Input Price Contracts and Strategic Delegation with ...

ACADEMIA ECONOMIC PAPERS 36 : 4 (December 2008), 387–404

Input Price Contracts and Strategic Delegation with Downstream Duopoly Pei-Cheng Liao ∗

Department of Accounting National Taiwan University

Keywords: Floating price contract, Fixed price contract, Strategic delegation, Managerial incentive scheme JEL classification: D21, D43, L13

∗

Correspondence: Pei-Cheng Liao, Department of Accounting, National Taiwan University, Taipei 106, Taiwan. Tel: (02) 3366-1127; Fax: (02) 2363-8038; E-mail: [email protected]. I am grateful to two anonymous referees for their constructive comments. The remaining errors are the responsibility of mine. I gratefully acknowledge the financial support of the National Science Council, Taiwan, under grant no. NSC 95-2415-H-002-017.

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ABSTRACT





This paper examines how input price contracts by an upstream monopolist affect

the incentive schemes that owners of downstream duopolists offer their managers. In the Cournot case, under a floating price contract in which the upstream supplier chooses the input prices after the managerial incentive schemes are made, the owners of the downstream firms compensate their managers for profits while penalizing them for sales. Conversely, a fixed price contract (where the input prices remain unchanged following the downstream delegation decisions) leads to more aggressive managerial behavior and higher market output, thereby benefiting the monopoly supplier. Similar results are obtained for the Bertrand case wherein the owners of the downstream firms direct their managers toward a more aggressive behavior under a fixed price contract than under a floating price contract. The supplier always prefers a fixed price contract to a floating price contract.

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1. INTRODUCTION


It is well known that most firms are characterized by a separation of ownership and management, which raises a wide range of agency problems. This separation leads to inefficiencies because of asymmetric information and different objectives of owners and managers, e.g., Jensen and Meckling (1976) and Fama and Jensen (1983). In formulating incentives for managers, it is generally argued that owners should compensate them according to profits instead of sales, output, or other variables. However, such an argument may not hold in a strategic context, and hence the owner-manager relationship can be regarded as a strategic delegation problem rather than a principal-agent problem. The literature on strategic delegation has shown that owners can benefit from delegating decisions to managers in oligopolistic markets. The compensation schemes for managers serve as commitment devices used by owners to precommit managers to certain actions in later stage, which in turn alter the actions taken by rival managers. The strategic delegation model developed along the line of Vickers (1985), Fershtman and Judd (1987), and Sklivas (1987) usually consists of two stages. In the first stage, owners choose the managerial incentive scheme, which is a weighted sum of profits and sales revenues.1 In the second stage, managers compete with each other in a Cournot or Bertrand fashion. In a duopoly model, Fershtman and Judd (1987) and Sklivas (1987) show that owners choose a positive (or negative) weight on sales in the incentive scheme, committing managers to a more (or less) aggressive behavior in quantity (vs. price) competition. Several papers have attempted to extend the Fershtman-Judd-Sklivas model (hereafter referred to FJS) in different contexts, and most of the papers primarily focus on the horizontal aspects of market structure. 2 An implicit assumption in these models is that firms are vertically integrated. Consequently, there has been little analysis on the impact of a vertically integrated industry relationship on strategic delegation except Park (2002), examining the effects of the upstream monopoly on the managerial incentive schemes of downstream firms. 1

Some papers consider relative performance incentive scheme, which is a weighted sum of the firm’s own profit and its rival’s profit, for example, Donaldson and Neary (1984), Fumas (1992), Lundgren (1996), and Miller and Pazgal (2001, 2002, 2005). Jansen et al. (2007) consider a market share delegation game in which the managerial incentive scheme is a weighted sum of profits and market share. 2 For example, Barros (1995), Basu (1995), Hwang and Mai (1995), Goering (1996), Zhang and Zhang (1997), Ishibashi (2001), Barros and Grilo (2002), Kopel and Riegler (2006).

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In this paper, we extend the literature on strategic delegation to a model with a vertical industry structure. We investigate how input price contracts (floating price vs. fixed price) adopted by a supplier affect managerial incentive schemes the owners of the downstream firms offer their managers and the profits of the upstream monopolist and downstream duopolists. This extension facilitates the study of how contracts across the boundaries of firms (between the supplier and the downstream firms) interact with contracts within the boundaries of the firms (between an owner and a manager). 3 In a floating contract, the supplier determines the input prices it charges to downstream firms after the owners of the downstream firms sign incentive schemes with their managers. The delegation decision of each owner has two effects: a horizontal effect and a vertical effect. Under Cournot competition, compensating a manager for both profits and sales makes him produce more output, leading to horizontal profit shifting from the rival firm to one’s own firm as shown in the FJS model. It also leads to increased demand for the input used to produce the final good. The increased demand for the input provides the upstream monopolist an opportunity to increase the input prices to vertically extract rents from the downstream firms. We show that there are two countervailing vertical effects of the delegation decision; that is, when determining an incentive scheme, each owner will take into consideration how the incentive scheme may affect the input price charged by the supplier to his own firm (own-price effect) and the input price charged to the rival firm (cross-price effect). The own-price effect induces the owner to direct his manager to less aggressive behavior in order to avoid being charged a higher input price by the supplier. However, the cross-price effect induces the owner to direct his manager to more aggressive behavior in order to increase the input price of the rival firm. We show that the own-price effect dominates the horizontal effect and the cross-price effect, and thus the owners compensate their managers for profits but penalize them for sales. The opportunistic behavior of the upstream supplier to increase the input prices after incentive schemes are determined under a floating price contract actually hurts the supplier. One may consider a fixed price contract under which the input prices are chosen before the incentive schemes are determined and they cannot be changed thereafter. Under a fixed price contract, the input price charged to each downstream firm intuitively acts just like an increase in the marginal production cost of the firm. Thus, the qualitative result of the FJS model is not changed in that mangers are compensated

















3

We thank a referee for providing this point to strengthen the motivational aspects of this paper.

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for both profits and sales under a fixed price contract. This paper is related to Park (2002), who also examines the effects of the upstream monopoly on the incentive schemes for the managers of downstream firms and, in effect, corresponds to the special case of a uniform input price under a floating price contract in our model. There are two main differences between Park (2002) and this paper. First, we consider the discretionary power of the supplier to charge the downstream firms different input prices and we show that Park’s results are not valid under this case. Second, in addition to a floating price contract, we also consider a fixed price contract under which the supplier sets the input prices before the owners of the downstream firms sign contracts with their managers. Our model facilitates a comparison between the two price contracts. The main contribution of this paper is to demonstrate that suppliers prefer fixed price contracts to floating price contracts. This is due to the proposition that under a fixed price contract each owner directs his manager to more aggressive behavior, leading to higher demand for the input and thus benefiting the supplier. Since a fixed price contract is equivalent to the FJS model, our findings imply that the FJS result validates this kind of upstream monopoly market structure. 4 It is worth relating this paper to the work of Banerjee and Lin (2003) who, in a comparison of a floating price contract and a fixed price contract in an oligopoly model, found that a fixed price contract where the input price remains unchanged following downstream R&D promotes downstream R&D and improves social welfare. Although they also compare a floating price contract and a fixed price contract in a vertical industry structure, the model and the issue they addressed differ from ours. As organized, Section 2 describes the model and analyzes the equilibrium of the game under a floating contract. Section 3 analyzes the equilibrium of the game under a fixed price contract. Section 4 compares the effects of input price contracts on producer surplus, consumer surplus, and social welfare. Section 5 examines the robustness of our results by considering the case of Bertrand competition, and Section 6 provides some concluding remarks.

















2. FLOATING PRICE CONTRACT


The analysis follows the FJS model extended to a vertically related industry. We con4

We thank a referee for providing this point to strengthen the contribution of this paper.

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sider a three-stage, three-firm model, in which a monopoly supplier sells an input to two competing downstream firms that use the input to produce a homogeneous final product. For simplicity, we assume that one unit of the input is required to produce one unit of the final product. To focus on examining how input price contracts affect the managerial incentive schemes of the downstream firms, we assume that the monopoly supplier is a profit-maximizer. The downstream market is modeled as in the FJS model, each downstream firm with one owner and one manager, and the production decision is delegated to the manager. Following the FJS model, the managerial incentive scheme is given by M i = αi πi + (1 − αi )Ri , where πi and Ri are the profits and sales of firm i, respectively (i = 1, 2). In the first stage, owners 1 and 2 simultaneously select α1 and α2 , respectively, so as to maximize their profits.5 If αi = 1, firm i is a pure profit-maximizing firm; if α i < 1, owner i directs manager i away from profit maximization towards sales; and if α i > 1, owner i overcompensates manager i for profits by penalizing sales. In the second stage, the monopoly supplier charges firm i a per-unit price ki for the input.6 For simplicity, it is assumed that the supplier produces the input at zero marginal cost, because this will not affect the equilibrium of the game. In the third stage, manager i determines the quantity that maximizes M i in a Cournot fashion.7 The per-unit cost for the output of firm i is k i + ci , where ci is an additional marginal cost of production, and we assume that c i = 0, i = 1, 2.8 Our results remain valid when ci > 0.

5 As shown in Fershtman and Judd (1987), the real reward for manager i is of the form A i + Bi Mi for constants Ai and Bi , with Bi > 0. Owner i chooses Ai and Bi such that Ai + Bi Mi equals the manager’s opportunity cost of participation, which is essentially a fixed cost. Thus, maximizing profits net of compensation paid to the manager is equivalent to maximizing profits. 6 It may seem to be unreasonable that the supplier will set the input price contingent on the managerial incentive scheme that the owner offers to his manager. However, what the supplier observes in the second stage is αi rather than compensation Ai + Bi Mi . αi can be regarded as the type of the manager in terms of aggressiveness, and it is assumed to be known to every party in the game. The smaller α i is, the more aggressive and sales-oriented manager the owner hires. The supplier determines the input price based on the type of the manager he observes. 7

Mi .

Managers are assumed to be risk-neutral, so maximizing Ai + Bi Mi is equivalent to maximizing

8

DeGraba (1990) shows that when the upstream supplier is allowed to price discriminate, he charges the downstream firm with lower marginal cost a higher price than he charges the firm with higher marginal cost. Moreover, Das (1997) shows that an increase in ci increases αi ; that is, the higher marginal cost of a firm, the less aggressive manager the owner chooses. Thus, with the assumption that c1 = c2 = 0, we eliminate the effects of different productivities of the downstream firms on the choices of input prices and managerial incentive schemes, thereby concentrating more on the effects of input price contracts on the choices of managerial incentive schemes.

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To make our analysis interesting, we assume that the downstream market is big enough so that the output level, the downstream market price, and the upstream input prices are all nonnegative. Following the FJS model, we assume that the downstream duopolists compete in a market, and that the inverse demand function is given by p = a − b(q1 + q2 ), where p is the market price, and q1 and q2 are the outputs of firms 1 and 2, respectively. The game is solved by backward induction. In the third stage, taking (α 1 , α2 ), (k1 , k2 ), and the output of the other firm as given, manager i chooses q i so as to maximize Mi . The equilibrium output levels are











qi∗ (k1 , k2 , α1 , α2 ) =

a − 2αi ki + αj kj , 3b

i, j = 1, 2, and i = j.

It is easy to show that αi and ki have the same effect on the output: a decrease in α i (or ki ) will increase qi∗ and the total output Q∗ , but it will decrease qj∗ .9 In the second stage, taking (α1 , α2 ) as given, the upstream monopolist determines k1 and k2 so as to maximize his profits: k1 q1∗ + k2 q2∗ . The equilibrium input prices are ki∗ (α1 , α2 ) = (αi +5αj )a/(14α1 α2 −α21 −α22 ), and the input price differential is equal to ki∗ − kj∗ = 4a(αj − αi )/(14α1 α2 − α12 − α22 ). Thus, ki∗ ≤ kj∗ if and only if αi ≥ αj , implying that the upstream supplier charges the downstream firm with a more salesoriented (i.e., more aggressive) manager a higher input price than the downstream firm with a less sales-oriented manager.





Proposition 1 A floating price contract by the upstream supplier makes him charge the firm with a more aggressive manager a higher input price than the firm with a less aggressive manager. In the first stage, owner i chooses αi so as to maximize the profits of firm i : πi = (a−bqi∗ −bqj∗ −ki∗ )qi∗ . Solving for a symmetric equilibrium yields α ∗ = 2. Thus, unlike Park (2002), we show that the simple Nash equilibrium outcome (i.e., α = 1) cannot be achieved under a floating price contract. To see why the owners will overcompensate their managers for profits by penalizing sales, we express dπ i /dαi |α1 =α2 =1 as follows:





9 As shown in the FJS model, the reaction function of firm i shifts out as owner i decreases α i , directing manager i towards sales. As a result, manager i behaves more aggressively to produce more output.

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∂πi dπi  =  dαi α1 =α2 =1 ∂qj∗



∂qj∗ ∂ki∗ ∂qj∗ ∂kj∗ ∂qj∗ + + ∂ki ∂αi ∂kj ∂αi ∂αi

∂πi ∂qj∗ = + ∂qj∗ ∂αi
(−)  (+)






∂πi ∂πi ∂qj∗ + ∂qj∗ ∂ki ∂ki∗ (−)

(+)

P Si



OPi

(−)

(+)

(−)





+

∂πi ∂ki∗ ∂ki∗ ∂αi

∂πi ∂qj∗ ∂kj∗ ∂ki∗ + , ∂αi ∂qj∗ ∂kj ∂αi (−)




(−)



(−)



(−)

CPi

(−)

where PSi , OPi , and CPi are interpreted as the profit-shifting effect, own-price effect, and cross-price effect, respectively, of an increase in α i on πi , starting from profitmaximizing contracts (i.e., αi = 1). In the standard FJS model, delegation to managers has only a horizontal effect (i.e., the profit-shifting effect), and PS i < 0, so αFJS < 1. Our model contains a vertical effect in addition to a horizontal profit-shifting effect. That is, when determining a managerial incentive scheme, the owner of a downstream firm takes into consideration how the scheme may affect the input price charged by the supplier to his own firm (own-price effect) and the input price charged to the rival firm (cross-price effect). The own-price effect is positive because an increase in α i leads to a decrease in ki∗ , thereby benefiting firm i. The cross-price effect is negative, because a decrease in αi leads to an increase in kj∗ , which in turn decreases qj∗ and benefits firm i. The vertical effect (own-price net of cross-price) is positive and dominates the negative horizontal effect so the total effect is positive. Thus, α ∗ > 1 > αFJS , and the FJS argument for directing managers toward sales is dominated by the owner’s incentive to reduce the input price charged by the supplier. Therefore, managers are compensated for profits while they are penalized for sales.

3. FIXED PRICE CONTRACT 

In the previous section, we show that the opportunistic behavior of an upstream supplier to increase the input prices after incentive schemes are determined under a floating price contract creates a strategic incentive for each owner to direct the manager to less aggressive behavior in order to reduce the own input price while increase the rival’s input price. Less output produced in turn leads to less demand for the input, thus hurting the upstream supplier. To mitigate such an opportunistic behavior of the upstream supplier, one may consider a fixed price contract under which the suppler commits to 394

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the fixed input prices, which are chosen before managerial incentive schemes are determined. There are three stages in this game. In the first stage, the supplier chooses ki to charge firm i for the input. In the second stage, the two owners simultaneously determine the managerial incentive schemes. In the third stage, the two managers compete in quantity. Taking (k1 , k2 ) as given, a fixed price contract is equivalent to the FJS model. Thus, we have αi∗∗ (k1 , k2 ) =

8ki − 2kj − a , 5ki

i, j = 1, 2, and i = j.

(1)

The equilibrium input prices in the first stage are k i∗∗ = kj∗∗ = a/2. Substituting ki∗∗ and kj∗∗ into (1) yields α∗∗ = 4/5 < 1.

4. FLOATING OR FIXED PRICE? 

In this section we compare two price contracts. Table 1 summarizes the symmetric equilibrium outcomes under the two price contracts, and we have the following proposition: Proposition 2 Suppose that the downstream firms compete in quantity. A floating price contract by the upstream supplier makes the owners of the downstream firms overcompensate their managers for profits by penalizing sales. However, a fixed price contract by the upstream supplier makes the owners of the downstream firms compensate their managers for both profits and sales. Proposition 2 indicates that the FJS argument for directing managers toward sales is still applicable in a vertically related industry as long as the upstream supplier commits to a fixed price contract. The input price determined in the first stage under a fixed price contract intuitively acts just like an increase in the marginal production cost of a downstream firm, and hence the qualitative result of the FJS model still holds. However, under a floating price contract, from Proposition 1 we know that the supplier will charge a higher price to a more sales-oriented firm in order to extract more rents. The incentive of an owner to reduce the input price charged by the supplier is sufficiently large to dominate the profit-shifting effect and cross-price effect. Thus, owners choose α∗ > 1 to make their managers more profit-oriented. 



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Table 1 A Comparison of Equilibrium Outcomes under Two Price Contracts Outcome Weight on Profit Incentive Input Price Market Output Profits of the Supplier Profits of the Downstream Firm Consumer Surplus Social Welfare

Floating Price Contract α∗ = 2 a 4 a ∗ Q = 3b a2 πs∗ = 12b 5a2 πi∗ = 72b a2 CS ∗ = 18b 2 5a W∗ = 18b k∗ =

Fixed Price Contract 4 α∗∗ = 5 a k ∗∗ = 2 2a ∗∗ Q = 5b a2 πs∗∗ = 5b a2 πi∗∗ = 50b 2a2 CS ∗∗ = 25b 2 8a W ∗∗ = 25b

Comparison α∗ > 1 > α∗∗ k ∗ < k∗∗ Q∗ < Q∗∗ πs∗ < πs∗∗ πi∗ > πi∗∗ CS ∗ < CS ∗∗ W ∗ < W ∗∗

Proposition 3 The input price under a fixed price contract is higher than that under a floating price contract. The profits of the downstream firms are higher under a floating price contract than under a fixed price contract. However, the profits of the upstream supplier, consumer surplus, and social welfare are higher under a fixed price contract than under a floating price contract. Under a floating price contract, the owners of the downstream firms determine the managerial incentive schemes before the supplier chooses input prices, so the owners have a first-mover advantage. In order to reduce the input price charged by the supplier in the subsequent stage, each owner chooses α ∗ > 1 to make the manager relatively less aggressive so that the input price is lower than under a fixed price contract. One striking result of this paper is that the supplier benefits from the fixed contracts not only by commanding a higher price but also by selling more of the input; that is, k∗ < k ∗∗ , Q∗ < Q∗∗ , and πs∗ < πs∗∗ . This result may seem to be contrary to the traditional belief that the firms will choose to lower their production as the common input price increases. Our results suggest that this proposition does not hold in the current model for the following reason. Under a floating price contract, the owners of the downstream firms overcompensate their managers for profits by penalizing sales, 



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leading to a disincentive for them to produce more output even though the input price is lower than it is under a fixed price contract. On the other hand, downstream firms earn more under a floating price contract than under a fixed price contract. Fershtman and Judd (1987) and Sklivas (1987) show that owners are in a prisoners’ dilemma in the sense that the profits are lower for managerial firms (both choosing a weight less than 1) than for profit-maximizing firms (both choosing α equal to 1). The intuition is that the noncooperative game makes the owners choose more aggressive managers, leading to excessive output that in turn intensifies the quantity competition between the firms. Since a floating price contract makes the owners of the downstream firms choose less aggressive managers (both choosing α greater than 1), the quantity competition between the firms is mitigated, leading to lower output, a higher market price, and higher profits for the firms. Moreover, it can be shown that πi∗ (α∗ ) > πi∗ (α = 1) = πi∗∗ (α = 1) > πi∗∗ (α∗∗ ), implying that managerial firms earn more (less) than profit-maximizing firms under a floating (fixed) price contract. If we define social welfare as the sum of consumer surplus and producer surplus (the profits of the supplier and the downstream firms), a fixed price contract is beneficial for social welfare in comparison with a floating price contract. Note that the credibility of a fixed price contract by the supplier and the commitment of the supplier to it are crucial to the results. If the owners of the downstream firms do not consider the fixed price contract credible, they would choose a weight on a profit incentive greater than 1 to make their managers behave less aggressively, based on the belief that the supplier will change the input prices after the owners make their decisions. 











5. BERTRAND COMPETITION 

In this section we examine the robustness of the effects of input price contracts on managerial incentive schemes of downstream firms under a Bertrand competition model. We assume that the downstream duopolists sell differentiated products and compete in price. Following the FJS model, the demand is given by q i = a − pi + βpj , 0 < β < 1, i, j = 1, 2, and i = j, where pi and qi are the price and quantity of firm i, respectively. The game is similar to the one described under a Cournot competition model except that the managers choose prices in the third stage. 397

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5.1 Floating Price Contract 

The owners of the downstream firms first determine the managerial incentive schemes followed by the supplier choosing the input prices, and finally the downstream managers compete in the product market by setting prices. The game is solved by backward induction. In the third stage, manager i chooses p i so as to maximize Mi . The equilibrium prices are p∗i (k1 , k2 , α1 , α2 ) =

a(2 + β) + 2αi ki + βαj kj , 4 − β2

i, j = 1, 2, and i = j.

In the second stage, the upstream monopolist determines the values of k 1 and k2 that maximize k1 q1∗ + k2 q2∗ . The equilibrium input prices are 



ki∗ (α1 , α2 ) =

(2 + β)[βαi + (4 + β − 2β 2 )αj ]a . 4α1 α2 (4 − β 2 )(1 − β 2 ) − (α1 − α2 )2 β 2

Again, it can be shown that ki∗ ≤ kj∗ if and only if αi ≥ αj . Thus, Proposition 1 holds regardless of the mode of competition. In the first stage, owner i chooses α i so as to maximize the profits of firm i : πi = (a − p∗i + βp∗j )(p∗i − ki∗ ). Solving for a symmetric equilibrium yields α ∗ = (2−β 2 )2 /[β(1+β −β 2 )] > 1. To see why owners will overcompensate their managers for profits by penalizing sales, we rewrite dπ i /dαi |α1 =α2 =1 as follows: 





∂πi ∂p∗j dπi  = + dαi α1 =α2 =1 ∂p∗j ∂αi
(+)  (+) P Si

(+)



∂πi ∂πi ∂p∗j + ∗ ∂pj ∂ki ∂ki∗





(+)

(+)

(−)



(−)







∂πi ∂p∗j ∂kj∗ ∂ki∗ + , ∂αi ∂p∗j ∂kj ∂αi (−)




(+)

(+)



(−)



CPi

(−)

OPi

(+)

where PSi , OPi , and CPi are interpreted as the profit-shifting effect, own-price effect, and cross-price effect, respectively. In the FJS model, delegating the price decisions to managers has the horizontal profit-shifting effect only, and PS i > 0, so αFJS > 1. In the present model, there are two countervailing vertical effects: positive own-price effect and negative cross-price effect. The former dominates the latter, so the vertical

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effect is positive. The FJS argument for directing managers toward profits incentives is enhanced by the additional positive vertical effect (own-price net of cross-price), and hence α∗ > 1.

5.2 Fixed Price Contract 

Now we suppose that the upstream supplier can commit to a fixed price contract before the owners of the downstream firms determine the incentive schemes. Taking (k 1 , k2 ) as given, a fixed price contract is equivalent to the FJS model. Thus, we have αi∗∗ (k1 , k2 ) =

β 2 (4 + 2β − β 2 )a + 4(2 − β 2 )2 ki + β 3 (2 − β 2 )kj . (4 + 2β − β 2 )(4 − 2β − β 2 )ki

(2)

The equilibrium input prices in the first stage are k i∗∗ = kj∗∗ = a/[2(1 − β)]. Substituting ki∗∗ and kj∗∗ into (2) yields α∗∗ = (4 − 2β − β 3 )/(4 − 2β − β 2 ) > 1. It can also be shown that α∗ > α∗∗ > 1, which makes the following proposition: Proposition 4 Suppose that the downstream firms compete in price. Regardless of the input price contract, owners overcompensate their managers for profits by penalizing sales. Proposition 4 indicates that the FJS argument for overcompensating managers for profits under a Bertrand competition model is still applicable in a vertically related industry, regardless of the input price contract. Combining Propositions 2 and 4, we have the following proposition: 



Proposition 5 Regardless of the mode of competition (Bertrand or Cournot), owners of downstream firms direct their managers to less aggressive behavior under a floating price contract than under a fixed price contract. Proposition 5 reveals that irrespective of whether or not the downstream firms compete in quantity or price, the equilibrium weight on a profit incentive is always higher under a floating price contract than under a fixed price contract. Proposition 1 indicates that the supplier will charge the firm with a more aggressive manager a higher input price if he chooses the input prices after the delegation decisions of the owners. The own-price effect discourages the owner’s incentive to choose a more aggressive manager. Thus, the equilibrium weights on a profit incentive chosen by the owners 



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will be higher under a floating price contract than under a fixed price contract. As in the Cournot case, the owners of the downstream firms have the first-mover advantage under a floating price contract, so the profits of the downstream firms are higher than under a fixed price contract.10 On the other hand, under a fixed price contract the profits of the supplier are higher, implying that the supplier always prefers a fixed price contract to a floating price contract. 11 



6. CONCLUDING REMARKS


This paper extends the FJS model to a vertically related industry, focusing on how input price contracts adopted by a monopoly supplier affects the managerial incentive schemes that owners of downstream firms offer their managers. As is well known from the FJS model and other studies, delegation to managers is a profit-shifting device used by owners to precommit managers to certain later actions that in turn alter the actions taken by rival managers. In a vertically related industry, in addition to the horizontal profit-shifting effect, the incentive scheme may also have a vertical effect on the input prices charged by the supplier. In particular, if a supplier chooses input prices after managerial incentive schemes are made, the supplier will charge a more sales-oriented firm a higher price in order to extract more rents. Therefore, the owners compensate their managers for profits but penalize them for sales under a floating price contract. Although the results obtained are based on the assumption that the two downstream firms have the same organization structure, the results still hold when one firm is a managerial firm and the other is an owner-managed firm. That is, the owner of the managerial firm always has an incentive to direct his manager away from profitmaximization, and makes his manager less aggressive under a floating price contract than under a fixed price contract. Our comparison of floating and fixed price contracts in terms of the profits of the supplier and the downstream firms reveals that the supplier obtains higher profits under a fixed price contract than under a floating price contract, while the profits of downstream firms are lower under the former than under the latter. Our result suggests that the supplier can benefit from a precommitment to a fixed price contract because





10

It can be shown that πi∗ =

11

It can be shown that πs∗ =

(3α∗ +β−2α∗ β−2)a2 (2−β 2 )a2 , πi∗∗ = 2(4−2β−β 2 )2 , and πi∗ > πi∗∗ . 4α∗ (1−β)(2−β)2 (2−β 2 )a2 a2 , πs∗∗ = 2(1−β)(4−2β−β 2 ) , and πs∗ < πs∗∗ . 2α∗ (1−β)(2−β)

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Input Price Contracts and Strategic Delegation with Downstream Duopoly (Pei-Cheng Liao)

the owners of the downstream firms direct their managers to more aggressive behavior, leading to larger output and higher demand for the input, thereby benefiting the supplier. Moreover, a fixed price contract brings a higher consumer surplus and social welfare, implying that long-term contractual relationships between vertically related firms are welfare-improving. Our results also shed light on the role of the supplier and how input price contracts significantly influence the production costs and the delegation decisions of the downstream firms in duopolistic markets. Thus, the owners of downstream firms should take into consideration these factors when they are designing managerial incentive schemes. The primary purpose of this paper is to compare the equilibrium outcomes under the two price contracts. Therefore, the analysis has to rely on the assumption that the supplier uses the same contract (either floating or fixed) for both downstream firms. If the supplier uses the floating contract for one firm while the fixed price contract for the other, the decision process of the two owners to determine the managerial incentive schemes could be simultaneous or sequential, and the analysis is beyond the scope of this paper. Conducting analyses of such a more complicated situation might prove fruitful indeed.











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