Microeconomics q3

Question 3 Devlin-McGregor is contemplating an R&D investment in a new anticoagulant (blood thinner) with revolutionary new properties to be called Provasic. Provasic's marginal cost of production is a constant zero dollars per unit. It is not possible to secure patent protection for Provasic and once developed by Devlin-McGregor, it can easily be reverse engineered by their competitor Gen-Sys. Devlin-McGregor's R&D costs are 0.2. The cost to Gen-Sys of reverse engineering Provasic is 0.1, i.e., less than Devlin-McGregor's R&D costs. Here is the way the rivalry between Devlin-McGregor and Gen-Sys will unfold. . Devlin-McGregor decides whether or not to invest in R&D and incur the cost of 0.2. If not, the game ends. . If Devlin-McGregor invests in R&D, it produces an initial run of q1 units of Provasic. . Before Devlin-McGregor's output hits the market, Gen-Sys will decide whether or not to enter the market. If it does, it incurs the reverse engineering cost of 0.1 and chooses an output level of q2. . Provasic arrives on the market and its price is determined by the inverse demand curve p = 2(1 - q), where q is the total quantity of Provasic on the market. 1. Assuming Gen-Sys enters, what quantity (as a function of q1 ) should it choose to maximize its profit? 2. Assuming Gen-Sys enters, what is its profit as a function of q1? 3. If Devlin-McGregor chooses q1 > 1 - v0.2 will Gen-Sys enter? 4. Suppose Gen-Sys will not enter unless it can make a strictly positive profit. Should Devlin- McGregor invest in the R&D to produce Provasic, if so, how much should they produce to maximize their profit? 5. If Devlin-McGregor were granted patent protection, then, Gen-Sys would not be permitted to enter the market. Would consumer's be better off if Devlin-McGregor were granted patent protection