SØK/ECON 535 Iperfet Copetition an Strategi Interation RESEARCH AND DEVELOPMENT Leture notes 11.11.02 Introution Issues private inentives vs overall gains fro R&D introution of new tehnology Types of R&D basi researh applie researh innovation iffusion of new knowlege (learning) Prout vs proess innovation Externalities an publi goos Patents provies opportunities for (onopoly) profit inentive to innovator; reues opetition an auses loss of onsuer surplus. Market struture an inentives for R&D Shupeter (1943): onopoly is neessary for R&D onopoly profits provie finaning for R&D (also, large firs ay experiene eonoies of sale an eonoies of sope that akes R&D less ostly an risky); onopoly profits provie the inentive for R&D. What is the private inentive for R&D? Is it optial? Exaple: proess innovation (onstant) arginal osts are reue fro to ;
ean funtion is D( p ). Welfare gain Inrease in onsuer surplus per perio (given that prie equals arginal osts): V s = ( ) D Monopolist Figure: area uner the ean urve. We have Π Π p Π Π = + = = D p p The onopolist s gain is onsequently Sine ( ) > ( ( ) ) V =Π ( ) Π ( ) = D( p ( ) ) s p, it follows that V < V. Figure: area uner ean urve between onopoly pries.. Perfet opetition Assue that initially all firs have osts an hene the arket prie equals this level (Bertran opetition). Then soe fir has osts reue to. We istinguish between a rasti innovation: p ( ) ; an a non-rasti innovation: p ( ) >. In the ase of a non-rasti innovation, the inentive to innovate is 2
[ ] ( ) V = D. It follows that V < V < beause D p < D < D,,. V s ( ) ( ) ( ) ( ) [ ] Figure: area between osts for given ean. In the ase of a rasti innovation, the inentive to innovate beoes ( ) ( ) ( ) ( ) ( ) ( ( )) V =Π = p D p = D p Again, we fin V < V < V s. Figure: onopoly profits at lowest possible ost. p Conlusion The lak of opportunities for prie isriination iplies that the inentive to innovate beoes too sall. A onopolist has less to gain fro a fir that is initially expose to strong opetition beause the latter has a saller profit initially (the replaeent effet). Entry Assue there is one establishe inubent an one potential entrant. The entrant enters only if he or she gets aess to the new tehnology. If only the onopolist an innovate, his or her inentive is V. If only the entrant an innovate, his or her inentive is V (assuing there is Bertran opetition). Assue now that the two firs opete for the innovation (eg. by biing on patent rights): the entrant woul be willing to pay at ost Π (, ) ; while. the inubent woul be willing to pay at ost Π ( ) Π (, ) 3
, ( i.e., a perfet artel results in Assuing that Π ( ) Π (, ) +Π ( ) higher inustry profits than uopoly), it follows that the inubent s inentive to innovate is greater than that of the entrant. Intuition: beause innovation an entry leas to greater opetition the inubent has ore to lose (effiieny effet). f. sleeping patents (Gilbert an Newbery, 1982). Patent rae Copetition to be the first to innovate an obtain a patent. Exten the above oel to a ynai oel: the probability, h, for a given fir to innovate at a given tie t epens on the fir s own R&D effort only; the probability of innovating over a perio [ tt, + ] h( x) t ( 0) t when the fir invests xt is, where h is inreasing an onave an h = ; the fir that innovates obtains an infinite patent (an no new innovations take plae). The inubent s (Fir 1 s) inentive to innovate is given by ( ) ( ) 1 ( 1) ( ) ( 2) (, ) r + h( x ) + h( x ) (, ) ( ) + ( ) rt hx Π Π 1 hx2 t V1( x1, x2) = e e Π ( ) x1+ h( x1) + h( x2) t 0 r r Π x + h x Π r + h x Π r = ( ) ( ) hx1 + hx2 t where e is the probability that no-one has innovate before tie t. The entrant s (Fir 2 s) inentive to innovate is given by ( ) Π (, ) r + h( x ) + h( x ) (, ) ( ) + ( ) rt hx Π 1 hx2 t V2( x1, x2) = e e h( x2) x2 t 0 r h x r x = 2 2 The relative strengths of Nash equilibriu R&D efforts is eterine by two opposing effets 4
the effiieny effet, an the replaeent effet. Two extree ases: rasti innovation: Π (, ) =Π ( ) an (, ) Π = 0, so there is no effiieny effet an hene the inubent invests less than the entrant, i.e. x x ; < the probability of innovation is very high even for low levels of R&D effort ( li x h( x) = ), whih iplies that firs will invest uh in any ase an hene the probability of an early innovation is high: then there is no replaeent effet an hene the inubent invests ore x x. > Optial R&D effort Dupliation of effort ay lea to over-investent. Learning The probability of innovation ay epen on auulate efforts. It is then typial that there will be strong opetition an large investent when firs are level, while lagging firs quikly falls off. Spillovers Knowlege spillovers reue the payoff fro being first; an reue the loss fro not being first. Consequently, spillovers reue inentives for innovation. Diffusion Consier a Bertran uopoly an a non-rasti proess innovation. Investent in the new tehnology osts C( t ) at tie t, with C < 0, C > 0, an C( 0 )'large'. Due to the assuption of Betran opetition, at ost one fir will invest in the new tehnology. 5
Copetition to be the first to innovate leas to innovation at tie t, where t is efine by 1 C t D r ( ) = [ ] ( ), that is, t is the first point in tie that the investent is profitable the onopoly rent is opletely issipate (f rent-seeking ); no overall gain fro the innovation (beause the ex ante an ex post pries are the sae). ( ) A onopolist woul hoose t so as to axiise rt V C t e. 6