This chapter reexamines the strategic export subsidy competition with the separation of ownership and management in a third market model. I explore the owners’ subsidization incentives in designing a managerial incentive contract and discuss the total subsidy ef-fect on the firms’ performance in the market. Although the model is constructed in the same way as that of Das (1997), this chapter conveys some new implications that are not clarified in Das (1997). The essence in Das (1997) is that both the firms are subsidized with a smaller government subsidy as compared to the case without delegation. However, this result cannot explain the change in the firm’s output and social welfare since lower government subsidy merely lowers the total output and increases the monopoly rent in the exporting country, while the model ends up in a contradictory result. The rather paradox-ical result can be explained by the total subsidy defined in my model. I show that firms are subsidized in a larger total subsidy, and both firms overproduce in equilibrium. The nature of strategic managerial delegation in the export subsidy competition lies in the fact that it intensifies the competition between the exporting firms and reduces the distortions in oligopoly pricing, thus improving world welfare. This is the main point that my model has emphasized differently from Das (1997).
This chapter also recognizes owner’s subsidization incentive through managerial del-egation. Indicating the equivalence result between the FJS model and the BS model, I regard owners’ managerial delegation as subsidization behavior. It elucidates the result in Das (1997) as to why the governments weaken the subsidization incentives in the presence of managerial delegation. It also clarifies the Stackelberg solution in the unilateral delega-tion case, which resulted in the government playing Stackelberg against the owner in the subsidy competition.
The extension of delegation game shows that no firm has incentive to delegate under governments’ commitments to intervene. However, the results are largely dependent on the order of the moves. If firm owners move first and the governments subsequently, the total subsidy in equilibrium is a subsidy `ala Brander-Spencer. This is because the govern-ments always determine the optimal subsidy rates to maximize the total subsidy exclusive profit of the national firm. Irrelevant of firm owners’ subsidy rates, the governments al-ways decide the total subsidy rate to `a la Brander-Spencer subsidy. Bearing in mind this subsidization behavior, the firm owners actually choose to delegate and greatly tax the firms to induce higher government subsidy. The analysis that the owners move as leaders against governments is somewhat difficult and is left for future research.
Appendix
5.A Price Competition
Wei (2009a) examined the strategic trade policy and managerial delegation under Bertrand competition. The model is constructed in the framework of Eaton and Grossman (1986), a price competition version of the BS model.
Each firm produces a differentiated good. The demand function of good iis given by xi(p) =a−pi+bpj (i, j = 1,2;j ̸=i),
where a >0 and 0< b <1.
To simplify the analysis, the cost conditions are symmetric, i.e., ci = cj = c. Each firm’s profit function is given by
πi(p, ti) = (pi−c+ti)xi(p).
Both exporting countries’ governments tax their exports at a special tax of ti. Under price competition, firms’ managerial delegations yield owner’s tax equivalent denoted as τi.
τi := (βi−1)(ci+ti).
Total tax Ti is defined as a sum of government tax and owner’s tax equivalent.
Ti :=ti+τi =βi(ci+ti)−ci
Price Stage Equilibrium The equilibrium price of good iin the third-stage is given by p∗i(T) = a(2 +b) + 2(ci+Ti) +b(cj +Tj)
4−b2 .
The equilibrium output can be derived as below.
x∗i(T) = (2 +b)a−(2−b2)(ci+Ti) +b(cj +Tj)
4−b2 .
Taxation lowers domestic production and expands foreign production.
Contract Stage Equilibrium Without government intervention, the model is the FJS model. The equilibrium owner’s tax equivalent is identical to the optimal government tax in Eaton and Grossman (1986).
τiF J = b2
2(pi−ci) = tEGi (i= 1,2),
where superscript EG represents the equilibrium values in Eaton and Grossman (1986).
With government intervention, firm i’s reaction function is given by γi(τj,t) = b2[(2 +b)a−(2−b2)(ci+ti) +b(cj+τj +tj)]
4(2−b2) ,
which shows that ∂γ∂τi(.)
j = ∂γ∂ti(.)
j >0 and ∂γ∂ti(.)
i <0. Each firm’s owner subsidy equivalent is a strategic complementary to the rival’s. Government’s taxation weakens domestic firm’s owner taxation incentive and strengthens foreign firm’s owner taxation incentive.
Denote
Zi(t) : = (4 + 2b−b2)a−(4−3b2)(ci+ti) +b(2−b2)(cj+tj), Y : = (4 + 2b−b2)(4−2b−b2) = 16−12b2+b4 >0.
The optimal owner’s tax equivalent of firm i is τie(t) = b2Zi(t)
Y >0 (i= 1,2).
The positive taxation incentive is assured by the duopoly equilibrium given by xei(t) =x∗i(τie(t) +ti, τje(t) +tj) = (2−b2)Zi(t)
Y .
It is evident to show that ∂τ∂tie(t)
i <0 and ∂τ
e j(t)
∂ti >0. Government taxation reduces domestic firm’s owner tax equivalent and increases foreign firm’s tax equivalent in the equilibrium.
In the quantity competition discussed in Section 5.3, since government subsidization raises domestic firm’s subsidy equivalent, government intervention policy seem as a complement to managerial delegation. However, in the price competition, government intervention policy acts as a substitution to managerial delegation.
Tax Stage Equilibrium Each country’s welfare function is given by Wie(t) = πi(pei(t), pej(t), ti) +tixei(t).
Optimal government tax yields
tˆi = b4C
(2−b2)D >0,
where C :=a−(1−b)c > 0 and D:= 8−4b−4b2+b3 >0. Although each firm’s owner taxes its exports, each government further has incentives to tax the exports, pushing the domestic firm to yield Stackelberg leader’s profit.
Comparing ˆti with tEGi yields
ˆti−tEGi =−b2(1−b)(2 +b)(8−6b2+b3)C (2−b2)(4−2b−b2)D <0.
That is, each country’s government taxes in a lower rate in the presence of managerial delegation.
Equilibrium owner’s tax equivalent can be derived as below.
ˆ
τi =τie(ˆt) = b2(4−3b2)C (2−b2)D >0.
Simple calculation yields ˆτi < tEGi = τiF J. Equilibrium owner’s subsidy equivalent also results in a lower value with government intervention.
However, total tax is larger than tEGi shown as below.
Tˆi−tEGi = ˆτi+ ˆti−tEGi = b4(2−b)C
(4−2b−b2)D >0.
Each country’s equilibrium welfare is given by
Wci =Wie(ˆt) = (4−b2)(4−3b2)C2
D2 .
Comparing with the equilibrium welfare without managerial delegation in Eaton and Grossman (1986) yields
Wci−WiEG = b5(16−16b−4b2+ 5b3)C2 (4−2b−b2)2D2 >0.
In the presence of separation of ownership and management, each good’s price rises up due to a larger total tax. The two firms behave close to a monopolistic firm. The exporting countries’ welfare improves and the third country is in a welfare loss. Thus, with govern-ment intervention, managerial delegation in the price competition increases distortions in the oligopoly competition and worsens world welfare.
Chapter 6
International Separation of Ownership and Management
6.1 Introduction
Chapters 4 and 5 concern the ownership and management structures of the firms. To the best of my knowledge, no paper has examined the traditional strategic export policies in the presence of both international cross shareholding and separation of ownership and man-agement. This chapter combines the analyses in the previous two chapters and discusses how the strategic subsidization incentives are affected by managerial delegation when the shares of the firms are internationally owned by the residents of both countries, i.e., in the presence of international separation of ownership and management. This chapter at-tempts to study how the complexity of managerial decision process and cross shareholding structure alter the standard welfare implication of strategic export promotion policies.
The works related to this chapter is summarized in the following table.