1. Lecture 7:Research and Development Cooperative and Nonccoperative R&D in Duopoly with Spillovers d’Aspremont and Jacquemin, 1988, American Economic Review, 78: 1133-1137. (simplified version: Shy, section 9.3, 229-233.) Regulatory policy typically prohibits cooperation among firms (due to concerns that such cooperation will raise prices, limit entry, etc.) This prohibition includes cooperation on R&D as well. When there are spillovers in R&D, cooperation may actually enhance consumer welfare by restoring research incentives. 1984 U.S. - National Cooperative Research Act (NCRA) – research joint ventures (RJVs) subject to “rule of reason” Model in d’Aspremont and Jacquemin addresses this issue

2. Framework Stage 1: Firms decide how much to invest in research and development Stage 2: Firms compete in quantities (Cournot competition) Stage 2 is always non-cooperative, that is firms compete. The paper compares two possible regimes in stage 1: (I)non-cooperative interaction (i.e., no cooperation in R&D) (II)Cooperation at the R&D stage Stage 2Stage 1 (R&D) Cournot Competition Competition in R&D Regime I Cournot Competition Cooperation in R&D Regime II

3. The Model Demand Function: P(Q)=a-bQ x 1 = R&D progress of firm 1, x 2 = R&D progress of firm 2 K 1 =  x 1 2 /2 -- Cost of R&D to firm 1 (similar for firm 2) Marginal Cost of production for firm 1 c 1 (x 1, x 2 ) = (A – x 1 –  x 2 ) 0<  <1 is the spillover parameter; Some of the benefits from firm 2’s research spills over to firm 1 (and vice versa). Technical Assumptions: 0 a, there will be no market without R&D) x 1 +  x 2  A (otherwise MC can be negative) -- endogenous Q  a/b (otherwise price will be negative) -- endogenous

4. Solving the Model By backwards induction – begin with the second stage In both regimes, there is Cournot competition in the 2 nd stage. Given (x 1, x 2 ) from the first stage, we can write down the second stage profits for the firms:  1 = (a-bQ)q 1 - c 1 q 1, where c 1 =A – x 1 –  x 2.  2 = (a-bQ)q 2 - c 2 q 2, where c 2 =A – x 2 –  x 1. We know how to solve Cournot models: Solution is q 1 *= (a+c 2 -2c 1 )/3b, q 2 *= (a+c 1 -2c 2 )/3b. Hence Q*= q 1 *+q 2 *=(2[a-A] + [  +1][x 1 +x 2 ])/3b. Since x 1 +  x 2  A & x 2 +  x 1  A, [  +1][x 1 +x 2 ])<2A & Q<2a/3b.

5. Solving the Model (Continued) First Stage: (Regime 1) no cooperation  1 = (a-bQ*)q 1 * – [A – x 1 –  x 2 ] q 1 *–  x 1 2 /2.  2 = (a-bQ*)q 2 * – [A – x 2 –  x 1 ] q 2 *–  x 2 2 /2. Substituting for q 1 * & q 2 * yields:  1 = ( [a-A]+ [2-  ]x 1 +[2  -1]x 2 ) 2 /9b –  x 1 2 /2. FOC: 2( [a-A]+ [2-  ]x 1 +[2  -1]x 2 )(2-  ) /9b –  x 1 =0. SOC: 2(2-  ) 2 /9b –  (<0 so SOC hold) Solution: x 1 *= x 2 *=x* = (a-A)(2-  )/(4.5b  –[2-  ][  +1])

6. Solving the Model (Continued) First Stage: (Regime 2) cooperation Second stage is still the same: q 1 ^= (a+c 2 -2c 1 )/3b, q 2 ^= (a+c 1 -2c 2 )/3b. Here the firms jointly choose x 1 & x 2 to maximize  1 +  2 Π =  1 +  2 =(a-bQ^)q 1 ^ – [A – x 1 –  x 2 ] q 1 ^–  x 1 2 /2+ (a-bQ^)q 2 ^ – [A – x 2 –  x 1 ] q 2 ^–  x 2 2 /2. Substituting for q 1 ^ & q 2 ^, and maximizing yields: x 1 ^= x 2 ^=x^ = (a-A)(  +1)/(4.5b  –[2-  ][  +1])

7. Comparing the Outcomes When  =1/2, the investments in R&D are the same under both regimes (x* = x^) and hence the output is the same (q* = q^); consumer surplus is the same. When  <1/2, so that spillovers are relatively small, both the investment and output in the “R&D cooperation regime” are less than in the “R&D competition regime”, (i.e., x^ < x*and q^ < q*); This means a higher price for consumers & lower consumer surplus in “R&D cooperation regime.” (standard result…) When  >1/2, so that spillovers are relatively large, both the investment and output in the “R&D cooperation regime” are greater than in the “R&D competition regime”, (i.e., x^ > x*and q^ > q*); This means a lower price for consumers & higher consumer surplus in “R&D cooperation regime.”

8. Understanding the Intuition Behind the Results Look at the second stage: q 2 *= (a+c 1 -2c 2 )/3b. = ([a-A]+[2  -1]x 1 +[2-  ]x 2 )/3b.  q 2 */  x 1 = [2  -1]. When  >1/2, an increase in the investment of firm 1 leads to increased production for firm 2. Hence when  >1/2, sign “d  1 /dq 2 =[  1 /  q 2 ][  q 2 */  x 1 ]” is “-”. This leads to “under-investment” in a duopoly without cooperation when spillovers are large. Investment incentives can be restored by allowing firms to cooperate. Public Policy Implications: when  >1/2, allowing cooperative R&D is unambiguously welfare enhancing.

9. Taxonomy of Business Strategies d  1 /dx 1 =   1 /  x 1 + [   1 /  q 1 ][  q 1 */  x 1 ] + [   1 /  q 2 ][  q 2 */  x 1 ] First Term= Direct Effect Second term=0 (Envelope Theorem) Third Term=Strategic Effect When sign of strategic effect is negative: underinvestment. (D&J model  >1/2) When sign of strategic effect is positive: overinvestment (D&J model  <1/2). Example: First Entry model we looked at in lecture 5:  1 = (1-K 1 -K 2 ) K 1, Since q 1 =K 1, q 2 =K 2,   1 /  q 2 =-K 1 Since q 2 *=K 2 * =(1-K 1 )/2,  q 2 */  x 1 =-1/2. sign of strategic effect: [   1 /  q 2 ] [  q 2 */  x 1 ] is positive: Hence, overinvestment (relative to Cournot model)