1. Slides Industrial Organization: Markets and Strategies Paul Belleflamme and Martin Peitz © Cambridge University Press 2009 R&D and intellectual property Part VII. R&D and intellectual property Innovation and R&D Chapter 18. Innovation and R&D MATH SLIDES

2. © Cambridge University Press 2010 2 Asymmetric patent races Model Innovation  marginal cost from c 0 to c 1 < c 0 Profits (per unit of time; time is continuous) When innovation affects market structure Chapter 18M - When innovation affects market structure

3. © Cambridge University Press 2010 3 Asymmetric patent races (cont’d) Model (cont’d) At each point in time, firm k spends x k on R&D k = I (incumbent) or E (entrant)  Determines firm’s probability of success: h(x) With h(0) = 0, h’ > 0, h” < 0 lim x  h’(x) = 0, lim x  0 h’(x) =  Stochastic process of Poisson type  memoryless  time has no effect At each date t, if neither firm has made a discovery, the game starting at this moment is identical to the initial game. Equilibrium strategies are constant over time. When innovation affects market structure Chapter 18M - When innovation affects market structure

4. © Cambridge University Press 2010 4 Asymmetric patent races (cont’d) Probability no firm makes a discovery before t Assume race starts at date 0 and use Poisson process   (x k ): date of success given R&D expenditure x k Probability that no firm succeeded at date t We can compute the PDV of the expected profit over time for the 2 firms: V I (x I,x E ) and V E (x I,x E ) When innovation affects market structure Chapter 18M - When innovation affects market structure

5. © Cambridge University Press 2010 5 Asymmetric patent races (cont’d) PDV of expected profits over time Nash equilibrium When innovation affects market structure Chapter 18M - When innovation affects market structure No innovation Incumbent is 1 st to innovate Entrant is 1 st to innovate Discounted to t

6. © Cambridge University Press 2010 6 Asymmetric patent races (cont’d) Equilibrium depends on balance between Efficiency effect Efficiency effect  higher incentives for incumbent Net flow profit incumbent receives by preempting the entrant is larger than what the entrant gains by being first. Replacement effect Replacement effect  lower incentives for incumbent The marginal productivity of R&D expenditure for the incumbent decreases with its initial profits. Intuition: x I   incumbent moves discovery date forward  hastens its own replacement When innovation affects market structure Chapter 18M - When innovation affects market structure

7. © Cambridge University Press 2010 7 Asymmetric patent races (cont’d) Net effect is not clear, except for extremes Minor innovation + h(x) almost linear Efficiency effect dominates R&D is high, discovery is made early. Incumbent concerned with possible innovation by entrant Replacement effect not important Major innovation Replacement effect dominates If entrant discovers major innovation, it becomes a de facto monopolist. Efficiency effect disappears. creative destruction Schumpeter’s concept of creative destruction. When innovation affects market structure Chapter 18M - When innovation affects market structure