Considering a duopoly industry, firm 1 and firm 2 are both managerial firms. We assume the duopoly model with linear demand and cost functions. Let inverse demand function , where Q is the sum of the output levels of firms 1 and 2,
respectively and . The cost function is Q
a p= −
q1 q2 Ci(qi)=cqi, where . There is a two-stage game in consideration. It is assumed that the market demand is not too small; more precisely, , which ensures positive quantities in equilibrium.
2 ,
=1 i
c a>
Stage 1: The owner writes and publicly announces a contract with his manager that specifies how the manager will be rewarded. From Jansen et al. (2007), the manager of firm is paid i
Q qi
i
i α
π + , where αi is an incentive weight, πi and
Q qi
stand respectively, for profits and market share. Here, in order to deal with a three-stage game later, specify gi =πi+αi(lnqi −lnqj), where i≠ Let .j
Q k = qi ,
then will also be able to measure the market share of firm i, considering
) ln (lnqi − qj
k k k
f = −
ln1 )
( is an increasing function of . Assume that the owner seeks to maximize profit:
k
i i =(p−c)q π .
Stage 2: The managers simultaneously choose their firm’s output to maximize
i. g
The game is solved by employing the method of backward induction.
Stage II Stage I
Time
Figure 2.1 Game stages of Cournot competition model with market share delegation Managers make choice of quantity simultaneously.
Firm’s owners choose the incentive to the managers.
According to the first-order conditions, the equilibrium quantities of the market game satisfy the following system of equations:
0
Solving (2.1) and (2.2), incentive solutions and reduced-form solutions of quantities are:
) )(
2 4 14(
1 a c
qim = + − ; (5 2 1)( )2
98
1 a c
m
i = − −
α . (2.3)
Substitute them into profit function to obtain
)2
)(
2 10 98(
1 a c
m
i = − −
π . (2.4)
Note that, in equilibrium, qim =qimj but αim αimj 4
=1 , where the superscript
represents our form of market share delegation while
m
mj denotes market share delegation à la Jansen et al. (2007). The new form of market share delegation we are introducing here not only preserves the spirit of Jansen et al. (2007) but also becomes useful in dealing with the three-stage game of concerned issues as well.
Fershtman and Judd (1987), Sklivas (1987) considered the case of sales delegation in that according to the contract, managers receive a bonus which is proportional to a linear combination of profit and sales: αiπi +(1−αi)pqi. To compare equilibrium output and profit under market share delegation, sales delegation and simple Cournot
solution, we can rank in order and where c and s
denote simple Cournot and sales delegation respectively. Hence, in duopoly, when firms take different delegation forms, market share or sales delegation, it will result in different equilibrium outcomes.
c i m i s
i q q
q > > πic >πim >πis
2.2 One-Sided Delegation
Assume that firm 1 is a managerial firm in which the ownership and control is separated and firm 2 is an entrepreneurial firm in which the ownership and control is not separated. In stage 2, the manager of firm 1 maximizesg1 =π1+α1(lnq1−lnq2). The manager of firm 2 maximizesπ2 =(p−c)q2.
Stage I
Time Stage II
Firms make choice of quantity simultaneously.
Figure 2.2 Game stages of Cournot competition model with one-side market share The owner of firm 1
chooses the incentive to his manager.
Simultaneously solving (2.5) and (2.6), we obtain incentive weight and quantities solutions:
2
1 ( )
8 1 a−c
α = , 1 ( ) 2 2 2
1 a c q
q = − = . (2.7)
Substituting (2.7) into profit functions, the profit solutions are:
2 2
1 ( ) 2
8
1 π
π = a−c = . (2.8)
This result is the same as a Stackelberg leader solution. Hence, in an asymmetric duopoly, if only one firm adopts delegation -whether sales delegation2 or market share delegation-as long as the other is an entrepreneurial firm, it acts as Stackelberg leader, but with different equilibrium outcome. See Fingure 3, qc <qm <qs.
q2
R1m R1s
R1c
R2
q1
qc qm qs
Figure 2.3 When only one firm adopts delegation it acts as Stackelberg leader in output competition.
2 See FJS model for sales delegation case.
Proposition 2.1: Regardless of the form of delegation in duopoly, if only one firm adopts delegation it acts as Stackelberg leader in output competition.
2.3CONCLUDING REMARKS
In this chapter, it can conclude two points. First, in order to deal with a three-stage game in later chapters, we offer a new market share delegation form,
) ln
(ln i j
i i
i q q
g =π +α − , where i≠ , to instead the original manager’s salary j function in Jansen et al. (2007). After calculating, the equilibrium, qim =qimj but
mj i m
i α
α 4
=1 , where the superscript represents our form of market share delegation
while denotes market share delegation à la Jansen et al. (2007). The new form of market share delegation we are introducing here not only preserves the spirit of Jansen et al. (2007) but also becomes useful in dealing with the three-stage game of concerned issues as well. We summarized in Table 2.1.
m mj
Table 2.1 Compare the new market share form with Jansen et al.(2007) Original Jansen et al.
(2007) model
New market share delegation form Manager’s salary
function gi =πi+αi(lnqi −lnqj) gi =πi+αi(lnqi −lnqj)
Outcome
) )(
2 4 14(
1 a c
qimj = + −
)2
)(
2 2 10 49(
1 a c
mj
i = − −
α
mj i m
i q
q =
mj i m
i α
α 4
=1
Secondly, in an asymmetric duopoly, if only one firm adopts delegation -whether sales delegation or market share delegation-as long as the other is an entrepreneurial firm, it acts as Stackelberg leader in output competition.
CHAPTER THREE： EXPORT-COMPETING MODEL
Brander and Spencer (1985) have shown that export subsidies can appear as attractive weapons because they improve the relative position of the domestic firm in non-cooperative rivalries with other firms, and allow it to expand its “market share”.
Delegation of trade policy decisions in a customs union has been considered by Gatsios and Karp (1991, 1995). They show that the countries in a customs union may gain by delegating trade policy to the most aggressive member of customs union. Das (1997) demonstrated that the scale of trade policy intervention with symmetric sales delegation in an oligopolistic export market is reduced, and further argued that any other form of incentive scheme to the managers which is set strategically (via-á-vis those offered by other firms) will have a bearing on optimal trade policy. Ma (2000) showed that the instrument of managerial incentive in the form of sales delegation as a credible commitment which could substitute for export subsidy and making firm acts as a Stackelberg leader.
In this chapter, we add market-share delegation into export rivalry model to demonstrate the instrument substitutability between different forms of managerial delegation and export subsidy in both simultaneous and sequential move games. In particular, we show the ranking of optimal export subsidy under different forms of incentive scheme.
The chapter is organized as follows. Section 1 and 2 consider an export rivalry model with one-sided and two-sided managerial delegation respectively. Section 3 concludes the paper.
3.1 STRATEGICTRADE POLICY WITH ONE-SIDED DELEGATION
3.1.1 One Country Intervention
Extend the model of chapter two to consider the export rivalry model. Assume that are two countries, a home and a foreign country and that each country has one firm producing homogeneous goods, the home firm is a managerial enterprise which is labeled as firm 1 and the foreign firm is an entrepreneurial firm which is labeled as firm 2. Both firms export to a third-country market where they compete in a Cournot duopoly. Assume only the home government decides to provide export subsidy. In such a setting, a three-stage game evolves.
Stage 1: the home government chooses specific subsidy to maximize social welfare:
s1
1 1 1
1 s q
w =π − , where π1 =(p−c)q1+s1q1
Stage 2: the owner of firm 1 offers incentive scheme g1=π1+α1(lnq1−lnq2) to his manager, but himself choosing α to maximize profit function1 π . 1
Stage 3: managers simultaneously compete in quantities.
Stage I Stage III
Time
The owner of firm 1 chooses
the incentive to the manager. Firms compete in quantity.
Home government decides the subsidy.
Figure 3.1 Game stages of export-competing model with one-side market share delegation and one-side intervention.
Stage II
Now system (2.1) and (2.2) must be rewritten as
As before, firstly simultaneously solving (3.1) and (3.2) to obtain , and welfare, the home government decides on the export subsidy. We have . The other variables can be obtained as follows:
1 =0
These results imply that when the owner can “manage” the manager by providing a suitable incentive contract, there is no need for government to intervene; it complies with the requirement of export-subsidy prohibition by World Trade Organization, Economic Cooperation and Development, etc. Because of the results (3.3) are identical with (2.7) and (2.8), we have the following proposition.
Proposition 3.1: When only the domestic firm’s owner decides on delegation whether it is sales or market-share case, it makes the domestic firm acting as a Stackelberg leader, export subsidy is no longer needed; hence, delegation and export subsidy is strategically substitutable for profit shifting.
3.1.2 Two Countries Intervention
We now would like to see that both governments intervene while firm 1 is a managerial enterprise with market-share or sales delegation and firm 2 is an entrepreneurial firm.
3.1.2-1 One-Sided Market Share Delegation
Assume that firm 1 is a market-share delegation firm while firm 2 is an entrepreneurial firm. It is a three-stage game to be solved. In stage 1, both governments choose a specific subsidy si to maximize social welfare,
i i i
i sq
w =π − ; In stage 2, the owner of firm 1 offers incentive scheme )
ln (ln 1 2
1 1
1 q q
g =π +α − to his manager, but himself choosing α1 to maximize profit function ,π1; In stage 3: managers simultaneously compete in quantities.
Stage I Stage II Stage III
Time
The owner of firm 1 chooses the market share delegation incentive to the manager.
Firms compete in quantity.
Figure 3.2 Game stages of sequential export-competing model with one-side market share delegation and two countries intervention.
Both governments decide the subsidy.
We can rewrite equation (2.1) and (2.2) as:
0
We first simultaneously solve (3.4) and (3.5) to obtain , , and maximize social welfare, both governments decide on the export subsidies,
and
In the case of one-sided market share delegation - firm 1 is a managerial firm, the optimal trade policy of the home country is no intervention, but for foreign government it can take an export subsidy to defend against the profit-shifting. Here, we show that policy intervention and market share delegation exits a relationship of substitution which is been stated in proposition 2, but the welfare of country 2 under export subsidy is higher than country 1 when firm 1 adopts managerial incentive which is mainly because the foreign government pre-commits to policy intervention.
Because the export subsidy of home government is substituted by private firm’s delegation, we want to examine the following scenario that in the first stage, firm 1 adopts market-share delegation without government intervention, but the foreign government offers a subsidy to firm 2 simultaneously, and in the second stage both
firms compete in quantities.
Stage II Stage I
Time
Managers make simultaneous choice of quantity.
The owner of firm 1 chooses the market share delegation incentive to the manager, and foreign government decides the subsidy, simultaneously.
Figure 3.3 Game stages of simultaneously export-competing model with one-side market share delegation and one country intervention.
In stage 2, the system from first order condition is
0
In stage 1, the system from first order condition is
[ ]
By simultaneously solving (3.7) and (3.8), we obtain the following results:
)
2 1
1 ( )
98 9 a c
w =π = − , 2 ( )2
196 25 a−c
π = , 2 ( )2 196
15 a c
w = − . (3.9)
Comparing equilibrium outcomes of sequentially chosen and simultaneously chosen instruments in market-share delegation, the welfare effects can be seen from (3.6) and (3.9) which is presented in Table 3.1.
Table 3.1 Market-share delegation game
Market-share delegation Welfare Comparison Sequentially chosen
instruments
2 2
2
1 ( )
12 ) 1
18(
1 a c w a c
w = − < = −
Simultaneously chosen instruments
2 2
2
1 ( )
196 ) 15
98(
9 a c w a c
w = − > = −
Proposition 3.2: When the foreign government pre-commits export subsidy to its entrepreneurial firm, such policy is used to shift profit from the rival firm. The private sector of the home country will provide incentives to its manager that replaces home government intervention. However, if the foreign government and domestic firm can commit simultaneously, the home country performs better than the foreign country when the domestic firm decides on market-share delegation.
3.1.2-2 One-Sided Sales Delegation
Assume that firm 1 adopts sales delegation instead of market-share delegation while firm 2 is an entrepreneurial firm. In stage 1, both governments choose a specific subsidy si to maximize social welfare wi =πi −siqi; In stage 2, the owner of firm 1 offers incentive scheme g1 =α1π1+(1−α1)pq1 to his manager, but himself choosing α1 to maximize profit function π1; In stage 3: managers simultaneously
compete in quantities.
Stage I Stage III
Time Stage II
The owner of firm 1 chooses the sales delegation incentive to the manager.
Firms compete in quantity.
Both governments decide the subsidy.
Figure 3.4 Game stages of sequential export-competing model with one-side sales delegation and two countries intervention.
The equilibrium outcomes are obtained as follows:
1 =0
s , ( )
3 1
2 a c
s = − ,
c c a
6 ) 1 (
1
− −
α = , ( ) 3 1
1 a c
q = − , ( )
2 1
2 a c
q = − ,
2 1
1 ( )
18 1 a c
w =π = − , 2 ( )2
4 1 a−c
π = , 2 ( )2 12
1 a c
w = − . (3.10)
We get the same results as shown in section 3.1.1; managerial delegation and government intervention are substitutable instruments no matter what form of delegation firm 1 is under.
Next, we examine the following scenario that in the first stage, firm 1 adopts sales delegation without government intervention, but the foreign government offers a subsidy to firm 2 simultaneously, and in the second stage both firms compete in quantities.
Stage I Stage II
Time
Managers make simultaneous choice of quantity.
The owner of firm 1 chooses the sales delegation incentive to the manager, and foreign government decides the subsidy, simultaneously.
Figure 3.5 Game stages of simultaneously export-competing model with one-side sales delegation and one country intervention.
After solving the system of equations, we obtain the following results:
) 5( 1
2 a c
s = − ,
c c a
5 ) 1 (
1
− −
α = , ( ) 5 2
2
1 q a c
q = = − , 1 1 ( )2
25 2 a c
w =π = − ,
2
2 ( )
196 4 a−c
π = , 2 ( )2 25
2 a c
w = − (3.11)
From (3.9) and (3.11), we can see that when the home firm adopts sales delegation, the foreign government is forced to decide on larger subsidy ( )
5 1
2 a c
s = − than )
7( 1
2 a c
s = − , the case of home firm who adopts market-share delegation.
Comparing equilibrium outcomes of sequentially chosen and simultaneously chosen instruments in sales delegation, the welfare effects can be seen from (3.10) and (3.11) which is presented in Table 3.2.
Table 3.2 Sales delegation game
Sales delegation Welfare Comparison Sequentially chosen
instruments
2 2
2
1 ( )
12 ) 1
18(
1 a c w a c
w = − < = −
Simultaneously chosen instruments
2 2
1 ( )
25 2 a c w
w = = −
Comparing Table 3.1 and Table 3.2, we have
Proposition 3.3: In the sequentially chosen instruments game, sales delegation and market share delegation is substitutable. In the simultaneously chosen instruments game, sales delegation and export subsidy are substitutable, but market-share delegation is a welfare-dominant strategy.
3.2 STRATEGIC TRADE POLICY WITH TWO-SIDED DELEGATION
3.2.1 One Country Intervention
Now we consider the case where the home government decides to offer export subsidy to its firm. In stage 1, home government maximizes its social welfare to decide on the subsidy; in stage 2, both firms simultaneously offer incentives to their managers; in stage 3, managers compete in quantities.
Stage II
Stage I Stage III
Time
Owners choose the incentive
to the managers. Managers compete in quantity.
Home government decides the subsidy.
Figure 3.6 Game stages of export-competing model with two-side market share delegation and one country intervention.
Now, the equation (2.1) and (2.2) can be rewritten as
0
We first simultaneously solve (3.12) and (3.13) to obtain , , maximize social welfare, home government decides on the export subsidy. We can obtain the optimal subsidy (5 3 2)( )
7 1
1 a c
sm = − − ; other variables can be obtained as follows:
2
) )(
2 3 14(
1
2 a c
qm = + − , 1 (2 2)( )2
4
1 a c
m = − −
π , 1 (4 2)( )2 28
1 a c
wm = − − ,
2 2
2 (10 2)( )
196
1 a c
wm =πm = + − . (3.14)
The optimal subsidy and profit under two-sided sales delegation but only the home country intervenes are: ( )
12 1
1 a c
ss = − , 1 ( )2
12 1 a c
s = −
π , 1 ( )2 20
1 a c
ws = − ,
2 2
2 ( )
18 1 a c
ws =πs = − . We show that under the market share delegation case, the welfare of the home country and the two firms’ profit are larger than the results of sales delegation case. Because the degree of competitiveness for market-share delegation is less than sales delegation, = (5−3 2)( − )>
7 1
1 a c
sm ( )
12 1
1 a c
ss = − , under market share delegation the subsidy is larger than sales delegation for encouraging its firm to be more aggressive.
Proposition 3.4: When only one country intervenes, the welfare of both countries under market share delegation is higher than that of sales delegation.
3.2.2 Two Countries Intervention
Now we consider the case that both governments decide to offer subsidies to their export firms. In stag 1, the home government maximizes its social welfare to decide on the subsidy; in stage 2, both firms simultaneously offer incentives to their managers; in stage 3, managers compete in quantities. Now, the equation (2.1) and (2.2) can be rewritten as
Stage I Stage III
Time Stage II
Owners choose the incentive
to the managers. Managers compete in quantity.
Both governments decide the subsidies.
Figure 3.7 Game stages of export-competing model with two-side market share delegation and two countries intervention.
0
We first simultaneously solve (3.15) and (3.16) to obtain , , substituting them into stage 1 to maximize social welfare, home government and foreign government decide on the export subsidies to obtain the following results:
)
In the profit-maximization case of Brander and Spencer (1985), the simple Cournot model is
5 ) (a c
sc −
= and ( )2
25 2 a c
wc = − . In Das (1997), the sales delegation case,
14 ) (a c
ss −
= and ( )2
49 3 a c
ws = − . From (3.17), we find that the ranking of the optimal subsidy and welfare under simple Cournot, market share and sales delegation is and . We draw conclusions on this in proposition 3.5.
s m
c s s
s > > wc >wm >ws
Proposition 3.5: When both firms delegate and governments intervene, the subsidy and welfare under market share delegation is higher than that of sales delegation.
Clearly, in the case of bilateral choices of incentives, the two firms are involved in a “Prisoner’s Dilemma”, but market share delegation is in less degree.
3.3 CONCLUDING REMARKS
In this chapter, we demonstrated that when a domestic firm’s owner decides on delegation whether it is a sales or market-share case, it makes the domestic firm acting as a Stackelberg leader; delegation and export subsidy is substitutable for profit-shifting. Considering the timing of instrument choice with one-sided delegation, in a sequentially chosen instrument game, the foreign government pre-commits export subsidy to its entrepreneurial firm, such policy is used to shift profit from a rival firm;
in consequence, the home government “stays put” without intervention and let the private sector provides incentives to its managers for competing with the foreign rival firm, sales delegation and market share delegation are substitutable. However, in a simultaneously chosen instrument game, the domestic firm and foreign government
commit strategic instruments simultaneously; sales delegation and export subsidy are substitutable, but market-share delegation is a welfare-dominant strategy.
Furthermore, for the case of two-sided delegation, the welfare of both countries under market share delegation is higher than that of sales delegation whether one country or two countries intervene. At end, we must point out that in the case of bilateral choices of incentives, two export firms are involved in a “Prisoner’s Dilemma”, but market share delegation is in less degree.
CHAPTER FOUR: OPTIMAL DISCRIMINITORY TARIFF AND MANAGERIAL INCENTIVE UNDER OLIGOPOLISTIC
COMPETITION
Brander and Spencer (1984) discussed with the profit-shift effect in imposing tariff. Hwang and Mai (1991) adapted that the optimal structure of discriminatory tariff is determined mainly by the cost differences among the foreign exporting countries, and that the countries with the highest costs will be charged the lowest tariffs. Kuo and Mai (1991) demonstrated that in the short term, import country can increase its social welfare by discriminatory tariff rather than uniform tariff.
In this chapter we extend the model of Hwang and Mai (1991) and Kuo and Mai (1991) by adding managerial delegation into consideration to see how it affects the configuration of discriminatory and uniform tariff rate.
This chapter is organized as follows. The basic model is presented in section 1.
Section 2 and 3 consider discriminatory and uniform tariff, respectively. Section 4 concludes this chapter.
4.1 Basic Model
Consider an oligopolistic industry that spans two countries, 1 and 2. There is only one firm within each country. The domestic country imports a homogeneous product
and from countries 1 and 2, respectively. For simplicity, we assume that this commodity is not produced in the domestic country. Let inverse demand function in the domestic market is , where Q is the sum of the output levels of firm 1
q1 q2
Q a p= −
and firm 2, respectively, and . Moreover, assume that the domestic
government understand the structure of the industry and is able to set credible tariff on
government understand the structure of the industry and is able to set credible tariff on