Market structure and Innovation

Transcription

1 Market structure and Innovaton Ths presentaton s based on the paper Market structure and Innovaton authored by Glenn C. Loury, publshed n The Quarterly Journal of Economcs, Vol. 93, No.3 ( Aug 1979) I. Introducton. The possblty of acqurng monopoly power and assocated quas rents s necessary to provde entrepreneurs an ncentve to pursue nnovatve actvty..both theoretcal and emprcal studes have suggested the exstence of a degree of concentraton ntermedate between pure monopoly and perfect competton that s best n terms of R&D performance..the present paper drawng on the work of Scherer and Kamen and Schwartz (1972,1976), formulates a model n whch each frm nvests n R&D under both technologcal and market uncertanty. 1

2 . Gven the ndustry s market structure, equlbrum occurs when each frm s nvestment decson maxmzes ts expected dscounted profts, subject to the other frm s R&D nvestment strateges beng gven.. The model s used to study the mpact of market structure on R&D performance at both the frm and ndustry level, as well as the consequent effect on socal welfare. 2

3 II The model Assumptons: 1. n dentcal frms compete for the constant flow of rewards V that wll become avalable only to the frst frm that ntroduces an nnovaton. 2.nfnte patent protecton so that belated nnovators get no net rewards.. Frm makes an nvestment n R&D wth a present value of cost x. And τ ( ) represents the uncertan date at x whch the R&D project wll be successfully completed..assume the followng technologcal relatonshp: hx ( ) t pr[ τ ( x ) t] = 1 e (1 ) That s, τ ( x ) s exponentally dstrbuted wth an expected tme of ntroducton gven by 3

4 Eτ ( x ) = Thus, hx ( ) 1 h ( x ) (2 ) s the nstantaneous probablty that the nnovaton wll be successfully completed (or ready for the market) at any subsequent moment..we take h (.) to be twce contnuously dfferentable, strctly ncreasng, satsfyng h ' (0) 0 lm ( ) x = = h x (3 ) and '' ()0 hx < as xx > 4

5 Equaton (3) expresses the assumpton that whle there may be an ntal range of ncreasng returns to scale n the R&D technology, dmnshng returns are encountered eventually. Let x% denote the pont where hx ()/ x s greatest..defne ˆ τ as the random varable representng the th frm s market uncertanty regardng the tme at whch any rval wll ntroduce the nnovaton. τ ˆ s related to the behavor of other frms by ˆ τ = mn { τ ( xj)} (4) 1 j < n. Assume the random varables τ ( x ) ndependent pr[ ˆ τ t] = 1 exp( t h( x )) = 1 e, =1,2,..,n are at j (5) j where a h( xj) and a s taken as constant by the th frm. j. At any tme t 0 the th frm earns a revenue flow V n the event thatτ ( x ) mn( ˆ τ, t). 5

6 Integratng the jont densty of ( τ ( ), ˆ τ ) over the relevant x regon, we have ( 6 ) pr[( τ x ) mn( ˆ τ,)] t t at h( x) t h( x) s as (1 ) (1 ) 0 = e e + a e e hx ( ) = (1 exp( ta [ + hx ( )])) a + h( x) ds The th frm chooses x, gven (dscount rate) and V to maxmze expected dscounted profts, t must solve the followng problem: ar, Vh( x) Max{ x} Max ( a, x; V, r) ra ( + r+ hx ( )) (7) F.O.C: h ( xˆ )( a+ r) r = 0 2 [ a+ r+ h( xˆ )] V (8) S.O.C : ) h x a r ) h x h xˆ ) ) (8) defnes x = x( a, r, V) mplctly 2 ( ).[ + + ( )] 2 ( ) 0 (9 ) 6

7 A symmetrc Nash equlbrum mples each frm pursue the same nvestment strategy. For each frm, we have that a= ( n 1) h( x ) ) x = x(( n 1) hx ( ), rv, ). From (8), we have: (10 ) Equaton (10) mplctly defnes the equlbrum level of frm R&D nvestment x = x ( n, r, V) Now, we examne the mpact of greater rvalry on a frm s nnovatve actvty by studyng the dependency of n. x on Proposton I: As the number of frms n the ndustry ncreases, the equlbrum level of frm nvestment declnes. Proof: Regardng n as a contnuous varable, totally dfferentate (10) to fnd ( n 2 ) that x xˆ / ah( x ) = < 0 n 1 ( n 1) h ( x ) xˆ / a Thus, we have found that ncreasng the extent of rvalry reduces an ndvdual frm s ncentve to nvest n R&D 7

8 Proposton II : Suppose that wth the ndustry n equlbrum, a margnal ncrease n R&D nvestment by any sngle frm causes the nvestment of each other frm to fall by a smaller amount. Then ncreasng the number of frms always reduces the expected ndustry ntroducton date ( the date on whch the nnovaton frst becomes avalable to socety). Proof: Defne a random varable τ ( n) mn{ τ( )} 1 n x, the random date on whch the nnovaton frst becomes avalable to Eτ ( n) = 1 nh[ x ( n)] socety. In equlbrum, we have Industry expected ntroducton date declnes wth the number of frms f and only f d = + dn xˆ = hx n + 1 ( n 1) h [ x ( n)] a d dn ( nh[ x ( n)]) h[ x ( n)] nh [ x ( n)] nh [ x ( n)] [ ( )][1 a ] xˆ ( nh [ x ( n )]) > 0 x n 8

9 From the proof of Proposton I, thus xˆ h ( x ) 1 a > d nh x n dn ( [ ( )]) 0 < as Ths proposton shows that gven a reasonable stablty condton, ncreasng the number of compettors n an ndustry reduces the expected tme that socety has to wat for the nnovaton despte the fact that each compettor nvests less n R&D. III. Welfare analyss of ndustry equlbrum. Now consder the effcency propertes of short-run and long-run equlbrum 1. In the short run, duplcaton effort wll cause neffcency. Each frm chooses an nvestment level to maxmze ( ax, ) Nash equlbrum, π, takng a as gven. In a symmetrc a = ( n 1) h( x). The expected present value of socal benefts at an equlbrum s equal to nπ (( n 1) h( x ), x ( n)). Each frm faces probablty 1 n 9

10 of beng frst, but socety s ndfferent as to whch frms wn the race. Then n short-run equlbrum frms tend to overnvest n R&D because they do not take account of the parallel nature of ther actvtes. Proposton III : Gven a fxed market structure ( ), n ndustry equlbrum each frm nvests more n R&D than s socally optmal. n Proof: Let x ( n) denote the socally effcent frm nvestment level when market structure s fxed at. Gven, socal welfare s maxmzed when π π (( n 1) h( x), x) + ( n 1) h ( x) (( n 1) h( x), x) = 0 x a but ndustry equlbrum s characterzed by π (( n 1) h( x), x) = 0 x Snce π / a < 0 and x n > x n ( ) ( ) 2 2 π / x 0. It follows that n n 10

11 2. In long-run ndustry equlbrum, there s also a source of neffcency. Proposton IV: If x >0 ( see equaton (3) ), then compettve entry nduces too many frms to jon the nnovaton race. When entry s unmpeded, f the technology possesses economes of scale ntally, and f nnovatng frms struggle for the entre socal payoff, there wll be too much competton. In ths nstance, no scale economes are beng exploted, and mergers of parallel R&D efforts would obvously mprove performance. These neffcences may be corrected through the judcous choce of a patent lfe and an entry tax-subsdy. Proposton V : There exsts a fnte patent lfe and an entry tax (possbly negatve) n the presence of whch the long-run ndustry equlbrum s socally optmal 11

12 IV concluson. Ths s an equlbrum model of nvestment n R&D under rvalry. In ths model, frms are assumed to maxmze ther expected profts under condtons of technologcal and market uncertanty..more competton reduces ndvdual frm s nvestment ncentves n equlbrum, yet leads ( under certan reasonable condtons ) to an ncreased probablty that the nnovaton wll be ntroduced by any future date..more competton s not necessarly socally desrable. In equlbrum, more frms wll enter the nnovaton race than socally optmal. Competng frms also nvest more n R&D than socally optmal because they do not take account of the parallel nature of ther efforts. 12

13 Some shortcomngs of ths model:. Imtaton may reduce prvate nvestment ncentves. In ths case, compettve frms may not overnvest. But ths model ddn t take ths effect nto account..ths model assume that competng frms lose nothng but ther R&D nvestment when a rval beats them to the nnovaton. In realty the market shares of competng frms are constantly changng as new nnovatons attract compettors customers. 13