5. Solve for both hospitals quantity of patients served, the equilibrium price, and profit for both firms when the SPNE is played . 6. What is total surplus (Consumer surplus + Profit )? 7. Suppose after State makes their choice of quantity of patients, University is able to react and easily expand or contract their service . What is the outcome of this model and why is it different from above ? (No need to solve the model , just intuitively explain what will happen and why). Problem 7 (This problem is NOT to be handed in ). Incor is currently the only sup- plier of widgets and earns monopoly rents of $700k . Enterprise is considering entering the market. It would cost Enterprise $100k to set up a factory. However, Incor has threatened to start a price war if Enterprise enters. Your research shows that if Incor follows though on its threat , Incor would earn only $100k from producing widgets while Enterprise would earn only $25k (before accounting for building costs). How- ever, if Incor does not start the price war, it would make $300k, while Enterprise would earn $200k. 1. Draw this game in extensive form . Be sure to fully label the game tree . 2. What is the subgame perfect equilibrium outcome ? 3. Would you advise Enterprise to build the widget factory? Problem 8 (This problem is NOT to be handed in). Assume two firms compete in Cournot competition , but compete for an infinite amount of time . The one -shot payoffs are listed below and the discount rate iso = .8. We'll focus on three different choices for quantities to produce. Call the "collusive quantity" for firm i of and the "competitive" quantity q. The competitive quantity strategies are a Nash equilibrium of the stage -game . A deviation occurs when a firm agrees to produce of but instead produces 45, which is i's best response to q", in the stage game . Call the collusive profits 15, and the competitive profits . If one firm deviates , it receives ad for this period , while its opponent receives and