Literature Summary

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.

decisions, respectively. Section 5 compares the equilibrium results and their values in Chapters 4 and 5. Section 6 shows two special cases of symmetric and partial ownership structures. The concluding remarks are summed in section 7.

domestic owner’s subsidy and leads to fiercer competition in the output market. The domestic firm’s profit gain shrinks and the dividend given to the foreign firm decreases.

The second part −(1−σ_i)x_i shows thesubsidy outflow effect, which has the same expression as in the case without managerial delegation.

The third part (1 − σj)xjP^′(X)r_S^iD∂S_∂s^eDi

i shows the dividend suppression effect through managerial delegation. Further, note that r^iD_S ^∂S_∂s^eDi

i < ^∂x_∂s^eDi

i , and hence, man-agerial delegation scales down the decrease in the dividend from the shared foreign firm.

The above three negative parts weaken subsidy incentives in the presence of cross-country shareholding.

Denote R^iE(s_j;σ) as country i’s reaction function, where superscript E represents the values under international separation of ownership and management.

An increase in the domestic residents’ ownership share over the domestic firm (or the foreign residents’ ownership share over the foreign firm) strengthens both countries’ subsidy incentives, leading to an increase in the optimal export subsidy. The results follow from

R^iE_σi(s_j;σ) = ∂R^iE(s_j;σ)

∂σ_i =−∂²W_i(s;σ)/∂σ_i∂s_i

∂²W_i(s;σ)/∂s²_i =− ∂π_i^eD(s)/∂s_i

∂²W_i(s;σ)/∂s²_i >0, R^iE_σ

j(s_j;σ) = ∂R^iE(s_j;σ)

∂σj

=−∂²W_i(s;σ)/∂σ_j∂s_i

∂²Wi(s;σ)/∂s²_i = ∂π^eD_j (s)/∂s_i

∂²Wi(s;σ)/∂s²_i >0, where use was made of (5-16) and (5-17).

6.3 Effects of Cross-Country Shareholding

6.3.1 Equilibrium Government Subsidy

Denote s^E_i (σ) as the equilibrium government’s subsidy of country i. The full-game Nash equilibrium subsidy profile is thus defined as a solution to

s^E_i (σ) =R^iE(s^E_j (σ);σ) (i, j = 1,2;j ̸=i).

Under the symmetric cost conditions, that ci =cj =c,

s^E_i (σ) = (16σ_i+ 13σ_j−10σ_iσ_j−18)(a−c)

2[24−11(σ_i+σ_j) + 5σ_iσ_j] . (6-3) The optimal subsidy rate is dependent on the cross shareholding structure (σ_i, σ_j). From Assumption 4.1, the denominator in (6-3) is positive, i.e., 24−11(σ_i+σ_j) + 5σ_iσ_j >0, and hence s^E_i (σ) is positive if and only ifσ_j > ¹⁸₁₃⁻₋^16σ_10σⁱ

i. Figure 6.1 illustrates (σ₁, σ₂) for which country 1’s government finds zero subsidy optimal with origin (0.5,0.5). In view of Figure 6.1, when the domestic shares of both firms are large enough, each country’s government subsidizes the firm; otherwise, export tax is the optimal policy.

Without cross-country shareholding, Das (1997) showed that s^E_i (1,1) = s^D_i = ₁₄¹(a− c) > 0 in (5-20), and each government always has a positive incentive to subsidize its exports. In the presence of cross-country shareholding, (6-3) shows that ^∂sEi_∂σ^(σi,σj)

k >0(k = i, j), which yields

s^E_i (σ_i, σ_j)< s^E_i (1,1).

Proposition 6.1. Given managerial delegation, the presence of cross-country shareholding weakens both countries’ subsidization incentives, i.e., s^E_i (σ_i, σ_j)< s^E_i (1,1).

6.3.2 Equilibrium Owner’s Subsidy Equivalent

In view of (5-10), the owner’s subsidy equivalent is always positive in the duopolistic market. Solving for the owner’s subsidy equivalent in the equilibrium yields

d^E_i (σ) =d^eD_i (s^E_i (σ), s^E_j (σ)) = 3(2−σj)(a−c)

2[24−11(σ_i+σ_j) + 5σ_iσ_j] >0. (6-4) It is easy to show that ^∂dEi(σ)

∂σi > 0. Increasing domestic ownership strengthens the domestic owner’s subsidy incentives.

Differentiating (6-4) with σj yields

∂d^E_i (σ)

∂σ_j = −3(2−σ_i)

2[24−11(σ_i+σ_j) + 5σ_iσ_j]²(a−c)<0.

The above equation is equivalent to ^∂dEi(σ)

∂(1−σj) >0. Increasing the shares of foreign equities owned by domestic residents also increases the domestic owner’s subsidy equivalent.

Comparing d^E_i (σ_i, σ_j) with d^E_i (1,1) yields²

d^E_i (σ_i, σ_j)−d^E_i (1,1) = 3(2−σ_j)(a−c)

2[24−11(σ_i+σ_j) + 5σ_iσ_j] −3(a−c) 14

=− 3[10−11σ_i−4σ_j + 5σ_iσ_j]

14[24−11(σ_i+σ_j) + 5σ_iσ_j](a−c).

Thus, d^E_i (σ_i, σ_j) < d^E_i (1,1) if only if σ_i < ¹⁰₁₁⁻₋^4σ_5σ^j

j, or equivalently, ∆σ_i = σ_i − σ_j <

5(1−σj)(2−σj)

11−5σj . The owner’s subsidy equivalent may be larger in the presence of cross-country shareholding if the two firms’ domestic share difference is large enough.

6.3.3 Equilibrium Output

Under the linear demand function, the equilibrium output yields x^E_i (σ) = 2d^E_i (σ) = 3(2−σ_j)(a−c)

24−11(σ_i+σ_j) + 5σ_iσ_j.

The same result holds for the equilibrium output, i.e., x^E_i (σ_i, σ_j)< x^E_i (1,1) if and only if σ_i < ¹⁰₁₁⁻₋^4σ_5σ^j

j.

Proposition 6.2. Given managerial delegation, the presence of cross-country shareholding may increase firm i’s equilibrium output if firm i’s domestic share σ_i is large enough.

d^E_i (σi, σj)Td^E_i (1,1) ⇐⇒ x^E_i (σi, σj)Tx^E_i (1,1) ⇐⇒ σi T 10−4σj

11−5σ_j.

Note that if σ_i < ¹⁶₁₇, cross-country shareholding always lowers firm i’s equilibrium output, i.e., x^E_i (σ_i, σ_j)< x^E_i (1,1) irrespective of values of σ_j.

6.3.4 Equilibrium Total Subsidy

Solving for total subsidy, it yields

S_i^E(σ) = s^E_i (σ) +d^E_i (σ) = (8σ_i+ 5σ_j −5σ_iσ_j −6)(a−c) 24−11(σ_i+σ_j) + 5σ_iσ_j . S_i^E(σ) is positive if and only if σ_j > ²⁽³₅₍₁⁻₋^4σ_σⁱ⁾

i). (σ₁, σ₂) for S₁^E(σ) = 0 are depicted in Figure 6.1. Although the owner’s subsidy equivalent is always positive, total subsidy may become negative when foreign residents’ ownership in the home firm’s shares is large enough. That is, the government’s optimal tariff outweighs the owner’s optimal subsidy.

Since ^∂SiE(σ)

∂σ_k >0(k =i, j), S_i^E(σ_i, σ_j)< S_i^E(1,1) always holds.

2d^E_i (1,1) is equivalent to ˆd^D_i in (5-22).

Next, I examine the effects of managerial delegation under cross-country shareholding.

Without managerial delegation, the optimal government subsidy (see Dick (1993), Welzel (1995)) yields

s^C_i (σ) = (16σ_i+ 12σ_j−12σ_iσ_j−15)(a−c) 33−20(σ_i+σ_j) + 12σ_iσ_j . s^C_i (σ) > 0 is positive if and only if σ_j > ₁₂₍₁¹⁵⁻₋^16σ_σⁱ

i). (σ₁, σ₂) for s^C₁(σ) = 0 are shown by the dashed line in Figure 6.1, which lies between the lines for s^E₁(σ) = 0 and S₁^E(σ) = 0.

Figure 6.1 shows that without managerial delegation, the government is more likely to subsidize its own firm.

(0.5,0.5) σ₂

σ₁ 1

1 0.8

7/11

2/3 5/6

S₁^E >0

S₁^E >0

S₁^E <0 s^E₁ <0

s^E₁ <0

s^E₁ >0 0.9

0.6 S₁^E = 0

s^E₁ = 0

s^C₁ = 0 3/4

0.9

(1,1)

Fig. 6.1: s^E₁ and S₁^E

Without managerial delegation, the equilibrium output yields x^C_i (σ) = 2(3−2σ_j)(a−c)

33−20(σ_i+σ_j) + 12σ_iσ_j. 104

6.4.1 Optimal Subsidy

Comparing s^E_i (σ) withs^C_i (σ) yields

s^E_i (σ)−s^C_i (σ) = (16σ_i+ 13σ_j −10σ_iσ_j −18)(a−c)

2[24−11(σ_i+σ_j) + 5σ_iσ_j] − (16σ_i+ 12σ_j−12σ_iσ_j−15)(a−c) 33−20(σ_i+σ_j) + 12σ_iσ_j

= 4(1−7σ_i)σ_j²−(117−216σ_i+ 32σ²_i)σ_j + 126−210σ_i+ 32σ_i²

2[24−11(σ_i+σ_j) + 5σ_iσ_j][33−20(σ_i+σ_j) + 12σ_iσ_j] (a−c).

(6-5) Since the denominator in (6-5) is positive, the sign ofs^E_i (σ)−s^C_i (σ) is determined by the numerator. Define

f(σ) = 4(1−7σ_i)σ²_j −(117−216σ_i+ 32σ_i²)σ_j+ 126−210σ_i + 32σ²_i (6-6) which is a quadric equation of σj. The discriminant for f(σ) is given by ∆(σi)^def= (117− 216σ_i+32σ_i²)²−16(1−7σ_i)(126−210σ_i+32σ_i²). There are four solutions for ∆(σ_i) = 0, but because of Assumption 4.1, I only consider the range aroundσ_i ∈(0.5,1). Since ∆(0.5)>0 and ∆(1) <0, there exist at least one solution satisfying ∆(σi) = 0 for allσi ∈(0.5,1) in view of the intermediate-value theorem.

Lemma 6.1. For all σ_i ∈(0.5,1), there exists a unique σ_i =bσ satisfying ∆(bσ) = 0.

Proof. (Reduction to absurdity) If there are two solutions σ_a, σ_b (0.5 < σ_a < σ_b < 1) satisfying ∆(σ_a) = ∆(σ_b) = 0, by the mean-value theorem, there must existσ_c ∈(σ_a, σ_b) satisfying ∆^′(σ_c) = 0. Since ∆^′′(σ_i) = 64(941−960σ_i + 192σ²_i) > 0 for all σ_i ∈ (0.5,1),

∆^′(σ_i)> 0 for all σ_i > σ_c. This leads to ∆(σ_i) >0 for all σ_i > σ_b, which contradicts the result that ∆(1)<0.

From above and Lemma 6.1, it yields

∆(σ_i)T0 ⇐⇒ σ_i Sbσ , ∀σ_i ∈(0.5,1). (6-7) Since 1−7σ_i <0 in (6-6), from the results in (6-7), s^E_i (σ) vs. s^C_i (σ) can be shown for the following three cases.

(I)When σ_i >bσ, ∆(σ_i)<0 holds.

f(σ)<0 ⇐⇒ s^E_i (σ)< s^C_i (σ)

(II)When σ_i < bσ, ∆(σ_i) > 0 holds. There exist two real roots σ_j(σ_i) and σ_j(σ_i) satisfying f(σ_i, σ_j) = f(σ_i, σ_j) = 0.





f(σ)>0 ⇐⇒ s^E_i (σ)> s^C_i (σ) when σ_j(σ_i)< σ_j < σ_j(σ_i) f(σ) = 0 ⇐⇒ s^E_i (σ) = s^C_i (σ) when σ_j =σ_j(σ_i) or σ_j(σ_i) f(σ)<0 ⇐⇒ s^E_i (σ)< s^C_i (σ) when σj(σi)< σj or σj > σj(σi), where σ_j(σ_i) = ^{117−216σi+32σ}

2 i+√

∆(σi)

8(1−7σi) and σ_j(σ_i) = ^{117−216σi+32σ}

2 i−√

∆(σi) 8(1−7σi) .

(III)When σ_i =σ,b ∆(σ_i) = 0 holds and σ_j(bσ) = σ_j(σ).b

{ f(σ)<0 ⇐⇒ s^E_i (σ)< s^C_i (σ) when σ_j ̸=σ_j(σ)b f(σ) = 0 ⇐⇒ s^E_i (σ) =s^C_i (σ) when σj =σj(σ)b  

The values of the two roots, σ_j(σ_i) andσ_j(σ_i), for ∆(σ_i) = 0 yield the following lemma.

Lemma 6.2. For all σi ∈(0.5,σ),b σj(σi) and σj(σi) satisfy:

(i) σ_j^′(σ_i)<0 , σ_j^′(σ_i)>0.

(ii) σj(σi)T1 ⇐⇒ σi Sσm. (iii) σ_j(σ_i)T0.5 ⇐⇒ σ_i Tσ_n. Here 0.5< σ_m < σ_n<bσ <1.

Proof. See the Appendix.

The curves forσ₂(σ₁) and σ₂(σ₁) obtained from Lemma 6.2, are depicted in Figure 6.2.

The two curves intersected at σ₁ =σ, whereb σ₂(σ) =b σ₂(bσ). Figure 6.2 is largely divided into two areas by the curves of σ₂(σ₁) and σ₂(σ₁). The left area shows s^E_i (σ) > s^C_i (σ) and the right area shows the opposite one; the curves represent s^E_i (σ) = s^C_i (σ). Note that regardless the value of σ₂, if σ₁ > bσ, s^E₁(σ) < s^C₁(σ) always holds; and if σ_i < σ_m, s^E₁(σ)> s^C₁(σ) always holds.

Proposition 6.3. Given cross-country shareholding, managerial delegation may raise or lower the governments’ optimal subsidy rates depending on the cross shareholding structure (σ_i, σ_j)whenσ_m ≤σ_i ≤bσ. Furthermore, if the domestic shareholding ratio is small enough that σ_i < σ_m, managerial delegation always strengthens the government’s subsidization incentive; if the domestic shareholding ratio is large enough that σ_i >bσ, the government’s subsidization incentive is always weakened under managerial delegation.

Without cross shareholding, as shown in the previous chapters, managerial delegation always weakens the government’s subsidization incentive. When the domestic shareholding ratio is large, a small fraction of foreign shareholding does not change this result. However, when the domestic shareholding is small enough, a nearly half, the large portion of foreign shareholding induces the government to tax the exports. Under managerial delegation, the negative cross-rent shifting and dividend suppression effects are dampened, and as such, the government’s tax incentive is also weakened.

(0.5,0.5) σ2

σ₁ 1

σn 1

σm σb

s^E₁(σ)< s^C₁(σ) s^E₁(σ)> s^C₁(σ)

σ₂(σ₁) σ2(σ1)

σ₂(bσ) = σ₂(bσ)

Fig. 6.2: Values of s^E₁(σ) vs. s^C₁(σ)

6.4.2 Owner’s Subsidy Equivalent and Total Subsidy

d^E_i (σ)> s^C_i (σ) and S_i^E(σ)> s^C_i (σ) hold for any given (σ_i, σ_j). With managerial delega-tion, both the owner’s subsidy equivalent and total subsidy always result in higher subsidy rates regardless of the cross shareholding structure.

6.4.3 Output Decision

Comparing x^E_i (σ) with x^C_i (σ) yields

x^E_i (σ)−x^C_i (σ) = 2(1−σ_i)(27−29σ_j+ 8σ²_j) +σ_j

[24−11(σ_i+σ_j) + 5σ_iσ_j][33−20(σ_i+σ_j) + 12σ_iσ_j] >0.

Given σ_k(k = i, j) > 0.5, x^E_i (σ) > x^C_i (σ) holds. Managerial delegation increases the equilibrium output irrespective of the cross shareholding structure.

Proposition 6.4. Given cross-country shareholding, managerial delegation always in-creases each firm’s equilibrium output, i.e., x^E_i (σ)> x^C_i (σ).

ドキュメント内 Trade and Industrial Policies under International Interdependence (ページ 107-117)