantity control after observing the random demand intercept. When both countries choose CS, expected per-firm profits (net of subsidies) are given by eq. (6) and when both countries choose DQ, expected per-firm profits are given by eq. (13). If country i chooses CS while country j chooses DQ, country j maximizes per-firm profits [given by eq. (2)] an d country i maximizes expected per firm profits (net of subsidies) given by r4
max Eni(xi(Si,
xj(Si)), xj(Si)),
i #j.
(17)
Si 131n fact, the lemmas are true regardless of the number of firms in each country. ‘%ince country i chooses a level for its subsidy before country j chooses its export country i takes country j’s response, x,(S{)=(a-c+B-N,S,)/2bN,, into account.
quota,
R. Shivakumar,
178
Strategic trade policy Table 3
The
CS-DQ
game:
Expected per-firm country i.
cs
Country
DQ
~?&+++&
j
DQ
(a-c)’ 18b
u2 +%I
Substituting the solution for this problem” to show that
- 4bNj(2 + Ni)2
I
_
(a-c)*+o’ 9b
in eqs. (2) and (17), it is possible
fJ2
EnDQ,CS_(a-c)2(Ni-11)+ J
E~CW’Q
in
i
Country
cs
profits
(a-c)’
. .
4bNj(Ni + 1)2’ ‘#j’
o2
-4bNi(2+Ni)+4b(Ni+1)2’
. . ‘#j’
(18)
(19)
Table 3 lists the payoffs for country i for the special case of an international duopoly. In order to characterize equilibria in this game, define the following function:
VC(H) denotes the unique level of noise which leaves country between CS and DQ, given that country j chooses CS. The next two lemmas characterize equilibria in this game.
i indifferent
Lemma 7. Zf f125 VC(H), there are two equilibria. In one equilibrium, both countries choose CS, and in the other, both countries choose DQ. Proof
By inspection of payoffs from table 3.
When country j chooses CS, country i finds it optimal to choose CS rather than DQ because the greater flexibility of DQ is not sufficient to offset the disadvantage of being a Stackelberg follower. When country j chooses DQ, ‘%iven
by Si =(a-c)/N,(2+Ni).
179
R. Shivakumar, Strategic trade policy
country i finds it optimal to choose DQ rather than CS. Although deviating to CS makes country i a Stackelberg leader vis-&vis country j, country j obtains a Stackelberg leadership advantage vis-$-vis firm i. Lemma 8. Proofi
Zf o2 > I/C(H), both countries choose DQ.
By inspection
When n2 >VC(H), flexible than CS.
of payoffs in table 3. both
countries
prefer DQ
to CS because
DQ is more
6. Subgame perfect equilibria
Now suppose that the countries have the option of choosing between CS, CQ and DQ. Each country’s equilibrium choice of policy will depend on the noise and the number of firms in each country. The next two propositions address the special case of an international duopoly. In characterizing subgame perfect equilibria, it is useful to note that VC(H)>VC(S)>VC(Q)=VC(F)>VC(G). The first proposition
characterizes
the equilibrium
choice of policy.
Proposition 1. (a) For o2 < I/C(G), both countries choose CQ. (b) For VC(G)~CT~ < VC(Q)= I/C(F), one country chooses CQ and the other chooses DQ. (c) For VC(Q) = VC(F) sa2 < I/C(S), both countries choose DQ. (d) For I/C(S) so’< I/C(H), there are two subgame perfect equilibria. In one equilibrium, both countries choose CS and in the other, both countries choose DQ. (e) For a2 2 I/C(H), both countries choose DQ. Proof.
See the appendix.
To understand Proposition 1, first consider the case where there is no noise. Each country prefers CQ to CS and DQ because, with no noise, commitment is valued more than flexibility and CQ represents maximum commitment. Because the payoffs are continuous, CQ remains a dominant policy for ‘small’ noise, i.e. a2 < VC(G). In the range, VC(G) 5 a2 < VC(Q) = VC(F), countries prefer CQ to CS and in the CS-DQ game, DQ is an equilibrium. However, in the CQ-DQ game, one country chooses CQ while the other chooses DQ. Thus, the subgame perfect equilibrium is asymmetric with one country choosing CQ and the other choosing DQ.16 As the noise 16Note that this asymmetric choice of timing is endowed with a first mover advantage.
arises endogenously
even though
neither
country
180
R. Shivakumar, Strategic trade policy
increases, CQ becomes less desirable relative to CS and DQ because the countries begin to value flexibility. For this reason, countries prefer DQ to CQ in the range VC(Q) = VC(F) 5 g2 s VC(S). Since DQ is an equilibrium in the CS-DQ game and since asymmetric equilibria are the only equilibria in the CS-CQ game in this range (see Lemma 3), the unique subgame perfect equilibrium is DQ. As the noise increases further, i.e. VC(S) za2< VC(H), CS is preferred to CQ and DQ to CQ. And since both CS and DQ are equilibria in the CSDQ game, both are subgame perfect equilibria. Thus, it would appear that either policy could be chosen. However, the principle of payoff dominance allows us to eliminate CS as an equilibrium. That is, DQ payoff dominates CS because the payoffs for both countries under DQ are greater than under The payoff dominance principle expresses the idea that equilibrium cs.” points with greater payoffs for all players should be given preference in problems of equilibrium point selection. What this principle implies is that the two countries should not have trouble coordinating their expectations at the preferred equilibrium, DQ. When c? > VC(H) (call this ‘large’ noise), both countries prefer DQ to CS and CQ, This is not surprising since DQ allows for maximum flexibility. Proposition 1 is an interesting result because is suggests that countries will prefer quantity controls to exports subsidies. This is in contrast to Cooper and Riezman’s results which suggest that export subsidies will be preferred to quantity controls in volatile environments. It is also in contrast to Brander and Spencer’s and Arvan’s results which preclude countries from choosing 1 raises questions concerning the quantity controls. Thus, Proposition positive role ascribed to export subsidies in the profit-shifting literature. Proposition 1 has had to rely on the extreme assumption that countries can, by delaying the implementation of policy, observe the random demand intercept perfectly. Suppose instead that countries observe only a component of the random demand intercept. For instance, suppose that the demand intercept is given by a + Q+ E, where 8 and E are independent zero mean random variables and countries observe 0 but not E if they choose delay. When the noise in E, a:, equals zero (as is implicitly assumed in this paper), export quotas will be preferred to export subsidies. For CJ~ ‘small’, it is plausible that export quotas will continue to dominate export subsidies. But as the size of of increases, CS will be more attractive than DQ because it allows for a potential Stackelberg leader’s role and provides firms with flexibility. The implication is that some form of residual uncertainty is neccessary in order to rationalize the reliance on export subsidies. An implication of the countries choosing export quotas is that total output “Note also that since the payolls in the game are symmetry invariant, the DQ equilibrium is also payoff effkient. See Harsanyi and Selten (1988) for a formal definition of payoff dominance and payoff efficiency.
R. Shivakumar,
Strategic
trade policy
181
is lower and prices higher than when the countries choose subsidies. For instance, in the CQ regime, total output equals 2(a-c)/3b whereas total output in the CS regime, is, on average (0=0), equal to 4(a-c)/5b. Since total output in the CS regime exceeds total output under free trade, consumers are better off when countries attempt profit-shifting policies.” The following proposition shows that exports in the DQ regime are identical to exports under free trade. Furthermore, countries choosing DQ commonly associated with designing policy do not incur the menu costs” for different environments. Proposition 2. desired exports. Proof:
In
the
DQ
regime,
the
export
quotas
coincide
with firms
See the appendix.
Proposition 2 states that the de facto policy of each country is free trade. The reason the export quota coincides with the firm’s desired exports is that the firm’s problem and the country’s problem coincide when both have the same information set. This is an interesting result because it is in contrast to the widely held view that a role for activist trade policy generally emerges in models of imperfect competition. That free trade is the de facto outcome is crucially dependent on the assumption of a single firm in each country. When the number of firms in each country exceeds one, the export quota will bind since each country now has an incentive to limit excess competition between its firms.
7. Conclusion This paper considers a stylized model in which countries choose a type of policy (an export subsidy or a strict quantity control) and a time to implement policy (commit or delay). The choice between the four possible options, CS, CQ, DS and DQ, depends on the noise and the number of firms in each country. Results are presented for the special case of an international duopoly. When noise in demand is ‘small’, countries choose CQ and when noise in demand is ‘large’, countries choose DQ. There is an ‘intermediate’ range in which countries choose CS and DQ. However, DQ payoff dominates CS. That is, the payoffs for both players under DQ are higher than “These results suggest that the importing country may take steps to prevent its consumers from being exploited. Shivakumar (1992b) shows that the importing country can, by choosing trade policy strategically (an import tariff or an import quota), induce an exporting country to choose free trade. “Mankiw (1990) defines menu costs as ‘. the resource costs of posting new price lists. These include the time taken to inform customers, the customer annoyance caused by price changes and the effort required to even think about a price change .‘.
R. Shivakumar,
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Strategic trade policy
under free trade. These results show that countries will prefer export quotas to export subsidies. What is also interesting is that in the DQ regime, the export quotas coincide with the firms’ desired exports. That is, the de facto policy of each country is free trade. This result is in contrast to the prevailing view that Nash equilibria in models of imperfect competition typically call for intervention. Many special assumptions have been used to obtain these results. Hence, it is not clear whether the superiority of quantity controls to export subsidies demonstrated here is robust to changes in the assumptions of the model. For instance, changes in the specification of the form of uncertainty (additive vs. multiplicative),20 different types of uncertainty (cost vs. demand uncertainty), general formulations of demand and cost, the potential for countries to design policies that induce firms to reveal the state of nature, the presence of residual uncertainty, etc. may provide a rationale for export subsidies. Appendix 1 Proof of Proposition 1. (a) Lemma 1 shows that CQ is preferred to CS for c2 < VC(Q) and Lemma 4 shows that CQ is preferred to DQ for a2 < VC(G). Since VC(G)
DQ. (c) Let VC(F) = VC(Q) 5 0’ < VC(S) be called ‘intermediate 2’ noise. When o2 is in this range, Lemma 5 shows that DQ is preferred to CQ and Lemma 7 shows that DQ is an equilibrium in the CS-DQ game. Thus, DQ is a subgame perfect equilibrium. (d) Let VC(S) sa2
of Proposition
2.
Observe
that the optimization
problem
for the
20Klemperer and Meyer (1986) show that the form of uncertainty combines with the slope of marginal cost and the curvature of the demand function to influence firms’ choice of strategic variables: price or quantity.
R. Shivakumar,
Strategic
trade policy
183
country is identical to the optimization problem for the firm [see eq. (2)] Q.E.D. when there is only one firm in each country. References Arvan, L., 1991, Flexibility versus commitment in strategic trade policy under uncertainty: A model of endogenous policy leadership, Journal of International Economics 31, 341-355. Brander, J.A. and B.J. Spencer, 1985, Export subsidies and international market share rivalry, Journal of International Economics 18, 83-100. Cooper, R. and R. Riezman, 1989, Uncertainty and the choice of trade policy in oligopolistic industries, Review of Economic Studies 56, 129-140. Dixit, A., 1984, International trade policy for oligopolistic industries, Economic Journal 94, 1-16. Eaton, J. and G. Grossman, 1986, Optimal trade and industrial policy under oligopoly, Quarterly Journal of Economics 101, 383406. Harsanyi, J.C. and R. Selten, 1988, A general theory of equilibrium selection in games (MIT Press, Cambridge, MA). Klemperer, P. and M. Meyer, 1986, Price competition versus quantity competition: The role of uncertainty, Rand Journal of Economics 17, 618-638. Mankiw, G., 1990, A quick refresher course in macroeconomics, Journal of Economic Literature 28, 1645-l 660. Shivakumar, R., 1992a, Strategic trade policy: Choosing between export subsidies and export quotas under uncertainty, Working paper (Department of Economics, Indiana University). Shivakumar, R., 1992b, The efficacy of export promotion, Working paper (Department of Economics, Indiana University).