Research and Development Part 2: Competition and R&D

R&D as a Race n If firms can patent a new process or product, R&D can be seen as a “winner-take- all” race. u Coming in first is all that matters, not how much you win by. n What are the consequences of such races in terms of the level of R&D and thus innovation? n How does market structure affect the race?

Patent Race Model n Assume there are two firms that are potential entrants in a race to develop the cure for cancer. n The R&D effort will require the firm to set up a special research unit at a cost of K which is non-recoverable. n The probability of discovering a cure within a year if the research unit is established is .

Patent Race Model, con’t n If both firms discover the cure this year, assume that they will split the market as Cournot competitors and each get  C. n If only one firm discovers the cure, it will get monopoly profits of  M.

Patent Race Model, con’t n If only one firm innovates, that firm’s expected profit is   M - K. n If both firms innovate, each firm’s expected profit is:  (1-  )  M +  2  C + (1-  )0 - K. n If a firm does not innovate, its profit is 0.

The Patent Race as a Game So what is the NE of this game?

For No R&D for either firm to be a NE:   M - K < 0 or (rewritten)  < K/  M, which means that the probability of discovering the cure is relatively unlikely.

For R&D for one firm but not the other firm to be a NE:   M - K > 0 or (rewritten)  > K/  M and  (1-  )  M +  2  C -K < 0.

For R&D for both firms to be a NE:  (1-  )  M +  2  C -K > 0.

We can graph the relationship between  and K/  M to show how these variable affect the amount of R&D. K/  M  K/  M =  No R&D  (1-  )  M +  2  C = K One Firm Does R&D Two Firms Do R&D

Optimality of R&D Investment n There will be no R&D in this model if  <K/  M. n If  >K/(  M +  consumer surplus), then R&D by one firm would be socially optimal, so there is too little R&D investment.

Optimality of R&D Investment, con’t n Both firms will undertake R&D if  (1-  )  M +  2  C -K > 0. n But this may be too much R&D u This occurs when the joint profit from both firms investing is less than that if only one invests: u 2[  (1-  )  M +  2  C -K] <  M -K or (rewritten) u  (1-2  )  M +2  2  C < K.

K/  M  K/  M =  No R&D  (1-  )  M +  2  C = K One Firm Does R&D Two Firms Do R&D Too much investment Too little investment Optimal investment K/(  M +CS) =   (1-2  )  M +2  2  C = K

Risk and Patent Races n Patent races can encourage firms to undertake “risky” strategies. n Assume firms have two R&D options: u “Safe” option: Invest $100 million in “durable” equipment. Probability of discovery is 33% each year. u “Risky” option: Invest $100 million in “perishable” equipment. Probability of discovery is 75% this year, 0% in the future.

Risk and Patent Races, con’t n Assume that everything else is the same for the two scenarios: benefit from innovation (B), costs of production, etc. n Further, for computational simplicity assume that this discount rate is 0.9 (which corresponds with an interest rate of 10%). n Then we can compare the expected value of the two options.

Risk and Patent Races, con’t n If only one firm invests in R&D: u Expected Value of the “safe” strategy is: 1/3B+ 2/3*1/3*0.9B+ (2/3) 2 *1/3*0.9 2 B+… =B*1/3[1/(1-2/3*0.9)] = B*5/6 u Expected Value of the “risky” strategy is: 3/4B+ 0 = B*3/4 u So the “safe” strategy is better if only one firm invests.

Risk and Patent Races, con’t n If both firms invest in R&D, the firm must win the race to get the benefit: u Both firms using the “safe” strategy has the highest value of actually getting the innovation and is socially optimal. u Each period, 1/3*1/3 chance both discover, 1/3*2/3 chance firm 1 discovers not firm 2, 1/3*2/3 chance firm 2 discovers not firm 1, 2/3*2/3 chance no one discovers. 5/9*B 1 + 4/9*5/9*0.9B+ (4/9) 2 *5/9*0.9 2 B+… =B*5/9[1/(1-4/9*0.9)] = B*25/27

Risk and Patent Races, con’t n If both use safe strategy there is a 50% chance that firm 1 innovates first and a 50% chance firm 2 innovates first. n If firm 2 uses safe strategy, firm 1 can improve chance by using risky strategy: u 3/4*2/3 firm 1 discovers not firm 2, 3/4*1/3 both discover. Assume tie breaker is both discover: u 3/4*2/3 +3/4*1/3*1/2 = 5/8>1/2 u So the risky strategy is dominant.

Monopoly and Sleeping Patents n A sleeping patent is a patent on a product or process that is not being used. n Why would firms keep sleeping patents? u Keep others from inventing around a patent. u Keep others from adopting the technology. Can be profitable to patent technology so potential entrants cannot use it even if you have a superior technology. F Potential entrants will have to invest in R&D to discover their own technology.

Patent Licensing n Allows others to use a patented process or sell a patented product for a fee. u Similar to trademark and copyright licensing. n Moves society away from a monopoly, so positive in terms of social welfare. n When will a firm license its technology? u Increases profits through the payment of royalties. u Decreases profits through increased competition (“cannibalization” of demand).

Patent Licensing, con‘t n Ideal situation is to license in markets in which you don’t currently compete (perhaps geographically separate markets). u Potential drawback: gives other firms more experience with process/product which many help them develop their own innovations. n In a Bertrand market licensing is generally not profitable. u Increase profits from royalties is less than the decreased profit from competition.

Patent Licensing, con‘t n Example: 2 firms, Firm A has MC=$15, Firm B has patented technology with MC=$12. n Without licensing: u Firm B prices at $14.99 and sells to whole market. Profit = $2.99 per unit. n With licensing: u The maximum royalty Firm B can charge Firm A is $2.99. At this royalty level, both firms price at $14.99 and split the market. Firm b continues to make Profit = $2.99 on each unit sold. No improvement in profit.

Patent Licensing, con‘t n In a Cournot market, licensing can be profitable, however. n Assume P = Q. As before Firm A has MC=$15, Firm B has patented technology with MC=$12. n In a Cournot market with different MCs: u q 1 = (a + c 1 - 2c 2 )/3b;  1 = (a + c 1 - 2c 2 ) 2 /9b

Patent Licensing, con‘t n Without licensing: u q B = ( )/3 = 91/3 u  B = ( ) 2 /9 = 8281/9  920. n With licensing: u B licenses to A for $3 and decreases quantity produced to 85/3. At this quantity, A’s best response is also 85/3. Market price will be $ u On each unit B produces, B earns $ On each unit A produces, B earns $3. u  B = $31.33*85/3+ $3*85/3  973.

R&D and Spillovers n R&D spillovers: My R&D directly benefits me and indirectly benefits you, i.e. there is a positive externality. n How do the existence of spillovers affect the incentives for R&D? n What are the impact of spillovers on the economy? n Should we encourage joint R&D?

R&D and Spillovers, con’t n Let X be the R&D level of a firm. n Assume that c 1 = c - X 1 -  X 2. u If  = 1, “perfect spillovers” i.e. there is no way to patent any new innovations. u If  = 0, no spillovers. n Assume that research exhibits diseconomies of scale, i.e. diminishing returns to R&D spending. For example, let the cost of R&D = X 2 /2.

R&D and Spillovers, con’t n For simplicity, assume that the market is a Cournot duopoly with demand P = a-bQ. n If firms do not cooperate on R&D: u q 1 = (a-2c 1 + c 2 )/3b u  1 = (a-2c 1 + c 2 )2/ 9b - X 1 2 /2 n Since c 1 = c - X 1 -  X 2 : u q 1 = (a-c + X 1 (2-  ) + X 2 (2  -1))/3b u  1 = (a-c + X 1 (2-  ) + X 2 (2  -1)) 2/ 9b - X 1 2 /2 n q 1 and  1 are increasing in X 1, and increasing in X 2 if  > 0.5.

R&D and Spillovers, con’t n The other firm’s R&D benefits you by decreasing your costs, however, since it decreases the other firm’s costs by a larger amount it also increases competition. n When  is low, the spillover is small. u An increase in X by one firm causes the other firm to decrease X. n When  is high, the spillover is large. u An increase in X by one firm causes the other firm to increase X.

When  is low, R&D levels are strategic substitutes. An increase in the other firms’ R&D makes their costs decrease significantly compared to yours, increasing competition and decreasing your profits, so you cut back on your own R&D. BR 1 X2X2 X1X1 BR 2

When  is high, R&D levels are strategic complements. An increase in the other firms’ R&D makes their costs decrease but not that much more than yours, so overall your profits also increase, so you can increase your R&D level. BR 1 X2X2 X1X1 BR 2

R&D and Spillovers, con’t n If firms cooperate on R&D to maximize joint profits, but continue to compete in the output market: u If  is low, joint R&D will be low. u If  is high, joint R&D will be high, since there is a higher benefit relative to cost.