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Lecture 7: Research and Development Cooperative and Nonccoperative R&D in Duopoly with Spillovers

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.)

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Lecture 7: Research and Development Cooperative and Nonccoperative R&D in Duopoly with Spillovers

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  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: • non-cooperative interaction (i.e., no cooperation in R&D) • Cooperation at the R&D stage

  3. The Model • Demand Function: P(Q)=a-bQ • x1 = R&D progress of firm 1, x2 = R&D progress of firm 2 • K1=x12/2 -- Cost of R&D to firm 1 (similar for firm 2) • Marginal Cost of production for firm 1 c1(x1, x2) = (A – x1 – x2) • 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<a (If A>a, there will be no market without R&D) • x1+ x2 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 2nd stage. Given (x1, x2) from the first stage, we can write down the second stage profits for the firms: 1= (a-bQ)q1 - c1q1, where c1 =A – x1 – x2. 2= (a-bQ)q2 - c2q2, where c2 =A – x2 – x1. We know how to solve Cournot models: Solution is q1*= (a+c2-2c1)/3b, q2*= (a+c1-2c2)/3b. Hence Q*= q1*+q2*=(2[a-A] + [+1][x1+x2])/3b. Since x1+ x2 A & x2+ x1 A, [+1][x1+x2])<2A & Q<2a/3b.

  5. Solving the Model (Continued) First Stage: (Regime 1) no cooperation 1= (a-bQ*)q1* – [A – x1 – x2] q1*– x12/2. 2= (a-bQ*)q2* – [A – x2 – x1] q2*– x22/2. Substituting for q1* & q2* yields: 1= ( [a-A]+ [2- ]x1 +[2-1]x2 )2 /9b – x12/2. FOC: 2( [a-A]+ [2- ]x1 +[2-1]x2 )(2- ) /9b – x1=0. SOC: 2(2- )2/9b –  (<0 so SOC hold) Solution: x1*= x2*=x* = (a-A)(2- )/(4.5b–[2- ][+1])

  6. Solving the Model (Continued) First Stage: (Regime 2) cooperation Second stage is still the same: q1^= (a+c2-2c1)/3b, q2^= (a+c1-2c2)/3b. Here the firms jointly choose x1 & x2 to maximize 1+ 2 Π= 1+ 2 = (a-bQ^)q1^ – [A – x1 – x2] q1^– x12/2+ (a-bQ^)q2^ – [A – x2 – x1] q2^– x22/2. Substituting for q1^ & q2^ , and maximizing yields: x1^= x2^=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: • q2*= (a+c1-2c2)/3b. = ([a-A]+[2-1]x1+[2-]x2)/3b. • q2*/  x1= [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 of [1/q2][ q2*/  x1]” 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/dx1 =  1/x1+[ 1/q1][ q1*/ x1]+ [ 1/q2][ q2*/  x1] • First Term= Direct Effect • Second term=Own Effect (positive) • 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-K1-K2) K1 , Since q1=K1 , q2=K2,  1/q2=-K1 Since q2*=K2* =(1-K1)/2,  q2*/  x1=-1/2. sign of strategic effect: [ 1/q2] [ q2*/ x1] is positive: Hence, overinvestment (relative to Cournot model)

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