Module 11: Innovation & Patents

Transcription

1 Module 11: Innovation & Patents Maket Oganization & Publi Poliy (E 731) Geoge Geogiadis Tehnologial pogess is uial fo impoving welfae, but (vey) ostly. How to inentivize fims to innovate? Suppose that a lage numbe of fims engage in Counot ompetition. We have seen that the equilibium pie will be lose to the maginal ost, and fims pofits lose to 0. Conside a fim s inentive to engage in ostly R&D. If othe fims an imitate a new innovation, then the innovating fim will have little inentive to invest in the fist plae. Theefoe, a new fim must be guaanteed enough (expet) pofits to eoup the R&D ost. Ente: Patents (that povide the innovating fim with a tempoay monopoly). Shumpete (1943): If one wants to indue fims to undetake R&D, then one must aept the eation of monopolies as a neessay evil. The Value of Innovation A simple model of poess innovation: Assume that innovation lowes the (onstant) maginal podution ost fom to <. How muh would a fim be willing to pay to edue its maginal ost, given that no othe fim will (be allowed to) buy it? 1

2 Soial Planne (Fist best): She sets pie equal to maginal ost; i.e., p = befoe the innovation, and p = afte. Additional net soial suplus p.u of time: v s = ū u D()d The soial planne s value fom innovating is: Monopoly: V s = ˆ 1 0 e t v s dt = 1 Suppose that a fim is in a monopoly situation. Let m denote monopoly pofit p.u of time. Then: D()d d m d = d [(p ) D(p)] d m dp d {z } =0 = D (p m ()) Appliation of the Envelope Theoem. The monopolist s value fom innovating is: V m = = 1 = 1 ˆ 1 0 e t [ m () d m d d D (p m ()) d m ( )] dt Beause p m () >and D 0 < 0, we have D (p m ()) <D() fo all, and hene V m <V s. A monopolist has weake inentives to innovate elative to a soial planne. Intuitively: Beause he sets a highe pie, the ost edution petains to a smalle numbe of units. Competition: Suppose that 2 fims engage in Betand ompetition. 2

3 Then p =, and fims ean 0 pofits. The fim that obtains new tehnology with ost is awaded a patent. Let p m () be the monopoly pie when the ost is. Case 1: If p m () apple, then we say that the innovation is dasti. The innovato then hages p = p m (), and obtains the entie maket. His value fom innovating is V m. Case 2: If p m () >, then we say that the innovation is nondasti. Both fims hage p =, and the innovato s pofit p.u of time is =( ) D ( ). The value fom innovating is V = 1 ( ) D ( ) Beause <p m () <p m (), we have D( ) >D(p m ()) fo all, so V m = 1 D (p m ()) d < 1 But D ( ) <D() fo all <, sov s = 1 Theefoe, V 2 (V s,v m ). Take-aways: D ( ) d = V D()d > 1 D( )d = V. Even with patents of infinite duation, the innovato does not intenalize the entie soial suplus fom the innovation. A monopolist has less to gain fom innovating than does a ompetitive fim. Why? Monopoly Theatened By Enty Simple setting with two fims. Initially: Fim 1 is a monopolist, podues at maginal ost, and eans pofit m ( ). Fim 2 does not uently podue, but is a potential entant. 3

4 If only one of the fims has the oppotunity to aquie the tehnology to edue maginal ost to, then we have the same situation as befoe: V >V m, so innovation is moe valuable fo the entant than fo the monopolist. Now suppose that a 3 d paty geneates the innovation, and autions it to the two fims. We will see that in this ase, the innovation is moe valuable fo the monopolist than fo the entant. If fim 1 obtains the innovation, then it emains a monopolist, and eans pofit m (). If fim 2 obtains the innovation, then both fims beome duopolists. Denote the pofits of fim 1 and 2 by d (, ) and d (, ), espetively. The value of innovation fo fim 1 is: The value of innovation fo fim 2 is: V m = m () d (, ) V = d (, ) Assume that: m () d (, )+ d (, ). A monopolist eans geate pofit than two non-olluding duopolists. Then: V m >V. (Opposite fom befoe!) Beause ompetition edues pofits, the monopolist s inentive to emain a monopolist is geate than the entant s inentive to beome a duopolist. A monopolist may have inentives to obtain popety ights on an innovation, even though he will make no use of it (often efeed to as patent shelving). The only pupose is to pevent an entant fom ompeting. 4

5 Subjet of many antitust ases; geneally onsideed anti-ompetitive behavio. In many ounties, the patent law inludes a ompulsoy liensing povision (i.e., patent holde is foed to liense if he does not utilize the innovation within a speified length of time). Patent Raes Insofa, we have onsideed 1. the value of innovation in a situation whee one fim has monopoly ove R&D ativities; and 2. the value of innovation when monopoly powe is autioned to a monopolist and a potential entant. In patie, R&D ompetition an be likened to a ae fo a patent. Multiple fims invest in R&D simultaneously, and whiheve fim innovates fist, obtains a patent. We will study the so-alled Poisson patent ae. Initially, thee is a monopolist with ost, and a potential entant. The two fims ompete in R&D ativities, and the fim fist to innovate (i.e., obtain a tehnology with ost ) obtains a patent. At evey moment t, eah fim i invests in R&D at ate x i,t, and its innovation ate is h(x i,t )dt, whee h 0 > 0 >h 00. If fim i invests x i duing (t, t + dt), then it inus ost x i dt and its pobability of innovating is h(x i,t )dt. This is alled a Poisson ae, beause the pobability of innovating duing (t, t + dt) is independent of investments at t 0 <t. It follows that eah fim s investment ate will be independent of t. If fim 1 obtains the patent, then the fims ean pofits m () and 0, espetively. 5

6 If fim 2 obtains the patent, then the fims ean pofits d (, ) and d (, ), espetively. Assume that: m () d (, )+ d (, ). Duing an abitay inteval (t, t + dt), fims 1 and 2 ean pofit [ m ( ) x 2 dt, espetively. x 1 ] dt and With pobability h(x 1 )dt, fim 1 is fist to innovate, and the fims will ean disounted pofits m () x 1 and 0, espetively. With pobability h(x 2 )dt, fim 2 is fist to innovate, and the fims will ean disounted pofits d (,) and d (, ), espetively. With pobability 1 h(x 1 )dt h(x 2 )dt, neithe fim innovates duing (t, t + dt). The value of innovation to fim 1 is apple V 1 = [ m ( ) x 1 ] dt + e dt h(x 1 )dt m () + h(x 2 )dt d (, ) +(1 h(x 1 )dt h(x 2 )dt) V 1 = m ( ) x 1 + h(x 1 ) m () and fo fim 2 + h(x 1 )+h(x 2 ) + h(x 2 ) d (,) apple V 2 = x 2 dt + e dt h(x 2 ) d (, ) +(1 h(x 1 )dt h(x 2 )dt) V 2 = x 2 + h(x 2 ) d (, ) + h(x 1 )+h(x 2 ) Note 1: e dt ' 1 dt fo small dt (Taylo expansion) Note 2: dt 2 ' 0 A Nash equilibium is a pai {x 1,x 2} suh that x i maximizes V i given x i. Whih fim will have stonge inentives to invest in R&D? Depends on whih of two e ets dominates. 1. E ieny e et: m () d (, ) + d (, ) suggests that the monopolist has stonge inentives, and theefoe, spends moe on R&D. 6

7 2. Replaement e et: By ineasing x 1, the monopolist (on expetation) bings the disovey date fowad, thus hastening his own eplaement. In ontast, the entant does not fogo a flow pofit duing the R&D phase, and theefoe has stonge inentives. What if we onside the ase of a dasti innovation? i.e., whiheve fim obtains the patent, beomes a monopolist, so d (, ) = m () and d (, ) =0. Poblems: Exessive dupliation of eseah With multiple stages, as the gap between the fim widens, inentives weaken. Welfae Analysis of Patent Potetion Oveall, eonomi eseah in this aea is still nasent. Main issues: Optimal patent length? Optimal degee of patent potetion? Subsidies? (e.g., in the US, tax edits fo R&D investments) An example fom United States vs. Miosoft Cop: Miosoft was aused of beoming a monopoly and engaging in abusive paties, in violation of the Sheman At. Cental Issue: Whethe Miosoft was allowed to bundle its web bowse (IE) with Windows. Allegedly, this estited the maket fo ompeting web bowses. Miosoft s agument: While it possesses a lot of stati maket powe, this is meely the fuel fo stimulating dynami R&D ompetition. Antitust intevention would un the isk of eduing the ate of innovation and welfae. 7

8 Govenment s agument: Miosoft s paties pevented enty of new fims and poduts, thus aising pies and etading innovation. Key tade-o : Poliies that potet new entants (e.g., stat-up) fom inumbents (e.g., Miosoft) aise a suessful innovato s initial pofits, and may theeby enouage innovation. But entants hope to beome the next Miosoft, and will want to engage in simila enty-disadvantaging behavios should they sueed. Thus by loweing the pofits of inumbeny, potetive poliies may atually etad innovation. Di ult poblem to analyze, beause it is inheently dynami. Need a model of suessive patent aes. See Segal and Whinston, (AER, 2007). Altenatives to Patents Patents inentivize R&D investments by onfeing monopoly ights to an innovato. Can we (somehow) avoid the deadweight losses assoiated with monopoly? Yes: 1. Awad system 2. Pouement o ontatual mehanism Awad system: An entity (e.g., govenment o a fim) designates a (well-defined) pojet, and gants a fixed sum of money to the fist fim that ompletes the pojet. Afte the pize is awaded, the innovation falls into the publi domain. Examples: XPize, Innoentive, et... Advantage: Does not podue a monopoly! Disadvantage: Di ult to implement! 8

9 Unlike with patents, the govenment must be highly knowledgeable about the demand fo the pojet, whih is uial fo detemining the size of the awad, whih in tun, influenes R&D inentives. In patie, the size of the awad will often be detemined afte the innovation has oued, whih aises hold-up issues. Administative authoities typially estimate the values of innovations onsevatively. Pouement o ontatual mehanism: Simila to the awad system, but the govenment ontols aess to the eseah maket. i.e., hooses a etain numbe of fims and signs a ontat with them. Contat may speify that etain potion of the R&D osts will be bone by the govenment. Raises inentives poblems. Can limit dupliation of eseah. As with the awad system, the govenment must know the value of the innovation. Often used in onnetion with spae and defense pojets. Refeenes Segal I. and Whinston M.D., (2007), Antitust in Innovative Industies, Ameian Eonomi Review, 97(5), Tiole J., (1988), The Theoy of Industial Oganization, MITPess. 9