Answer Happy

Problem 2. (Product) Innovation Race (2 points] The value of a patent on discovered, developed and successfully clinically tested vaccine for SARS-CoV-2 (strain of the virus causing the coronavirus disease 2019, aka COVID-19) is 150 million dollars (V = $150). Three firms, let's call them firm 1, firm 2 and firm 3, try to attain the patent that would allow them to meet the increased demand for such a vaccine in the context of the currently spread COVID-19 pandemia. The gain would depend on the number of firms that succeed to discover the vaccine and patent it: . If only 1 firm discovers the vaccine, it will gain the whole value of the patent, V(1) = $150 • If 2 firms manage to attain a patent, they will split the gain by half, V(2) = $75 • If all the three firms attain the patent, the value is split equally among the three, V(3) = $50 If firms are private, i.e. investing separatly and independently in R&D, and each faces a chance p = to discover the vaccine, if investing 1 = $40 and zero chance to discover, otherwise (a) Compute the expected profit of firm 1 if it is the only investing in R&D. (1) Compute the expected profit of firm 1, if both firm 1 and firm 2 are investing. (c) Compute the expected profit of firm 1, if all the three firms are investing (d) How many firms would invest in R&D at equilibrium? (e) Compute the social welfare of having 1, 2 or 3 firms investing. What is the socially optimal number of firms investing? Do the results imply market failure?