Question 3 please

Problem 3: Strategic Competition In year 2040, there is a potential for creating an industry for flying cars. Flying cars can be produced in two different varieties: a modern design version (MD) or a generic luxury version (GL). Market research indicates that there are 200,000 potential customers and they are equally divided among two types which we call classical (C) and modern (M). Customers are willing to buy at most one flying car. The reservation price (maximum price a consumer is willing to pay) for one car of each variety for each customer type is in the table below: Varieties GL MD C 800 600 Types M 800 1, 000 There are two firms that have the technological know how for producing the flying cars: Permari and Forsche. An up-front investment of 10m enables these firms to produce any quantity of the GL-variety. An additional up-front investment of 25m enables the firms to also produce any quantity of the MD- variety. Thus, to reiterate, if a firm makes an up-front investment of 35m it is able to produce any quantity of GL and MD flying cars. For sake of simplicity the unit (variable) cost of production is zero. Customer payoffs are equal to their reservation price minus the price that they pay if they buy one flying car (of any variety) and they are zero otherwise. Thus, for instance, a consumer of type C that buys an MD-flying car at price p(MD) has a payoff equal to 600-p(MD). Firm's payoffs are equal to revenues minus the cost of the up-front investments they have undertaken. Firms post prices and if some prices are below reservation consumers buy in order to maximize their payoffs. Firms share the market demand equally when they post identical prices for some variety. 1) (Monopoly) Forsch has announced that it will not be producing flying cars, while Pervari will. The interaction between Perrari and customers unfolds as follows: . First, Perrari decides whether to make the up-front investment for the production of GL-variety only, or for both the GL and MD varieties. . Second, Permari posts the prices of the different varieties that it can pro- duce. . Third, customers observe posted prices and decide which variety to buy, if any, and Perrari produces the demanded quantities. How many varieties is Perrari going to produce? What prices is Perrari going to charge? Which variety of flying cars will the customers of each type demand? What are the payoffs of Perrari and of the customers? 2) (Strategic Competition) Suppose that both Perrari and Forsche de- cide to produce flying cars. The industry interaction unfolds as described below: . First, the two companies choose simultaneously whether to make the up- front investment for the production of GL-variety only, or for both the GL and MD varieties. . Second, after having observed up-front investment choices of the competi- tors, the two firms post simultaneously the prices for the varieties that they can produce. . Third, customers observe the prices posted by the firms and decide which variety to buy from what firm, if any. The firms produce the demanded quantities. Find the Nash equilibria of this interaction: what varieties are supplied by the two firms? At what prices? What do each of the two types of customers demand? What are the (Nash equilibrium ) payoffs of the two firms and of the customers of different types? 3) (Entry decisions) Suppose that both firms choose simultaneously whether to enter the flying car industry by deciding whether to start the production of flying cars or not. If they do not, both firms payoffs are zero. If they both do, firms' payoffs are those you found in your answer to question 2. If just one firm starts production it is a monopolist and its payoffs are those that you found in your answer to question 1, while the payoffs for the firm that stays out are J. Given your answers to questions 1) and 2), what do you think will happen to the flying car industry? Will both firms start production? Will only one start production? None? Will firms be necessarily "predictable" in their entry decisions