ISSN Nr. 0722-6748

FS IV 96 - 30

Ownership Structure, R&D and Product Market Competition

Zhentang Zhang

December 1996

ISSN Nr. 0722-6748

discussion papers

Forschungsschwerpunkt Marktprozeß und Unter nehmensentwicklung Research Area

Market Processes and Corporate Development

Zitierweise/Citation:

Zhentang Zhang, O w nership S tru ctu re, R & D and P roduct M a rk e t Com petition, Discussion Paper FS IV 96 - 30, Wissenschaftszentrum Berlin, 1996.

W’issenschaftszentrum Berlin fur Soziaiforschung gGmbH, Reichpietschufer 50, 10785 Berlin, Tel. (030) 2 54 91 - 0

ABSTRACT

Ownership Structure, R&D and Product Market Competition by Zhentang Zhang*

This paper studies the interdependence o f ownership structure, R&D and market competi­

tion. First, we examine the role o f ownership structure. It is found that in Cournot competition, when R&D spillovers are low (high), owners in managerial firms choose more (less) aggressive managerial incentives than their entrepreneurial counterparts. However, managerial firms have lower profits irrespective o f spillovers. Second, we analyze the role of RJVs. It is found that under RJVs, managerial firms have more aggressive managerial incentives, higher effective R&D, higher output, lower price and lower profits than under R&D competition. Finally, we examine the effect o f product market competition. It is found that market competition affects the incentives to innovate differently depending on the type o f ownership structure.

ZUS AMMENFAS SUNG

Eigentumsstruktur, F&E und Produkt-Marktwettbewerb

In diesem Beitrag werden die Wechselwirkungen zwischen Eigentumsstruktur, F&E und Marktwettbewerb untersucht. Zuerst wird die Rolle der Eigentumsstruktur betrachtet.

Für den Fall des Cournot-Wettbewerbs konnte folgendes Ergebnis abgeleitet werden:

Wenn F&E-Spillovers niedrig (hoch) sind, wählen die Eigentümer von managerkontrol­

lierten Unternehmen mehr (weniger) aggressive Managementanreize als dies bei Unter­

nehmen der Fall ist, die von Eigentümern geleitet werden. Managerunternehmen erzielen jedoch niedrigere Gewinne, unabhängig von den Spillovers. Dann wird die Rolle von Research Joint Ventures analysiert. Dabei stellt sich heraus, daß im Fall von Research Joint Ventures die Managerunternehmen über aggressivere Managementanreize verfu­

gen, effektivere F&E aufweisen, einen höheren Output, niedrigere Preise und niedrigere Gewinne erzielen als dies bei F&E-Wettbewerb der Fall wäre. Schließlich wird der Ein­

fluß auf den Produkt-Marktwettbewerb überprüft. Dabei stellt sich heraus, daß der Marktwettbewerb auf unterschiedliche Weise Innovationsanreize stimuliert, je nachdem welche Art der Eigentumsstruktur vorliegt.

I would like to thank Rabah Amir, Lars-Hendrik Roller and Frank Verboven for their helpful comments.

1. Introduction

Empirical and theoretical research has yielded numerous insights into the intricate relationship between technological innovation and market structure in a given industry.

However, the role o f ownership structure in this context has received relatively little but growing attention in the literature. What kind o f management form is most conducive to technological advancement and economic growth? How does m arket competition affect technological innovation under different ownership structures, and vice versa? How do different forms o f R&D affect ownership structure and market outcomes? This paper attempts to address these questions by developing a model which extends the strategic delegation literature by embodying R&D decisions and different market structures.

The role o f ownership structure in market competition has been analyzed in the strategic delegation literature. The main results stem from the fact that in oligopoly, providing managers with nonprofit-maximization objectives may bring strategic advantages to owners (see, for example, Vickers (1985); Fershtman (1985); Fershtman and Judd (1987); Sklivas (1987); Reitman (1993); Goering (1996)). In particular, Fershtman and Judd (1987) and Sklivas (1987) show that in a Cournot-quantity game, owners choose aggressive, nonprofit-maximization incentives for the managers.

Goering (1996) argues that the results o f Fershtman-Judd and Sklivas no longer hold when managerial beliefs are different from Cournot beliefs.1

The early strategic delegation literature assists us in understanding the impact o f ownership structure on market competition. However, most o f the papers above analyze

1 In contrast to Goering’s result, this paper shows that even if managers have symmetric Cournot beliefs, owners penalize sales if R&D spillovers are high.

Cournot competition only and ignore the impact o f different market structures on managerial incentives.2 In addition, the role o f technological innovation and its interdependence with ownership structure and market competition is ignored. Although a vast body o f empirical and theoretical IO literature studies the relationship between the incentives to innovate and market structure (see Cohen and Levin (1989), and Scherer and Ross (1990) for surveys), this literature is mainly concerned with entrepreneurial firms (owner-managed firms) rather than with managerial firms and thereby neglects the impact o f ownership structure.

On the other hand, there are many studies which show that market competition may affect managerial incentives and organizational slack (see, for example, Hart (1983);

Martin(1993); N alebuff and Stiglitz(1983); Schmidt (1994)). These studies, largely based on the traditional principal-agent model, give us insights into the correlation between product market competition and managerial incentives. In contrast, this paper examines the interdependence o f managerial incentives, innovation and market competition from a different perspective. Our setting is based on the strategic delegation model, and the managerial incentive is used by owners to strategically commit managers to certain actions, not to solve the incentive problems under asymmetric information, as in the principal-agent model.

The contribution o f this paper is three-fold. First, we extend the managerial incentive framework first introduced by Fershtman and Judd (1987) and Sklivas (1987) (hereafter, FJS) by adding various market structures in the final production stage. In this way we can

2 A notable exception is Fershtman and Judd (1987), who show that in perfect competition, owners choose profit maximization as their managerial incentive scheme. Goering (1996) defines managerial beliefs by using conjectural variations, which to some extent incorporates the impact of market competition into his model.

analyze the effects o f product market competition on R&D and ownership structure. Second, we introduce R&D to the FJS managerial incentive framework by endogenizing production cost in an R&D stage. This allows us to study the effects o f ownership structure on R&D decisions and moreover, the effects o f cooperative R&D on ownership structure and market outcomes. Third, we use a general demand function in our analysis. This is one o f the extensions to our earlier paper (see Zhang and Zhang (1995)) and various other papers in the strategic delegation literature.

In particular, we analyze a three-stage game. In the first stage, owners simultaneously design a managerial incentive scheme. Following FJS, managers are paid according to some function o f their firms’ profits and revenues. This function is endogenously chosen by owners as a strategic tool to commit managers to certain actions in the future R&D and product stages.

In the second stage, given the incentive scheme, managers choose the level o f R&D. We model cost-reducing R&D according to Kamien, Muller and Zang (1992) (hereafter, KMZ), in which the spillovers are positioned on the R&D input. It is found that spillovers in R&D across firms are pivotal in forming optimal managerial incentive schemes, R&D investment and market competition. Particularly, when the spillovers are low, owners design an aggressive, nonprofit-maximization managerial incentive scheme. Consequently, managerial firms have higher R&D, higher output and lower price than their entrepreneurial counterparts. On the other hand, when the spillovers are high, owners design a less aggressive nonprofit-maximization managerial incentive scheme, and thereby managerial

3 The alternative to model a cost reducing R&D with spillovers is by d’Aspremont and Jacquemin (1988), who position the spillovers on the final cost reduction.

firms have lower R&D, lower output and higher prices. Interestingly, managerial firms have lower profits than their entrepreneurial counterparts, regardless o f the level o f spillovers.

In addition, we analyze the impact o f RJVs on the managerial incentives and market outcomes. It is found that RJVs, as compared to R&D competition, result in more aggressive managerial incentives, higher R&D, higher output, lower price and interestingly, lower profits.

In the third stage, managers choose output under different market structures. It is found that for high spillovers, an increase in market competition unambiguously reduces the R&D investment by managerial firms. However, for low spillovers, market competition is non- monotonically related to both managerial incentives and the incentives for innovation.

The rest o f this paper is organized as follows. In Section 2, the model for a strategic delegation with R&D is described. Section 3 sets out the results for Coumot-quantity competition. Section 4 analyzes the effects of RJV cartelization. Section 5 examines the impact o f product market competition. Finally, Section 6 summaries and concludes.

2. A Model o f Strategic Delegation with R&D

In this section, we develop a model which embodies managerial incentive structures, managers' R&D decisions, and production decisions under a general demand function and homogenous goods. We assume there exists two firms, i and j, each with one owner and one manager, playing a three-stage game. In the first stage, the owners simultaneously sign an incentive scheme with their managers noncooperatively. In the second stage, the managers make their cost-reducing R&D decisions either noncooperatively or cooperatively. In the third stage, managers make their production decisions under different market structures. It is

assumed that one manager’s game strategies in the R&D and production stage are not conditional upon the incentive scheme o f the other manager.4 Also, uncertainty on the owners’ part is suppressed.5

In Stage 1, following FJS, owner i maximizes profits by choosing some incentive parameter a , > 0. otj is the profit weight imposed by owner i on manager i’s incentive scheme, the latter given by U ; = a i m, + (1 — a ; ) R ,, where 7ti and R; are firm i’s profits and revenue respectively. By choosing a (, owner i uses IL as a strategic device to commit manager i to certain actions in future R&D and production stages.

We define an entrepreneurial firm (owner-managed firm) as one where a ; = 1. That is, entrepreneurs always maximize profits. For managerial firms, the separation o f ownership and management allows for the possibility o f nonprofit maximization to emerge endogenously. The value o f determines the aggressiveness o f managerial incentives. By choosing ot; < 1, owner i is designing an aggressive, nonprofit-maximization incentive scheme by including sales. On the other hand, by choosing a ; > 1, owner i is choosing a less aggressive nonprofit-maximization managerial incentive scheme by penalizing sales.

In Stage 2, manager i chooses R&D input x ; to maximize the incentive scheme U s . Following KMZ, firm i’s effective R&D investment is X ; = x, + 0x j , where x ; and Xj are the amount o f R&D investment by manager i and the rival manager j, respectively; 0 e [0,1]

measures the R&D spillovers between the two firms. Firm i’s marginal production cost is given b y C ; = c - f ( X ;) , where f(X;)is the R&D production function, i.e. the amount o f

4 Otherwise, as in Fershtman, Judd and Kalai (1991), co-operative outcomes may emerge as an equilibrium even in noncooperative games.

5 As in Fershtman and Judd (1987), the basic results can be generalized with owners’ uncertainty about demand.

reduction in i’s marginal production costs resulting from X ; . A larger 0 implies that one firm's R&D investment has a larger reduction on the rival firm's marginal production costs.

Following KMZ, it is assumed that f(Xj) is twice differentiable, increasing, concave and uniformly bounded, f (0) = 0 . There are no fixed costs.

In Stage 3, manager i chooses output q ; to maximize the incentive scheme U s . Uj = a i7ii + ( l - c t i )R i ; where T^and R; are firm i’s profits and revenue, respectively.

71; = p q ; - ( C - f ( X ; ) ) q ; ^{~ X ;} R; = P q ; .

Unlike the previous papers in the strategic delegation literature, this paper uses the general inverse demand function p(Q), where Q = q ; + q p q ; and q ^ r e firm i and j ’s output respectively.

In order to guarantee uniqueness o f equilibrium in the production stage and the R&D stage, we make the following assumptions on the inverse demand function and the R&D production function.6

Assumption 1: p ' < 0 ; p ” > 0 ; p ”qj + p ' < 0 .

Assumption 2: - f p h - a , 2U 1+(1A>)U !

( f , ¥ U f - U i 2 U ? + ( 1 + W ! ; where U^i = p " q j + 2 p ' is the second order derivative o f I f w.r.t. qt ; U? = p "q j + p ' is the cross partial o f £/,. w.r.t.

qt and q}

3. The Effects o f Ownership Structure on R&D and Product Market Competition

Empirical and theoretical evidence suggests that managerial firms and entrepreneurial firms tend to participate differently in R&D and production activities. Some possible cause of

6 Assumption 2 degenerates to the Assumption 2 in Kamien, Muller and Zang (1992) for linear demand.

these differences is elaborated in this section for duopolistic industries where firms engage in Cournot quantity competition. We do this by solving a subgame perfect equilibrium.

In Stage 3, manager i selects q ; to maximize U ; in Cournot quantity competition. The first- order conditions are given by

U? = P'Qi + p - 0 C ; ( c - f ) = 0 ; where f = f( X ä). (1)

Global uniqueness o f the Stage 3 equilibrium is guaranteed by Assumption 1.

I D 7

Denoting 9 0 = , we have the following Proposition describing the impact o f R&D

on final stage equilibrium output decisions/

Proposition 1: A n increase in firm i ’s R&D investment increases firm i ’s equilibrium

dq dq

output, i. e. — - > 0 ; but decreases the rival firm ’s equilibrium output, i. e. ---< 0 ij

dx, dx,

and only ifQ < 0 0.

Proof: To evaluate the effects o f a change in x ; on outputs, we implicitly differentiate equation (1) w.r.t. x s.

dx;

- « , ^ + e a ^ U g d q ^ - Q a ^ U g + q . f ^

r |q dx; r |q (2)

From U q = p"qj + 2 p ' < p"qj + p ' = U q . It is straight-forward that for any symmetric

equilibrium, we have > 0 ; ——- < 0 iff 0 < 0 O. Q.E.D.

dx; dx;

7 60 = in the case of linear demand.

8 Only symmetric equilibria are considered here.

Proposition 1 is rather intuitive. An increase in firm i ’s R&D raises its equilibrium output since it reduces its marginal production cost. However, an increase in firm i ’s R&D has two opposite effects on firm j ’s equilibrium output. On the one hand, it increases j ’s output by reducing j ’s production cost through the spillovers effect. On the other hand, it decreases j ’s output by strengthening i ’s competitiveness through the competition effect. For 0 < 0 O, the competition effect dominates the spillover effect, and thus, an increase in i ’s R&D decrease j ’s output. For 0 > 0 O, the spillover effect dominates the competition effect, and thus, an increase in i ’s R&D increases j ’s output.

Note that the industry aggregate output always increases as one o f the firms increases its cost-reducing R&D, regardless o f the spillovers.9

Next, we examine the (partial) effects o f managerial incentives on output decisions, on the condition that both firm s’ R&D investments are fixed. Implicitly differentiating equation (1) w.r.t. a ; , we have

(3)

da Sq ■

It is trivial that — - < 0 and — - > 0.

Hence, as owner i lowers a f, firm i ’s output increases but firm j ’s output decreases, provided that both firm s’ R&D investment remains unchanged.

It is straight-forward that

However, as a ( changes, both firm s’ R&D investment also changes. The (total) effects o f a change in a ; on output consist o f two parts.10 First, the partial effects, as shown in the above. Second, the R&D effects. These are the effects o f a ; on output through changing both firms’ R&D investment, which are discussed next.

In Stage 2, manager i chooses the R&D level x ; noncooperatively to maximize U ; . The first-order conditions are given by

U? = p 'q , y h + a , ( f , 'q , - 1 ) = 0 . (4)

dXj

The first term, p 'q jd q j/d X j, which is positive for e < e 0 and negative for 0 > 0 O, represents the effect o f manager i ’s R&D effort on its utility through changing the rival’s output. Note that a,, only affects the second term, otj(f/qj - 1 ) , which represents the effects o f manager i ’s R&D effort on its utility through changing its marginal production cost.

Uniqueness o f equilibrium in the R&D stage follows from Assumption 2, which suffices U*; < 0 , U* < 0, a n d r f = U*U^ - U XU X; > 0 . 11

Note that for 0 = 1, U? = U * , there is no symmetric equilibrium. Hence, we restrict attention to 0 < 1.

The effects o f ct; on x ( and Xj are giving by the following Proposition

10 As shown below, the total effects of a, on outputs are

dq, _ dq, + f dq^ dx, + dq, dx; ) _ dq, _ Sq^ + f dqj dx, + d q , dXj doq 5a, (d x , da, dXj d a ,J ’ da, 3a, (d x , da, dx, d a iz

Where UJ = ■ d2qj

-U’ C T Z + P"qi(5 2 i )2 + p'q, . 2

dx, dx, dx. + a ifi" q i ;U ’ = -2 p.d q ^ d q , dx, dx. p ’q.

9x,9x, -ba^/'q,.

Proposition 2: A s owner i lowers a j; firm i ’s R&D investment increases, i.e. — - < 0 ; d a t but firm j ’s R& D investment decreases, i.e. --- > 0.d xj

da

Proof: Implicitly differentiating Equation (4) w.r.t. a ; yields

- - m d

dot; q x dot; n x (5)

It is tedious but we have L; + K ( > 0 ; K ;Uy - L ;U ~ > 0. Hence, dx, d x : ----L + ---

dot; doCj < 0 ,

—4 -< 0 a n d — f > 0 . Q.E.D.

d a; d aj

The intuition behind this Proposition is as follows. From equation (4), manager i acts as if the net marginal R&D cost is a ^ l - f / q , ) instead o f ( l - f / q j . Therefore, as owner i lowers cc; , firm i ’s R&D reaction curve shifts out. This increases i ’s R&D investment but decreases j ’s R&D investment. Note that the total R&D expenditure decreases as one o f the owners lowers a ; .

Now let us reexamine the (total) effects o f managerial incentives on final stage equilibrium output, which is given by the following Proposition.

Proposition 3: A s owner i lowers a f f i r m i ’s equilibrium output increases, i.e. — - < 0;dq d a , d X i ( c - f f U q d X ,

but firm j ’s decreases, i. e. — — > 0 i f and only i f U qdq. ü — - - U l — <

d a t d a i d a t a , . / /

Proof: See appendix.

12 T q d q , 3 q , „ d q , S q , , 3 2q , d q j d q , 3 q , , d \

L i - (1 — f= q i) + U?= — -— - p q , — 1 — - - p q . ---— K , = I J *,— 1 — ’ - p q , — — - p q , ---—

dx, 3a, dx, 3a, 3x,3a, dx, 3a, dx, 3a, Sx^oa,

13Both firms’ R&D reaction curves are downward sloping, i.e. X; and Xj are strategic substitutes since u ; <U,*<0.

The intuition is as follows. From equation (1), manager i acts as if the marginal production cost is oCj (c — f(X ;)) instead o f (c - f ( X ;) ) ; manager j acts as if the marginal production cost is ctjC c-fC X j)) instead o f ( c - f ( X j ) ) . Hence, a change in OCj shifts both firms’

output reaction curves since it changes both X ; and X j .14 15 As owner i lowersoc; , firm i’s

output reaction curve shifts out since d X j/d a ; < 0. This increases i’s output but decreases j ’s output. However, as owner i lowers a ; , firm j ’s output reaction curve also shifts out whenever dXj / d a ; < 0. This decreases i’s output but increases j ’s output. Comparing the net change in both firms’ output, we have that as owner i lowers a ; , firm i ’s output

dX- dX- ( c - f i ) U ? increases; but firm j ’s output decreases iff U'j — - - Ujj — - < --- ■

d a; d a ; o^f;'

At Stage 1, owner i chooses a ; noncooperatively to maximize 7i; . The first-order conditions are

I - OC; =■

, 1 SU. dx,

p q ,— - + --- L— 1 da, a, dx., da.

(6)

Denoting 0 = ^Uh + U< c - f_{i 15}

Uh +2U y U S + 2 U ? f / dxI We can characterize the symmetric dCX,;

equilibrium (a * = a* = a ) by the following theorem.

Theorem 1: Whenever 0 < 0 , there exists a unique symmetric equilibrium such that a * < 1. However, when 0 > 0 , the equilibrium is characterized by a ' > 1.

14 Assumption 1 assures that both firms' production reaction curves are downward sloping.

15 U’

Note that 0„ < ---— < 0 < 1.

U ? + 2 U q

Proof: See appendix.

Theorem 1 provides the basis for comparing the effect o f different types o f ownership structure on R&D and product market competition. Recall that entrepreneurial firms are characterized by a - 1. Denote the equilibrium individual entrepreneurial firm ’s R&D, output, profits and market price by x E, q E, n'E, and p*E respectively. Using Theorem 1, Proposition 1, 2 and 3, we can compare the equilibrium for managerial firms to the equilibrium when both firms are entrepreneurially managed.

Corollary: I f 0 < 0 , then x* > x E, q* > q E, and p* < p*E. I f 0 > 0 , then x < x E, q* < q E, and p* < p*E.

This implies that apart from the strategic interactions between firms, the level o f industry R&D spillovers is critical in determining the optimal managerial incentive scheme and m arket outcomes o f managerial firms. When spillovers are low, owners strategically design managerial incentives away from profit maximization to include sales. As a result, managerial firms invest more in R&D, produce more output and charge lower prices than entrepreneurial firms. Therefore, consumers are better o ff from the separation o f ownership and management. Conversely, when spillovers are high, owners over-compensate managers for profits at the margin and penalize sales. As a result, consumers are worse o ff from the separation o f ownership and management..

Theorem 2 below compares producer surplus for the two types o f ownership structure.

Theorem 2: Managerial firm s are always less profitable than their entrepreneurial counterparts, i .e .n ' < f , irrespective o f the spillovers.

Proof: See appendix.

The intuition behind Theorem 1 and 2 is as follows. As manager i increases the investment in cost-reducing R&D, firm i ’s equilibrium output will unambiguously increase. However, an increase in R&D investment by manager i has two opposite effects on the equilibrium output o f the rival firm j. On the one hand, it increases j ’s output by reducing j ’s marginal production costs through spillover. On the other hand, it decreases j ’s output by strengthening i ’s competitive edge. Now, if spillovers are low, the first effect is dominated by the second. Consequently, when manager i increases investment in R&D, firm i ’s output increases and firm j ’s output decreases. This raises i ’s profits and lowers j ’s profits since the two firms are competing in a Cournot quantity game. Therefore, owner i designs an aggressive managerial incentive by including sales, which leads to higher profits. As a result, in equilibrium, both owners direct their managerial incentives away from profit maximization towards sales. However, as Theorem 2 illustrates, both firms end up with lower profits than they would have had, had they chosen profit maximization as their managerial incentive.16

Now, if spillovers are high, an increase in manager i ’s R&D investment increases i ’s output, but decreases i’s profits as j ’s output also increases. Therefore, owner i designs a less aggressive managerial incentive scheme by penalizing sales, which leads to higher profits. Consequently, in equilibrium, both owners overcompensate managers for profits and penalize sales, intending to free-ride on the rival firm but ending up with lower profits than that they would have had under a profit-maximization managerial incentive scheme.

16 In other words, the owners are in a prisoners’ dilemma.

From Theorem 1 and 2, it follows that the separation o f ownership and management reduces overall social welfare for high industry R&D spillovers. But for low R&D spillovers, the effect on social welfare is ambiguous.

4. The Impact o f Research Joint Ventures

The previous section has shown that managerial firms and entrepreneurial firms have different incentives to innovate. This section expands on this by allowing the formation of research joint ventures (RJVs). Do RJVs and R&D competition require different types o f optimal ownership structure, and how do these structures induce different market outcomes?

Following KMZ, RJV cartelization is defined as follows. Managers coordinate their R&D activities so as to maximize the sum o f their utilities. In addition, managers share R&D costs and avoid duplication o f R&D activities.

We now solve for a subgame perfect equilibrium under RJV cartelization. In Stage 3, the managers’ output decisions are the same as above where the effect o f X ^ , on q ; and q d is given by

dq, = ( - a ^ + q j U g j x f ' C X ^ )

dX q q

The following Proposition describes the impact o f forming RJV on final output decisions.

Proposition 4: An increase in R& D expenditure under R JV increases both fir m s ’

dq dq

equilibrium output, i.e. — L > 0 , — - > 0 . d X d X

This Proposition is straight-forward. An increase in R&D investment under RJV cartel reduces both firm s’ marginal production cost, and thereby raises their output.

V

In Stage 2, managers maximize ( U ( + L f), with x ; = Xj = and 0 = 1. The first order condition is given by17

U = p ' x (q. ^ - + q + | f ' x - t- a - q j

x J dX 1 dX I 11 J J

a s = 0 ; i * j . (7)

dq dq -

The first term, p '(q j — L + q; — - ) , represents the negative effect o f RJV on manager

dX dX

i ’s utility through changing outputs. Note that a ; and ot , only affect the second term, CCj + CX-

f ' x ( a iq i + a ^ ) --- — , which represents the positive effect o f RJV on manager i ’s utility through changing its marginal production cost.

The effect o f managerial incentive on RJVs is described by Proposition 5.

Proposition 5: A s either owner lowers a , the R&D investment under R JV increases, i.e.

d X n , d X . d a , d a ,

Proof: Implicitly differentiating (7) w.r.t. and a } respectively, we have

U dX ,d q f dq ; 3q. dX , dqj dq j dq.

dot; dX d a { d a t x dotj dX d a i d a t

dX . , dX . Hence, --- < 0 a n d --- < 0.

dctj dctj Q.E.D.

17 The second order condition U.™ < 0 is satisfied for any symmetric equilibrium.

From equation (7), manager i acts as if the marginal net RJV cost is Uzj -r vx •

— --- f ' x (otjqj 4 -a jq j) instead o f 1 - f ' x (q ; + q . ) . Therefore, as owners i (or

owner j) lowers a ; (or a J , manager i de-emphasizes marginal RJV cost and thereby raises the level o f RJV.

In Stage 1, owner i chooses a ] noncooperatively to maximize 7i;. The first order condition is

1-oci

P'q.

dX da.

5a; (8)

The comparison between equilibrium under RJV cartelization and equilibrium under R&D competition is given by

Theorem 3: Under RJV, there exists a unique symmetric equilibrium such that < l ln addition, as compared to R&D competition, RJV leads to a more aggressive managerial incentive, higher R&D, higher output, lower price and lower profits. That is, a ’fiy < a * ,

X p/[/ > X * , q * ^ > q*, p'ßjy < p* and n *„1V_{' RJV} < 7i * Proof: See Appendix.

Standard analysis in cooperative R&D suggests that RJVs yield both higher consumer surplus and higher producer surplus than R&D competition due to the internalizing o f spillover, the free-rider problem, and R&D duplication activities. However, this result does not necessarily hold true once one considers managerial incentives. Intuitively, RJVs increase profitability in the product market. This, in turn, leads to fiercer product market competition and curtails firms’ quasi-rents from RJVs. As a consequence, managerial firms are worse off by forming RJVs. Nonetheless, consumers are still better off from RJVs. By

maximizing joint profits and sharing R&D effort, managerial firms invest more in R&D, produce higher output and charge lower prices.

The logic behind this result is similar to that in the semicollusion literature. Fershtman- Gandal (1994) demonstrates that collusion in the later stage may yield lower overall profits because it intensifies competition in the previous stage. In our setting, firms are competing in three stages. The cooperation between managers in R&D stage makes owners choose more aggressive managerial incentives, i.e. it intensifies the competition between owners in the previous stage. This "overaggressive" managerial incentive drives managers to

"overinvest" in R&D and "overproduce" in the product market. Overall, managerial firms end up with less profits under RJV than under R&D competition.

5. The Effects o f Product Market Competition

In considering the relationship between market structure and incentives to innovate, the IO literature has shown that market structure is only one o f many important factors affecting innovation (see, for example, Scherer and Ross (1990)). Several studies have indicated an inverted U-shaped relationship between market competition and innovation, i.e. the incentives to innovate increase as we move from monopoly to oligopoly, but then decrease as the degree o f competition gets large. However, this literature deals with entrepreneurial firms’ incentives to innovate, and does not address managerial incentives. This section analyzes the impact o f market competition on the incentives to innovate in industries where firms are characterized by a separation o f ownership and management.

Let us first consider the basic model assuming perfect competition in Stage 3. Assuming n firms, each with one owner and one manager, playing a three-stage game. In the first stage,

the owners simultaneously sign an incentive scheme with their managers. In the second stage, managers make their R&D decisions noncooperatively. In the third stage, managers make their output decisions in a perfectly competitive market. A subgame perfect equilibrium can be described by the following Proposition.

Proposition 6: Under perfect competition, a PC = 1; X PC = 0 iff (1 - 0 ) f ' ( 0 ) Q < l . P roof In Stage 3, the first-order condition for manager i is

p = a i ( c - f i);w h e re f; = f ( x ; + 0 £ x j ) , i = l,2 ,...n .

j* i

In Stage 2, neither manager will deviate from x ; = 0 . Since by deviating, the net benefit to manager i is

dU^

dxj _i=l,...n^{x i= 0}

dQ dX:

dx, _i=l,...n^{x (=0}

= a ;[(l - 0 ) f '( O ) Q - 1] < 0 iff ( l- 0 ) f '( O ) Q < 1.

where Q is the monopoly output for manager i whenever manager i deviates from x ; = 0.

In Stage 1, 7ij = p q ; - ( c - f j q j - x ; = = 0

Thus, ctpC = 1, X*c = 0 . Q.E.D.

This result is intuitive and coincides with the traditional theory o f perfectly competitive markets. Under perfect competition, if all firms have the same technology, the long-run equilibrium price is equal to minimum average cost. Managers cannot afford to do anything

18 Where Q is the monopoly output.

but maximize profits. In addition, each firm refrains from investing in R&D since perfect competition erodes market profitability.

Consider now a monopoly. In this case it is always optimal for the owner to provide profit- maximization as the managerial incentives, i.e. a*M = 1. Therefore, in both monopolistic and perfectly competitive industries, managers are told to maximize profits. Only in oligopolistic industries, due to the strategic interactions among firms, do owners attempt to gain some strategic advantage over the rival firms and design nonprofit-maximization managerial incentives. From Theorem 1 and the above analysis, we have

Proposition 7: For 0 < 0 , afM = vfiPC = 1 > a *. On the other hand, fo r 0 > 0 ,

= a pc = f < « * -

According to this Proposition, for low R&D spillovers, owners in duopolistic firms design more aggressive managerial incentives than their counterparts in both monopolistic and perfect competitive firms. On the other hand, for low spillovers, the reverse holds true.

Denote the level o f equilibrium effective R&D for monopoly, duopoly and perfect competition by X ’M, X *, X*c (X *c = 0 ), respectively. Comparing them, we have

Theorem 4: When 0 < 0 , the equilibrium effective R& D is the highest fo r duopolistic firm s and the lowest fo r perfectly competitive firms, i.e. X*> X*M > X'K . When 0 > 0 , the equilibrium effective R&D decreases as market competition increases, i.e.

x 'M > x * > x * PC.

Proof See Appendix.

Hence, if spillovers are low, it is suggested that the usual inverted U-shaped relation between market competition and the incentives to innovate is reinforced in industries where firms are characterized by the separation o f ownership and control. As we move from

monopoly to duopoly, then R&D investment by managerial firms increases, but decreases as we move from duopoly to perfect competition. In contrast, if spillovers are high, managerial firms reduce their R&D investment as market competition increases.

In this section, we have shown that besides market competition, ownership structure is another important factor affecting firms’ incentives to innovate. In contrast with entrepreneurial firms, the effects o f market competition on the incentives to innovate for managerial firms are composed o f two parts. First, market competition directly affects managers’ incentives to innovate in an inverted U-shaped manner, as shown in many previous studies. Second, market competition affects owners’ incentives to innovate, as shown in Proposition 7. Owners’ incentives to innovate are monotonically transmitted to managers through the optimal incentive scheme. The combination o f these two effects yields Theorem 4.

6. Conclusion

This paper studies the impact o f separation o f ownership and management and its implications in firms’ R&D and product decisions. It is found that, in contrast with the previous strategic delegation game literature, whether owners direct optimal managerial incentives away from profit maximization crucially depends on the degree o f industry R&D spillovers. When spillovers are small, owners design aggressive, nonprofit-maximization managerial incentives. As a result, managerial firms have higher R&D, higher output, and lower prices than their entrepreneurial counterparts. On the other hand, when spillovers are large, owners design less aggressive nonprofit-maximization managerial incentives.

Consequently, managerial firms have lower R&D, lower output, and higher prices than their

entrepreneurial counterparts. Interestingly, managerial firms always have lower profits than entrepreneurial firms, regardless o f the level o f spillovers.

The effects o f RJV cartelization on managerial incentives and market outcomes are also elaborated in this paper. By forming RJVs, owners in managerial firms choose more aggressive managerial incentives. As a result, managerial firms have higher effective R&D, higher output, lower price, and also lower profits under RJVs than under R&D competition.

Finally in this paper, the correlation between market competition and innovation is examined. The usual inverted U-shaped relation between market competition and entrepreneurial firms’ incentives to innovate is reinforced in managerial firms, providing the spillovers are low. For high spillovers, managerial firms’ incentives to innovate decrease as market competition increases.

Appendix

Proof o f Proposition 3: Solving equation (1), we have q ; = q i ( a i , a j ,x i ,x j) , qj = q j ( a i , a j , x j , x j ) ; where x f = x i ( a i , a j ) and Xj = x j ( a i , a j ) are the solution to equation (4). Totally differentiating q ; and q ^ w.r.t. a ; , we have

dq, = dQi dor da,

dQi dXj d q ( dxj | dQj _ dQj f dQj dx; dQj dXj

d x j d a ; d x j d a i ? J d a ; d a { ^ d x ; d a f d x j d a ; y

+

dq dq, dq- dq . dq dq.

Where — = --- a n d ---= — - are given by equation (2), — L and — - are given by

d x ; d x j d x ; d x j dx; dx;

dx dXj

equation (3), — L and — - are given by equation (5).

d a ; d a;

Substituting them back to equation (6), it is straightforward that —— < 0; ——i- > 0 iff

d a , d a .

dX, a dX- ( c - f ) U

d a , J d a ; a , f / Q.E.D.

Proof o f Theorem 1: In equation (4), the denominator < 0 since dx, f

dq ;

dx; y d a,

/ r \d q j 1 dqj dX; tt, dX :

d x ^

j / d a ;

-^ +

J 1

<

1 1

= 4 [ ( ! + 0)(U? - U ! )a , (c - f ,) - (U? - e u ; )P](^^{d x} + —^{d x j}k ) < 0 . d a - d a ;

1 I

On the other hand, , Sqj 1 dUj dxj p 'q i ^ L+

d a ; a ; d x j d a ;

- ( c - f , ) u j + ((U ! + 2 U § ) 6 - U 5 ) f ? ^ < o , i f f 0 < 0

Therefore, a* < 1 for 0 < 0 ; a* > 1 for 0 > 0 ; a* = 1 for 0 = 0 .

cbi »

P roof o f Theorem 2: At equilibrium, we have — l- = -(1 - a ; )(c - f;) if

Q.E.D.

Therefore, 7i* < for all 0 . Q.E.D.

P roof o f Theorem 3: First, from equation (8), it is trivial that a ^ v < 1.

Now let’s compare equilibrium under RJV with equilibrium under R&D competition.

The Stage 3 first-order condition for R&D competition and RJV are respectively p 'q ; + p = a ’ ( c - f i) ; p 'q ; + p = ot^v (c - f)

For 0 > 0 , we have a* > 1 > a*RJV. For 0 < 0 , by comparing equation (6) with equation (8), we have 1 > a* > . Thus, a* > a ^ jV for all 0 .

Therefore, q* < q ^ v j Q ^ Q ’r w-

On the other hand, the Stage 2 first-order condition for R&D competition and RJV can be respectively rewritten as

Hence,

i ( u ;+ u ;) [ 2 u ;- ( i- e ) u ;]

f'(x ’) - f'(x ’ v) > ; ~ " r ,J' L— > o iff e > 11 o 1J ,19

2Q.W us[(i-0)us+ 2us] us

Therefore, X* v > X

Moreover, 7i ^jV < rc* since at equilibrium,

cbt^RJV

dX — (1 a RJv) dq 1

( c - f ) — + 1 ( l - 2 f ' q i)

V dX 2 41 < 0 . Q.E.D.

Proof o f Theorem 4: For 0 < 0 , from Theorem 1, a* < 1 for duopolistic managerial firms. Hence X * (a ‘) > X ’ (l) > X*M > X^c = 0 .

For 0 > 0 , solving for duopoly equilibrium effective R&D from equation (1) and (4), we have

[ ( c - f , ) - p ] f ' _ 1 T

us - us

(1 -0 )U S + 2 U S , a ’ > 1

On the other hand, monopoly equilibrium effective R&D can be easily solved as [ ( c - f ) ~ p ] f '

p '

Denote H(Q) = , then “ f) “ p]p" + < P')2] < 0 bY

Assumption 1. Moreover,

For linear demand, U? -2 U !

U? = 0.

n ] 1-

( u r u p ( l - 0 ) U ^ + 2 U y

( l - g ’ X c - f J f ' | U ^ - Q Uü cQ U ? - U ? ( 1 - 0 M + 2 U ?

Thus Qm> Q ’ .

In addition, Q ^ X ^ ) = 1, Q *f(X ‘) = and f " < 0.

Therefore, > X* > X*pc = 0

2 (U ^ + U ^ ) ( 1 - 0 ) U ! +2U y

Q.E.D

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