Incentive contracts under product market competition and R&D spillovers

Transcription

1 Incentve contracts under product market competton and R&D spllovers Evangela Chalot Unversty of Illnos at Urbana-Champagn yz Abstract Ths paper studes cost-reducng R&D ncentves n a prncpal-agent model wth product market competton. It argues that moral hazard does not necessarly decrease rms pro ts n ths settng. In hghly compettve ndustres, rms are drven by busness stealng ncentves and exert such hgh levels of R&D that burn up ther pro ts. In the presence of moral hazard, underprovson of R&D ncentves due to rsk-sharng can generate consderable cost-savngs mplyng hgher pro ts for both rvals. Ths result ndcates rms ncentves to adopt a collusvelke behavor n the R&D market. We also examne the agents contracts and the pro ts-rsk relatonshp when cross- rm R&D spllovers occur. Keywords: moral hazard, process nnovaton, Cournot competton, R&D spllovers, relatve performance JEL: D8, L13, O30 I am ndebted to Lambros Pechlvanos for the very useful dscussons on ths topc. I am also grateful to Dan Bernhardt, George Deltas, Johannes Hörner, Katharne Rockett, Larry Samuelson, Konstantnos Serfes and Spyros Vasslaks for ther comments and suggestons. I gve specal thanks to Costas Arkolaks, Drk Bergemann, Claude D Aspremont, Raymond De Bondt, Mathas Dewatrpont, Mehmet Ekmekc, Vtor Farnha, Ganluca Femmns, Sebastan Kranz, Slvana Krasteva, Vjay Krshna, Erc Maskn, Chrysovalantou Mllou, Ana Rodrgues, Phlpp Strack, Ncolaos Vettas, Anastasos Xepapadeas and the partcpants at varous conferences and meetngs. Fnancal support from the State Scholarshps Foundaton n Greece s also acknowledged. y Contact: Unversty of Illnos at Urbana-Champagn, Department of Economcs, 101 Davd Knley Hall, 1407 W. Gregory Dr, Urbana, IL 61801, USA. Emal: chalot@llnos.edu Tel.: , Fax : z Ths paper s based on Chapter 3 of my thess.

2 E. Chalot: Contracts, competton and R&D spllovers 1 1 Introducton In knowledge-based ndustres, rms nteractons and techncal advance favor a decentralzed organzatonal structure that nvolves separaton between busness unts and research teams. The owners of rms appont hghly-sklled researchers or autonomous unts to undertake cost-reducng R&D projects on ther behalf. Thus, there s a dvson between ownershp and control over R&Doutputs. In such markets, the ssue of ncentve provson deserves specal attenton when rms also compete n the product market. The prncpal-agent lterature based on Holmström (1979) remans narrow n ts focus on the e ect of moral hazard and rsk on rms pro ts when there are strategc nteractons among rms. Ths paper examnes whether the standard result n the lterature that rms enjoy hgher pro ts under full nformaton apples n ths settng. decrease rms pro ts. We argue that moral hazard does not necessarly The conventonal wsdom n models wth moral hazard, orgnatng from Holmström (1979) and Holmström & Mlgrom (1987), s that the optmal contract balances an ncrease n rsk wth weaker ncentves for e ort due to rsk-sharng. Thus, the owners of the rms are better-o under full nformaton where no nsurance s provded. We argue that the latter result need not hold f rms nteract n the product market. We take nto account the market envronment and dentfy the condtons under whch the pro t-rsk relatonshp turns out to be postve. We consder a settng wth two rsk-neutral rms that rst nvest n cost-reducng R&D and then, nteract n a d erentated- nal product market. To conduct R&D, the owner of each rm (the prncpal) apponts a rsk-averse researcher (the agent) whose e ort s unobservable. The barganng power s assgned to the prncpals allowng them to make take-t-or-leave-t o ers to the agents and extract the entre rents of R&D actvty. The ncentve packages are derved n a lnear prncpal-agent model (Holmström & Mlgrom (1987)) and the payments are contngent on margnal cost reductons (Rath (003)). 1; Each agent s R&D output depends on her own e ort and a project-spec c shock. We derve the optmal R&D ncentves and show that n hghly compettve ndustres, rms are drven by busness stealng ncentves and exert such hgh levels of R&D that they burn up ther pro ts. In the presence of moral hazard, rsk-sharng mtgates such R&D ncentves and rms appette for nnovaton. Lower e ort s exerted mplyng cost savngs for both rvals. We argue that there exsts a regme n whch cost savngs are substantal so that rms pro ts are hgher under moral hazard. Ths occurs when the product market competton s ntensve and the cost of R&D s relatvely small. Ths paper delves nto rms ncentves to adopt a collusve-lke behavor n R&D and even utlze the ntra- rm con cts of nterests. Separaton of busness and research unts under moral hazard, pror to product market competton, can be used as a collusve devce that mtgates rms nteractons n the proceedng stages. Frms become better-o as more nsurance has to be 1 Prendergast (1999) provdes a revew of the prncpal-agent lterature. Cost-based schemes are consstent wth real-world contractng practces. In Germany, for nstance, nventors compensaton schemes based on the expected value of the R&D-outputs have been establshed by law (German Employees Inventons Act passed n 1957).

3 E. Chalot: Contracts, competton and R&D spllovers provded to researchers. We also examne cost-reducng R&D motves and the e ect of rsk on equlbrum pro ts when R&D spllovers occur. Each rm s cost reducton now also depends on the sze of the spllovers;.e. on the amount of (unpad) appropraton of a rval s R&D (D Aspremont & Jacquemn (1990), Kamen, Muller & Zang (199), Qu (1997), Amr, Amr & Jn (000), among others). Due to technologcal nteractons between agents, each prncpal now o ers a relatve performance evaluaton scheme. The explct comparson of R&D performances s the consequence of the e cent use of nformaton conveyed by the ndvdual R&D-outputs about each agent s e ort. The exstng lterature uses such contracts when the market shocks that ht each agent s producton are correlated (Holmström & Mlgrom (1987)). In ths model, there s no correlaton between the random factors, however, spllovers necesstate the use of such schemes. In equlbrum, a negatve weght s placed on a rval rm s performance, mplyng that an agent s penalzed f the rval does better. Such contracts ntroduce competton between agents and can e ectvely lter out spllovers from ther compensaton packages. To study how pro ts change wth rsk n ths context, we rst dscuss the e ects of competton and spllovers on R&D ncentves. In partcular, the relatve locaton of the rms n the product and technology space determnes the nature of strategc nteractons n the R&D market. The analyss performs a decomposton of R&D ncentves and focuses on the underlyng e ects that arse due to product market competton. These are the (postve) strategc e ect due to busness stealng and the (negatve) spllover e ect due to knowledge transmsson. The latter e ect s detrmental to the R&D-takng rm;.e. spllovers enhance the e cency of the rval makng ths rm tougher n the product market. If the strategc e ect domnates the spllover e ect, e orts are strategc substtutes. 3 We show that n a regme where e orts are strategc substtutes, competton stmulates R&D n markets wth hghly elastc demand. Ths happens because a rm wth cost-advantage can more easly extend ts busness at the expense of ts rval. 4 Thus, each rm has stronger ncentves to conduct R&D as demand becomes more elastc. In ths regme, spllovers also foster R&D, f the cost of e ort exerton s relatvely small. 5 By nvestng n R&D, each prncpal wants to realze a slghtly lower margnal cost from ts compettor. As spllovers ncrease, rvals acqure more n R&D n order exactly to secure a cost advantage. Thus, both competton and spllovers nduce rms to overnvest n R&D. However, by dong so, R&D costs ncrease, wthout a commensurate ncrease n equlbrum pro ts. D erently, the presence of moral hazard on the part of the researchers leads to 3 Bulow, Geanakoplos & Klemperer (1985) provde a taxonomy of strategc varables. 4 Aghon, Bloom, Blundell, Gr th & Howtt (005), Scherer & Ross (1990), among others, study emprcally the e ect of competton on ncentves. Baggs & De Bettgnes (007), and Gr th (001) examne the relatonshp between competton and agency cost. 5 Levn (1988), among others, reports extensve spllovers manly n boengneerng and mcroelectoncs-based ndustres. Computer software, chemcal compounds, genetc sequences are subject to spllovers due to dsclosure of knowledge through publcatons or patents, researchers moblty or even embodment of knowledge n products (knowledge acquston by reverse engneerng). Bondt (1997) provdes a revew about the e ect of knowledge spllovers on R&D nvestments.

4 E. Chalot: Contracts, competton and R&D spllovers 3 underprovson of R&D ncentves. A cost-savng choce for both rvals s to delegate R&D decsons ex-ante or even to appont hghly rsk-averse agents n order to nnovate less n R&D and thereby enjoy hgher pro ts. Frms become better-o as the trade-o between e ort provson and nsurance s shfted towards the latter. We nd that prncpals captalze on such bene ts only f the cost of ncentvzng and nsurng the researchers from the stochastc nature of ther e ort does not exceed a threshold. If the R&D actvty s too costly, rvals pro ts are hgher under full nformaton. Ths result sheds nsght on the organzatonal structure rms may desre to adopt, gven the cost of exertng e ort and the market characterstcs. Gans from rsk-sharng are also generated for rms that compete à la Bertrand n the product market. Frms enter nto a prce war. By beng more e cent, they end up cuttng prces, thereby dmnshng ther equlbrum pro ts. In ths settng, nvestng less n R&D due to moral hazard can also ncrease the rms pro ts. Thus, a postve pro t-rsk relatonshp can be realzed n both Bertrand and Cournot settngs: t does not depend on the mode of competton n the product market. For ths to happen, agents e orts must be strategc substtutes. If they are strategc complements, rms wsh to undertake research under full nformaton and e ectvely montor the agents n order to explot all opportuntes from e cency enhancement. Ths analyss contrbutes to the exstng lterature on the theory of the rm that argues that consderng a rm n solaton may be msleadng. Strategc nteractons play a key role n the rms nternal organzaton. Ths lterature s based on Fershtman & Judd (1987) and Sklvas (1987). It focuses on "strategc delegaton" and examnes the e ect of product market competton of the agents compensaton schemes and ncentves. 6 From another perspectve, Aggarwal & Samwck (1999) study how agents ncentves can n uence the ntensty of the strategc nteractons between rms. These papers assume that agents perform n the product market and ther compensaton s contngent on rms pro ts and sales. E ort s observable and there are no agency problems. 7 In ths model, we assume that researchers tasks are focused on cost reducton and ther rewards are drectly related to the output of ther task. We use the standard prncpal-agent model n a compettve settng where the researchers decsons cannot a ect rms strategc nteractons. The severty of the prncpal-agent problem when t s faced by product market compettors has been examned by Hart (1983), Scharfsten (1988), Hermaln (199), Schmdt (1997), and Rath (003), among others. Rath (003) ponts out the d erence between the rsks rms face and the rsks to whch agents are exposed. He consders an endogenous number of rms that compete n prces along a Salop crcle. He argues that ncentves are postvely related only to rm rsk because changes n competton change the value of cost reductons and the varance of rms pro ts n the 6 Other works examne the e ect of competton on ncentves by consderng changes n the number of compettors (Schmdt (1997)), the market sze, the transportaton cost or the cost of entry (Rath (003)). Nckell (1996) and Vckers (1995) revew the exstng lterature about the e ect of competton on ncentves and Vves (008) provdes a survey about the e ect of competton on nnovaton. Mllou & Petraks (011) study the technology adopton ncentves of market rvals. 7 Hart (1983) and Pccolo, D Amato & Martna (008) also assume that the contracts are contngent on rms pro ts.

5 E. Chalot: Contracts, competton and R&D spllovers 4 same drecton. In our model, we examne the rsk faced by agents and argue that hgher degrees of rsk averson and the rskness of the performance measures decrease the R&D ncentves but they can ncrease rvals pro ts. More recently, Serfes (008) derves a postve pro ts-rsk relatonshp n an endogenous matchng model wth heterogeneous prncpals and agents. 8 Ths paper can also be ted to the lterature on rms ncentves to vertcally ntegrate. If the R&D and producton unts are separate, contracts are used to govern ther relatonshp and the moral hazard problem s present. Ths paper shows that n hghly compettve markets where pro ts ncrease wth rsk, vertcal separaton s preferable. In contrast, n a regme where competton s soft and the pro ts-rsk relatonshp becomes negatve, rms have ncentves to vertcally ntegrate and the moral hazard problem dsappears. Several recent papers explore rm boundares and nternal organzaton (.e., Hart & Holmström (010), Aghon, Dewatrpont & Rey (004), Alonso, Dessen & Matouschek (008)). Aghon, Gr th & Howtt (006) provde evdence of a U-shaped relatonshp between product market competton and vertcal ntegraton. An addtonal contrbuton of ths paper s the followng. Holmström (1979) shows that the certanty equvalence of agent s utlty can be wrtten n the mean-varance form, f constant absolute rsk averse preferences are consdered, lnear contracts are used and the random terms are normally dstrbuted. The optmal e ort only a ects the rst two moments of the dstrbuton of wages and the agent s problem has a closed-form soluton. We prove that ths s also the case f the random terms follow a truncated normal dstrbuton that s symmetrc around the mean. Truncaton s requred n order to guarantee postve post-nnovaton margnal costs. Ths assumpton s essental n all models based on Holmström (1979) that consder cost-reducng ncentves under moral hazard. The rest of the paper s organzed as follows. Secton presents the model. Secton 3 solves the rvalry game. It analyzes the underlyng e ects of rsk on pro ts and nterprets the results. In secton 4, we study the ncentve contracts and pro t-rsk relatonshps n the presence of spllovers. The cost-reducng motves of Bertrand rvals and the optmal contracts when there are two forms of correlaton between the researchers R&D outputs -.e., due to spllovers and the correlaton of the random terms - are also dscussed. Secton 5 concludes. The model The market features two rsk-neutral and pro t-seekng rms 1 and, ndexed by and j where 6= j. Each rm s run by a prncpal whose task s rst to nvest n cost-reducng R&D and then, to make output decsons. To acqure R&D, each prncpal hres a rsk-averse researcher, whose e ort s unobservable and non-contractble. Thus, the prncpal s problem s to o er a contract based on contractble measures that s ncentve compatble. The partes nteract and play the three-stage 8 Serfes (005) assumes a contnuum of prncpals and agents wth unform dstrbutons and studes the relatonshp between rsk and performance pay (ncentves) n a prncpal-agent market. He nds the condtons under whch the equlbrum relatonshp between rsk and ncentves s negatve, postve, or non-monotonc.

6 E. Chalot: Contracts, competton and R&D spllovers 5 game descrbed n Fgure 1. Stage 1 Each prncpal, smultaneously wth ts rval, makes a take-t-or-leave-t o er to an agent.! Stage If the agent accepts the o er,! Stage 3 Frms observe the she chooses an e ort level (x ). R&D-outputs and Events beyond the agents control compete à la Cournot occur, R&D-outputs are determned, n the product market. and contracts are executed. Pro ts are realzed. If the agent rejects the o er, no nnovaton occurs. Fgure 1. Tmng of the game.1 Frm s pro ts The market s populated by a contnuum of dentcal consumers wth mass equal to 1. Each rm faces the lnear demand p = A q bq j where p s rm s prce, p : R+! R +, and q s ts output. 9 The parameter A denotes the market sze, A > 0, and b captures the degree of product substtutablty, b [0; 1]. When b = 0, rms have ndependent demands and behave as monopolsts whle, at the other extreme, when b = 1; they act as homogeneous-product duopolsts. A hgher b ndcates tougher competton. Each rm begns wth an ntal margnal cost c, but takes advantage of cost-reducng R&D opportuntes. If rm acqures the R&D output z, t realzes the post-nnovaton margnal cost c = c z where A > c > 0. The R&D output, z, depends on the agent s e ort, x, and a projectspec c shock, ", takng the form z = x +". 10 The random terms are drawn from a truncated normal dstrbuton wth zero mean and varance. They le n [, ], where 1 < < < +1, and are dentcally and ndependently dstrbuted across agents. 11 Thus, rm wll commt to an R&D level x X where X [0; c ] and enjoy the R&D pro t = w where s the Cournot pro t and w s the agent s compensaton.. Agents compensaton and preferences Agent has constant absolute rsk-averse (CARA) preferences wth utlty functon U (w ; x ) = e r[w (x )], (1) where r s the Arrow-Pratt measure of rsk averson, r > 0, and (x ) s the cost-of-e ort functon. Ths functon s twce contnuously d erentable and convex. Followng Holmström (1979), the agent 9 Followng Sngh & Vves (1984), the representatve consumer s preferences are descrbed by the standard quadratc utlty functon V (q ; q j ) = A(q + q j ) 1 q + q j + bq q j. Ths functon s separable and lnear n the numerare good. There are no ncome e ects, and thus we can perform partal equlbrum analyss. 10 Instead of process (cost-reducng) nnovaton, one could consder product nnovaton;.e., qualty mprovement n exstng products. Product nnovaton can be represented by an ncrease n consumers wllngness to pay captured by the parameter A. Frms pro t functons reman the same mplyng that the optmal choces and the comparatve statcs n our model apply n both settngs (Vves (008)). 11 The value of s spec ed n subsecton 3: where assumptons on the pro t functons are made.

7 E. Chalot: Contracts, competton and R&D spllovers 6 receves a lnear contract that s contngent on her R&D output and generates a payment w = + z, () where denotes the xed salary component and s a pay-for-performance parameter, 0. If the agent rejects the o er, she pcks the outsde opton, whch s normalzed to zero. 3 Equlbrum and R&D ncentves We recursvely solve the game and derve the subgame perfect Nash equlbrum. Frms make ther decsons smultaneously and ndependently. We also analyze the e ect of moral hazard on agents e ort and compettors equlbrum pro ts. 3.1 Cournot competton In stage 3, rms observe the realzaton of the margnal costs and compete n outputs. partcular, rm maxmzes = [A q bq j c ] q and produces q = 1 A c + z bz j. (3) + b b Its Cournot pro t s = (q ). Note that rms genercally end up n an asymmetrc equlbrum q ; qj even f the R&D decsons taken n the prevous stages were dentcal. Ths re ects that rms may experence asymmetrc margnal costs dependng on how lucky the researchers were durng the R&D process;.e. the realzatons of " and " j may d er. In 3. Prncpals problem and R&D rvalry To acqure R&D, each prncpal, smultaneously wth her rval, makes a contract o er to her agent that maxmzes the expected pro t and s compatble wth agent s ncentves to perform and to partcpate. Thus, the prncpal s contract decson depends on agent s response to her (expected) payment as well as the rval s response to rm s R&D. Denotng her belefs about rm j s R&D by bx j, prncpal s problem becomes max ; ;x E f ( ; ; x ; bx j ) j " ; " j g = E f w j " ; " j g subject to x = arg max x E fu (w ; x ) j " g (IC ) E fu (w ; x ) j " g 0 (IR )

8 E. Chalot: Contracts, competton and R&D spllovers 7 The ncentve compatblty constrant (IC ) guarantees that agent chooses the (expected) utlty maxmzng e ort. The ndvdual ratonalty constrant (IR ) shows that agent wll partcpate n the R&D process only f her expected utlty of dong so exceeds her reservaton utlty of zero. In lemma 1, we state that the certanty equvalence of agent s utlty can be expressed n a meanvarance form and the truncaton of the dstrbuton of the random terms does not a ect the agent s optmal decson. The agent conducts the R&D level that would also be optmal f the dstrbuton of the shocks was normal but not truncated. Lemma 1 (Certanty equvalence of utlty & truncated normal dstrbuton) If agent has CARA preferences towards rsk, lnear contracts are used and the random terms follow a truncated normal dstrbuton symmetrc around the mean, then agent s expected utlty s gven by and E fu (w ; x ) j " g = e r[ e U (x )] where e U (x ) = E (w ) + r + r r V ar (w ) (x ),. ( ) ( ) ndcates the probablty of " fallng nto. Gven that s postve and does not depend on e ort, agent s optmzaton problem s equvalent to choosng the x that maxmzes the certanty equvalence of her utlty e U (x ). Proof. See appendx. Gven that e U (x ) = + x condton r (x ), the optmal e ort x sats es the rst-order = 0 (x ). (4) To derve the optmal contractual parameters, we solve smultaneously both prncpals constraned maxmzaton problems and take the Kuhn-Tucker condtons. The IR constrant bnds at the optmum and agents earn no rents: the xed salary component,, nduces agent s partcpaton at least cost. Thus, the optmal wage s w (x ) = r [ 0 (x )] + (x ). Each agent s rewarded for the cost of e ort she ncurs and the rsks she bears. By (3), we also have E fq (x ; x j )g = 1 A c + x bx j, (5) + b b mplyng that rms R&D decsons are strategc substtutes. To guarantee that there exsts an nteror soluton n ths contractng/r&d game, we use the followng Inada-type assumptons on the pro t functon (.e., Amr et al. (000)): (A:1) 4[A( b) c+b] (4 b ) > [1 + r 00 (0)] 0 (0)(A:3) 4 [A ( b) c + b] (A:) 4 ( b) (+b) < [1 + r 00 (x)] 00 (x) for all x X.

9 E. Chalot: Contracts, competton and R&D spllovers 8 Assumpton (A:1) requres market demand to be hgh enough relatve to the ntal margnal cost and sets an upper bound on the margnal cost of e ort at zero, so that each rm has ncentves to undertake some R&D regardless of ts rval s R&D choce. Assumpton (A:) requres a strong form of convexty of the cost-of-e ort functon, so that the equlbrum of ths game s unque. In partcular, gven that R&D decsons are strategc substtutes and thus the slope of R&D reacton functons s negatve, (A:) guarantees that ths slope s also hgher than 1. 1;13 Lemma (Exstence of unque nteror equlbrum) Under assumptons (A:1) (A:), there exsts a unque subgame perfect Nash equlbrum n R&D n the nteror of the jontly undomnated e ectve strategy space X. Proof. See appendx. The optmal R&D level s x = b ( + b) 1 + r 00 (x ) 0 (x ) (A c). (6) Rsk plays a key role n the optmal decsons. Under full nformaton, the prncpal extracts the complete rents va the base payment and agents wage s equal to the margnal dsutlty of labor, 0 (:). However, under moral hazard, rsk-averson on the part of agents and uncertanty about performance nduce the agents to seek nsurance aganst low realzatons of the R&D outputs and lower ncentves are provded. Thus, e ort falls short of ts e cent level. In other words, the optmal e ort decreases wth rsk, measured by ) < 0 for all x X Pro ts-rsk relatonshp The e ect of rsk on pro ts s not clear cut. In partcular, rm s equlbrum pro ts take the form = r [ 0 (x )] (x ) where the R&D level s gven by (6) and = 1 (A c + x ) (+b) by equaton (5). Takng (r ) = ( + b) (A c x (r ) we examne the underlyng e ects. 1 0 (x ) + 0 (x (r ) 0 (x (x (r ), (7) Frst, the Cournot pro ts decrease wth r : gven that ncreases wth e cency-enhancng R&D and hgher values of r dstort e ort downwards, lower Cournot pro ts are realzed as a result. Second, there are the drect and ndrect e ects on human 1 Let the cost of e ort functon be k x where hgher k ndcates lower e cency. Assumpton (A:1) always holds and 4 (A:) requres < k 1 + kr. Assumpton (A:) also su ces to guarantee that the su cent condton of ( b) (+b) prncpal s problem holds. 13 Provded that the assumptons hold for the extreme value, they also hold for the mean of the random terms, whch s zero. 14 Appendx (A:3) provdes a proof.

10 E. Chalot: Contracts, competton and R&D spllovers 9 captal nsurance. In partcular, hgher degrees of rsk-averson and uncertanty about performance nduce the agent to seek addtonal nsurance. In turn, the prncpal experences lower resdual pro ts. However, underprovson of R&D ncentves due to rsk-sharng also decreases the varable part of agent s compensaton and thus, the varance of the payment;.e., 0 (x ) 0 (x ) < 0. Agent s nduced to exert lower e ort and thus, ncurs lower rsks. Ths (ndrect) e ect works n favor of the prncpal snce she s requred to provde less nsurance. Thrd, there s the e ect on the dsutlty of e (x ) < 0. The latter two e ects capture the cost a rm saves by acqurng less R&D ) response to hgher rsk. We argue that there exsts a regme n whch cost-savngs by provdng lower-power R&D ncentves due to moral hazard are substantal so that the pro t-rsk relatonshp turns out to be postve. Ths occurs when the gan n pro t due to cost-savngs exceeds the loss of pro t due to lower market power a rm can possess by nvestng less n R&D. In ths regme, the optmal pro ts ncrease as more nsurance s provded. Ths result counters the predcton of the prncpal-agent theory where prncpals wsh to have full nformaton so as to perfectly montor agents and acheve the optmal allocaton of e ort from ther own perspectve. We show that such motves can be reversed when rms compete aggressvely n the product market. Proposton 1 (Postve pro ts-rsk relatonshp) Under assumptons (A:1) (A:), Cournot compettors pro ts ncrease wth rsk f the cost of ncentve provson s low and goods are close enough substtutes so that competton s st ;.e., [1 + r 00 (x )] 00 (x ). Proof. ) > 0 f and only f 4 (4 b )(+b)(1 b) > Proposton 1 states that, f e ort exerton s not too costly (low r ) and product market rvals compete (su cently) aggressvely aganst each other (hgh b), they acqure such hgh levels of R&D so that they burn up ther pro ts. 15 Under moral hazard, rsk-sharng dmnshes such appette for nnovaton. Underprovson of ncentves exactly due to the trade-o between e ort exerton and nsurance may generate consderable cost-savngs and thus, hgher pro ts for both rvals. 16 However, f r exceeds the threshold spec ed n proposton 1, the cost of conductng R&D s so hgh that decreases pro ts. [Fgure s about here] Ths result ndcates the desrablty of the R&D rvals to adopt a collusve-lke behavor n R&D so as to behave less aggressvely n the product market. Thus, the separaton between the busness 15 The product 4 b ( + b) (1 b) s decreasng n b. h 16 Suppose (x ) = k x > 0 f, and only f, r < 1 4 k (4 b )(+b)(1 b)k 1. Notably, for homogeneous-product duopolsts, b = 1, the pro ts-rsk relatonshp s postve for all parameter values;.e. c = (A c) [9k(1+kr ) 8]k(1+kr ) [9k(1+kr ) = 3(A c) k > 0. [9k(1+kr ) 4] 3

11 E. Chalot: Contracts, competton and R&D spllovers 10 and research unts, whch mples the dvson between the ownershp and control of R&D outputs under moral hazard, before rms meet n the market place, can be used as a commtment devce for both rvals that softens ther subsequent responses. Rvals wll enjoy hgher pro ts as a result. Ths analyss gves new nsghts nto rms organzatonal structure. In ndustres where competton s low and R&D s costly, rm should adopt an organzaton structure that elmnates the nformaton asymmetres about agents actons. By dong so, rms wll be able to manage the nnovaton process more e cently and decrease ncentve dstortons. In contrast, much of the use of ncentve pay could be n volatle ndustres, such as n hgh-technology ndustres and the nancal sector. For nstance, n mcroelectroncs-based ndustres where competton s ntensve, rms have strong ncentves to mutually commt themselves to lower R&D levels. By delegatng R&D decsons to a second party -.e., a research team, an autonomous unt etc - or even by appontng more rsk-averse researchers, rvals strategc nteractons are weakened and prncpals can become better-o. 4 R&D Incentves under spllovers Ths secton examnes rms R&D decsons n the presence of R&D spllovers. Spllovers (costlessly) decrease the rval s ntal margnal cost creatng a dsncentve for the R&D takng rm. However, we argue that, f mperfect spllovers occur and rms R&D decsons are strategc substtutes, spllovers can nduce the product market compettors to ntensfy ther R&D e orts n order to secure a cost advantage, decreasng ther pro ts even further. Thus, we show that, as spllovers ncrease, there are addtonal bene ts of usng a self-control devce that mutually decreases rvals R&D e orts and allows for hgher pro ts. To antcpate the e ect of spllovers and competton on rvals R&D, we decompose the R&D ncentves and perform a comparatve statcs analyss. 4.1 Equlbrum The R&D process s subject to cross- rm spllovers. As n D Aspremont & Jacquemn (1990), agent s R&D-output depends on the sze of (unpad) appropraton of ts rval s research, hx j. The R&D producton functon now takes the form z = x + hx j + ". (8) The parameter h measures the spllover rate, h [0; 1];.e. the fracton of agent j s R&D that mproves agent s performance. That h s less than one and ndcates the mperfect nature of R&D spllovers. Agent s compensaton s now restrcted to be lnear to both agents R&D-outputs snce they are correlated due to spllovers (Holmström (1979), Holmström & Mlgrom (1987), Holmström &

12 E. Chalot: Contracts, competton and R&D spllovers 11 Trole (1989)). Relatve performance evaluatons provde a rcher nformaton base on whch to wrte contracts and allow each prncpal to better assess ts agent s e ort by lookng at ts rval s performance. The contract takes the form ( ; ; ) and agent s receves w = + z + z j, (9) where denotes the pay-for-rval performance parameter. 17 Thus, each agent s reward s condtoned on how well she performs compared to another. The certanty equvalence of agent s utlty has as eu (x ) = + ( + h ) x + (h + ) x j r ( + h ) + (h + ) (x ) (10) and the optmal e ort s gven by + h = 0 (x c ) (11) The left hand sde represents the "total" senstvty of agent s compensaton to her own e ort. In ar(w )=@ ar(w )=@ mplyng that each prncpal has two equvalent ncentve 0 (x c 0 (x c )=@ avalable to use n order to a ect agent s behavor. Gven the concavty of the functons U and n x, agents CARA preferences and the (truncated) normalty of the random terms, we can use the rst-order approach and replace the IC constrant wth equaton (11). 18 have By (3) and (8), we also E fq g = 1 A c + ( bh) x (b h) x j. (1) + b b The nature of R&D strategc nteractons now depends on the sgn of b h. If spllovers are small enough, h < b, e orts are strategc substtutes, but f h > b, e orts are strategc complements. In the knfe-edge case where h = b, each rm has a domnant strategy on R&D. To guarantee that a soluton exsts n ths game, as n subsecton 3:, we make the followng assumptons: (A:3) ( bh)[a( b) c(1 h)+(b h)] (4 b ) > [1 + r 00 (0)] 0 (0) (A:4) (A:5) ( bh)(a ) (4 b )(+b) < [1 + r 00 (x )] 0 (x ) where x = c 1+h ( bh)[ bh+jb hj] (4 b ) < [1 + r 00 (x)] 00 (x) for all x X 17 Lacetera & Zrula (01) consder e ort to be mult-dmensonal;.e., e ort for appled research and e ort for basc research. E orts are unobservable and unver able, whle e ort for basc research s assumed to be d used. The margnal cost s non-contractble and the contracts are contngent on ver able sgnals of both types of e orts. We consder a d erent framework where the prncpal-agent relatonshp s one-dmensonal and the margnal cost s contractble. 18 In a mult-agent framework, the monotone lkelhood rato property (MLRP) and the convexty of the dstrbuton functon condton (CDFC) are not su cent for the rst-order approach to be vald as n a sngle-agent settng. Itoh (1991) argues that, n a model wth cross-agent nteractons, a generalzed CDFC for the jont probablty dstrbuton of the outputs s needed and the wage schemes must be nondecreasng. The coe cent of absolute rsk averson must also not declne too quckly. In our model, gven the assumptons about the form of the contracts, the R&D producton functon and the agents CARA preferences, the rst-order approach apples.

13 E. Chalot: Contracts, competton and R&D spllovers 1 Assumpton (A:3) nsures that each rm nds t best to do some R&D. Assumpton (A:4) su ces to guarantee the nterorty of the equlbrum. In partcular, the feasblty lnes x = c hx j guarantee that the post-nnovaton margnal cost wll be postve. Assumpton (A:4) requres the unt cost of dong R&D be large enough at the pont where these lnes ntersect n order to moderate the R&D ncentves. Assumpton (A:5) guarantees the unqueness of ths equlbrum. 19 Proposton (Spllovers & relatve performance) Under assumptons (A:3) exsts a subgame perfect Nash equlbrum n performance-based parameters n whch (A:5), there = 0 (x ) and = h, where the optmal R&D-e ort level x has as x = 1 (4 b ) ( + b) [1 + r 00 (x )] 0 (x ) 1 + h ( bh) (A c). Proof. See appendx. The postve sgn of ndcates that hgher own performance s compensated wth a hgher wage. In contrast, the prncpal sets to be negatve, gvng the agent a short poston n rval s performance. The prncpal antcpates the postve contrbuton of spllovers on R&D performance and penalzes the agent when the rval does better. Such evaluaton schemes can e ectvely be used as means of lterng out spllovers from agent s compensaton. Thus, agent s payment s no longer sen-, stve to j s R&D. Note also that the "compensaton rato", s hgher n compensaton packages that are o ered n ndustres wth ntensve spllovers. 0 The hgher s h, the more valuable s the nformaton contaned n rval s R&D measure and thus, the use of relatve performance evaluatons becomes more essental. 4. Moral hazard & spllovers The exstence of spllovers changes the nature of R&D strategc nteractons as well as the e ects of moral hazard on rms equlbrum pro ts. Corollary 1 states that a postve pro ts-rsk relatonshp only exsts f e orts are strategc substtutes and the cost of ncentvzng the researchers to conduct R&D s small enough. If e orts are strategc complements, rsk always decreases pro ts. 1 Corollary 1 (Pro ts-rsk relatonshp under spllovers) Under assumptons (A:3) the presence of moral hazard, Cournot compettors pro ts ncrease wth rsk, d d(r ) (A:5), n > 0, f and only 19 Assumpton (A:3) s needed only f h < b whle (A:4) plays a role only f h > b. 0 Any compensaton scheme that s a lnear transformaton of ths cost-based contract wll nduce the same level of e ort n equlbrum. For nstance, agent s compensaton could be contngent on outputs;.e. w = + q + q j. In h b such a case, the optmal compensaton rato s bh. Note that the ntensty of product market competton now a ects the optmal ncentve parameters. 1 The proof of corollary 1 s smlar to that of proposton 1 and provded n the onlne appendx.

14 E. Chalot: Contracts, competton and R&D spllovers 13 f, e orts are strategc substtutes, h < b, and ( bh) (1 + h) (4 b ) ( + b) [ (1 b) + h (4 b)] > 1 + r 00 (x ) 00 (x ) To nterpret corollary 1, we rst consder the underlyng e ects of R&D on rm s pro ts. Then, we examne how the optmal R&D ncentves change wth product market competton and spllovers. The decomposton of R&D @q @c [1 + r 00 (x )] 00 (x ). The drect e ect of e ort on pro ts comes through margnal cost reducton;.e. the more a rm at a lower cost, the more t @x = q. Ths s the scale e ect, whch s postve. If b > 0, the ndrect e ects on rms revenues are also j 1 j b(b = q 4 j @q j s mpled from the stablty condton. Frst, there s the (postve) strategc e ect: e ort enhances the e cency of producton allowng the R&D-takng rm to produce more and ncrease ts market share vs-à-vs ts rval. Second, there s the (negatve) spllover e ect: agent s e ort also reduces rm j s ntal margnal cost due to spllovers allowng the rval to be tougher n the product market. Ths e ect s detrmental to the R&D-takng rm. shows the trade-o among all these e ects aganst the ncrease n the cost of dong R&D. Rvals R&D responses depend on the relatve ntensty of the strategc and spllover e ect. E orts are strategc substtutes f h < b where the strategc e ect domnates the spllover e ect. We attempt a Slutsky-lke analyss to antcpate the e ect of product market competton on R&D, We get d(@ =@x ) = =@x ) dx = 0. Assumpton (A:5) su ces to guarantee that db pro t functon s concave n x mplyng < 0 for any X. Thus, competton ncreases the optmal e ort n the regme where t ncreases the margnal pro tablty of R&D. However, the sgn =@x ) s ambguous snce competton ntens es the strategc and (negatve) spllover e whle t makes the scale e ect less mportant. Corollary (E ect of competton on e ort) Under assumptons (A:3) (A:5), the optmal R&D e ort ncreases wth product market competton, dxc > 0, f, and only f, b > 3+h (9 h 7h ) 1. db h Proof. See appendx. Competton can ncrease R&D only f e orts are strategc substtutes. In ths regme, n lne wth the lterature, the relatonshp between competton and cost-reducng R&D nvestment s U-shaped;.e., for low values of b, the s negatve, but t becomes postve when the condton corollary s sats ed. The ntuton s as follows. On the one hand, the strategc e ect ncreases wth b: as demand becomes more elastc, a rm wth a cost-advantage can more easly steal busnesses from ts rval. Thus, ntens ed competton ncreases the margnal bene t of cost reducton. On the other hand, the scale e ect decreases: for hgher b, the wllngness to pay for rms goods decreases, mplyng lower prces. In turn, a drop n output s requred to compensate for the fall n pro

15 E. Chalot: Contracts, competton and R&D spllovers 14 (negatve) spllover e ect s also ntens ed. For hgher b, a reducton n rval s margnal cost due to spllovers harms the R&D-takng rm by more. A lower-cost rval can more easly gan n market share. Therefore, competton strengthens R&D ncentves when t makes the strategc e ect more mportant than the other two e ects, so that rms are drven by busness stealng ncentves. Spllovers can also nduce rms to nvest more n R&D. Corollary 3 characterzes when ths s so. Corollary 3 (E ect of spllovers on e ort) Under assumptons (A:3) e ort ncreases wth spllovers;.e. dx dh > 0, only f (A:5), the optmal R&D h < b b and ( bh) (A c) [ b (1 + h)] (4 b ) ( + b) < 1 + r 00 (x ) 0 (x ). Proof. See appendx. Spllovers ntensfy all three e ects and thus, R&D ncreases when the postve strategc and scale e ects become more mportant relatve to the negatve spllover e ect. In partcular, f e orts are strategc substtutes, h < b, a rm wth lower cost can extend ts busnesses at the expense of ts rval s. Thus, gven the (mperfect) nature of spllovers, as h ncreases, rms provde hgher-power R&D ncentves n order to secure a cost advantage. Ths requres the cost of e ort exerton to be relatvely small. Otherwse, f ths cost exceeds the threshold spec ed n corollary 3, prncpals seem to be unwllng to bear such hgh R&D costs and exert lower e ort n respond to hgher h. It all bols down to the followng: f e orts are strategc substtutes and the cost of dong R&D s relatvely small, the R&D actvty s ntens ed when a rm s drven by busness-stealng ncentves due to the product market competton and attempts to secure that the cost-advantage wll not be dsspated due to spllovers. In such a case, prncpals are eager to acqure more R&D and exert such a hgh level of R&D e ort that harms them. In the presence of under moral hazard, provdng nsurance aganst the rsk dmnshes such ncentves and cost-savngs by conductng less R&D exactly due to rsk-sharng may allow rms to realze hgher pro ts n equlbrum. In the regme where e orts are strategc complements, h > b, pro ts always decrease wth rsk. We rst consder the monopoly case, b = 0, where only the scale e ect holds. Complementartes n R&D allow rms to explot the spllovers only for e cency enhancng (not strategc) reasons. There are mutual bene ts from dong R&D. Thus, monopolsts are always better-o under full nformaton snce they can perfectly montor the agents. Less dstorted decsons wll enhance pro ts. For low R&D cost, ths result apples even f b > 0. However, f the R&D cost s hgh, rsk decreases pro ts, but the ntuton s d erent. Each rm has strong ncentves to free-rde on ts rval s research. Free-rdng decreases e ort and thus, further reducton n R&D due to rsk-sharng wll result n even lower pro ts. The free-rder s problem arses because, provded that rm j does not change ts R&D level, an ncrease n h allows rm to dmnsh ts own R&D and approprate j s R&D-output through spllovers.

16 E. Chalot: Contracts, competton and R&D spllovers Dscusson and extensons By analyzng the equlbrum R&D ncentves, one can also argue that whenever competton ncreases equlbrum e ort, as spec ed n corollary, the agency cost also ncreases. Smlarly, whenever e ort ncreases wth spllovers, as spec ed n corollary 3, so does the agency cost. 3;4 In partcular, under moral hazard, for hgher r, the prncpals are less wllng to exert e ort as the contracts are rewrtten to accommodate ntens ed competton and spllovers. There s far more dstorton n ncentves. E ort responds less to an ncrease n b or h, and thus, the use of a self-commtment devce that mutually weakens the ncentves for e ort exerton becomes ncreasngly more e ectve. The bene ts from delegatng the R&D decson under asymmetrc nformaton as a pro t-enhancng decson are augmented. Ths model can be extended n many ways and d erent drectons. Frst, one can show that hgher pro ts can be realzed under moral hazard even f rms compete à la Bertrand. Frms nteractons n Bertrand and Cournot settngs d er manly n the followng. For Bertrand compettors, the strategc e ect s negatve: cost-reducng R&D allows the R&D-takng rm to set a lower prce. Competng for market share, the rval responds by cuttng ts own prce too, mplyng lower pro ts for the nnovator. Thus, product market competton gves rse only to detrmental e ects on the nnovator s pro t. However, the cost-reducng ncentves are also strong for Bertrand rvals exactly because rms behave so aggressvely n the product market. Due to the antcpated prce war and the mperfect nature of spllovers, rvals over -nvest n R&D, dmnshng ther pro ts. If rms operate under moral hazard, they nnovate less and thus, prce cuttng as a market response becomes less pro table. As a result, rsk-sharng can ncrease pro ts for both Bertrand and Cournot rvals. A postve pro t-rsk relatonshp obtans only f rms compete smultaneously n both markets. In a sequental-move contractng/r&d game, the leader can solve the follower s problem and nduce the follower to undertake the R&D level that maxmzes the leader s pro t. Consequently, the leader wshes to act under full nformaton so as to e ectvely control the decsons taken by the agent and the follower. It s also nterestng to consder R&D ncentves when the random terms are correlated. Suppose that the correlaton coe cent s = j where jj 1 and j < 1 + r. Postve or negatve correlaton s lkely to occur when rms use smlar or d erent technologes respectvely. Due to the correlaton of the random terms, the varance of the agent s compensaton becomes V ar (w ) = ( + h ) + (h + ) + ( + h ) (h + ). In our model where there are two forms of correlaton between the agents R&D-outputs, the optmal compensaton rato becomes = = T [A c+(1+h)xc ] c ) = T N (1 + ) (x c ). N where T 4[3b ( b+b )h], N (4 b ) ) [A c + (1 + h) xc ] = N (Mxc ) where M b(1+h) b(a c) (4 b )(+b), h corollary = (x c (Mx c ) (4 b )(+b) ( bh)(1+h) (4 b )(+b) w 00 (x c ) < 0. (x c > 0, s s negatve. < 0, T > 0 by corollary > > 0, Mxc > 0 by

17 E. Chalot: Contracts, competton and R&D spllovers 16 h+ 1+h. [Fgure 3 s about here] The optmal contract lters out both spllovers and the common shock from agent s reward. If > 0, the prncpal sets negatve snce the agent acts n a favorable envronment, whch ncreases her performance. If < 0, the sgn of depends on the relatve ntensty of the two forms of correlaton of R&D-outputs. s negatve when spllovers matter more n agents evaluatons. However, f h < jj, settng postve s a plausble way to encourage e ort exerton. A prncpal ncentvzes an agent to nnovate by makng her su er less from a bad outcome. Her reward now ncreases wth a rval s performance. If h =, then z becomes a su cent statstc of x and agent s compensaton depends only on her own performance. In ths settng wth correlated random terms, rvals can also enjoy hgher pro ts under moral hazard. 5 Concluson We examne researchers ncentves to carry out cost-reducng R&D n a settng wth product market competton and R&D spllovers. Because R&D-nputs are not observable and the R&D process s subject to uncertanty over the R&D-outputs, moral hazard concerns and rsk averson of the agent become central. A lnear prncpal-agent model s employed n whch each prncpal s lkely to o er a relatve performance evaluaton scheme whose performance measures are both own- and rval- rm cost reductons, re ectng that each agent approprates some part of ts rval s research. Ths paper shows that compensaton schemes based on explct performance comparsons lter out spllovers from the reward packages by penalzng an agent when the rval performs better. We argue that f R&D-e orts are strategc substtutes, then n hghly compettve ndustres, rms nnovate more n order to gan market share. If the cost of dong R&D s small, rms exert such a hgh level of e ort that t decreases ther pro ts. In such an envronment, the exstence of moral hazard can be pro t-enhancng. In partcular, the under-provson of ncentves due to rsksharng generates cost-savngs and can ncrease rms equlbrum pro ts. Thus, rms may prefer an organzaton structure where busness and research teams are separated and agents abhor rsk so as to use t as a collusve devce that makes both rms better-o. Such results requre research e orts to be strategc substtutes but can hold n both Cournot and Bertrand settngs. Ths analyss mght be used to nterpret some emprcal evdence on the R&D performance of modern corporatons n markets where nnovaton s rushed and knowledge s d used. Scencebased rms d er n behavor, management strateges and responses to market changes. Ths model also suggests avenues for future emprcal research. The strategc nature of delegaton and the use of ncentve pay are themselves emprcally testable. One could examne whether the organzaton structure of the rms and the form of the R&D contracts depend on the R&D and product market

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