1.2 Complications Note that(r&D, R&D) may be a Nash equilibrium, but it will not necessarily be a Pareto optimum from the firms' perspective if the sum of profits under this equilibrium is less than the sum of profits under a(r&D, no R&D)or(no R&D, R&D)combination. This will be the case if 2pM(1-。0)-2K<M-KK>pM(1 nd combining this with the fact that(R&D, R&D)is a Nash equilibrium oM(1-P)>K>pM(1 10 Hence the above condition gives us the case where both firms doing R&D is a Nash equilibrium which is not Pareto optimal from the firms' point of view, in the sense that firms would be jointly better off with only one of the two firms having an R&D Ia 3 Consumer surplus In the case of monopoly consumer surplus is equal to (a-)(2M phile in the Cournot case it is equal to (a-"2)(号) CSc=2 4M 8M The expected social surplus ignoring the R&d costs if only one firm, say a established an R&d lab is equal to E(TA R&DA>0, R&DB=0)+E(TB R&DA>0, R&DB=0)+PCS M+0+p-==pM The expected social surplus ignoring the r&d costs if both firms set up an R&D lab are E(TA R&DA>0, R&DB >0)+E(TB R&DA>0, R&DB>0) CSc +2p(1-p)SM