Research and Development

Transcription

1 Chapter 9. March 7, 2011

2 Firms spend substantial amounts on. For instance ( expenditure to output sales): aerospace (23%), o ce machines and computers (18%), electronics (10%) and drugs (9%). is classi ed into two types Process innovation Product innovation

3 Classi cations of Process Innovation Magnitude of the cost reduction generated by the process Consider an industry producing an homogeneous product and Bertrand competition Initially all rms possess identical technology (c o > 0) Suppose only one rm has invested in : c < c o

4 Classi cations of Process Innovation Proposition 9.1: Let p m (c) denote the price that would be charged by a monopoly rm whose unit production cost is given by c. then. Innovation is large if p m (c) < c o and it is small if p m (c) > c o

5 Innovation Race Two reasons explaining why a rm that is the rst to discover a new technology gains an advantage over competing rms: 1 The rm is eligible to obtain a patent protection (monopoly pro ts) 2 Consumers associate the innovator with a higher-quality producer (higher prices) Do rms invest in more or less than the socially optimal level? Consider a two- rm industry searching for a new technology The discovery is uncertain The payo from is as follows Firms have a probability α of discovering a technology that yield a pro t of $V (if the rm is sole) if both rms discover the $ V 2 If it does not discover $0

6 Equilibrium in a race Denote E π k (n) the expected pro t of rm k from investing in, where n is the total number of rms n = 2 i k is the investment in expenditure of rm k A single rm undertaking : E π 1 (1) = α (V I ) + (1 α)(0 I ) = αv I Hence equating E π 1 (1) = 0, the investment decision of rm 1 is: I if αv I i 1 = 0 otherwise

7 Equilibrium in a race Two rms undertake : technology uncertainty and market uncertainty E π k (2) = α (1 α) V + α 2 ( V 2 ) I Hence equating E π k (2) =, the investment decision of each rm k is: i 1 = i 2 = I, if α(2 α)v 2 I

8 Equilibrium in a race

9 Society s optimal level From a social welfare point of view increasing n increases α but also increases the industry s aggregate cost Denote E π S (n) the industry s expected pro t when n rms undertake Only one rm: E π S (1) = αv I = E π 1 (1) Two rms: E π S (2) = 2α (1 α) V + α 2 (V ) 2I Comparing E π S (1) with E π S (2) : E π S (2) E π S (1) if and only if α (1 α) V I

10 Cooperation in The antitrust legislation prohibits rms from reducing competition and increasing prices. However the antitrust legislation is less clear about cases where establish research joint ventures (RJV) assume a two-stage game in t = 1 rms determine how much to invest (1st noncooperatively and then cooperatively) in cost-reducing in t = 2 rms are engaged in a Cournot quantity game in a market for a homogeneous products Demand: p = 100 Q x i is the amount of undertaken by rm i = 1, 2

11 The process-innovation technology c i (x 1, x 2 ) 50 x i βx j, i 6= j is the unit production cost by rm i if β > 0 them technologies exhibits positive spillover e ects. is costly, that is, TC i (x i ) = (x i ) 2 2 [Research labs operate under decreasing returns to scale]

12 Noncooperative We look for the subgame perfect equilibrium Second Period: Cournot competition where π i (c 1, c 2 )j t=2 = (a 2c i +c 2 ) 2 (N +1) 2 b = (100 2c i +c 2 ) 2 9 The First Period: each noncooperatively chooses its level of max x i π i = 1 9 [100 2 (50 x i βx j ) + 50 x j βx i ] 2 (x i ) 2 2 = 1 9 [(2 β) x i + (2β 1) x j ] 2 (x i ) 2 Solve the FOC w.r.t x i Given that the payo functions are symmetric between the two rms we look for a symmetric NE where x 1 = x 2 x NC x NC = 50(2 β) 4.5 (2 β)(1 + β) 2

13 Cooperative Firms jointly choose R%D levels that will maximize their joint pro ts, knowing that in t = 2 they will compete in quantities max (π 1 + π 2 ) x 1,x 2 0 = (π 1 + π 2 ) x i = π i x i + π j x i 0 = 2 9 [(2 β) x i + (2β 1) x j ] (2 β) x i + where x c 1 = x c 2 = x c = 2 9 [(2 β) x j + (2β 1) x i ] (2β 1) 50(β+1) 4.5 (β+1) 2

14 Cooperative Proposition 9.2: Cooperation in increases rm s pro ts If the spillover e ect is large, then cooperative levels are higher than the noncooperative levels. x c > x NC If the spillover e ect is small, then cooperative levels are lower than the noncooperative levels. x c < x NC