In a market we have the following demand in a certain period: X = 250 P Where P is the price and then X is the quantity. At present there is only one producer, called OLD, in this market. The cost of production is 40 per unit, and the established firm has no additional costs (its entry cost is sunk, and then irreversible). a) Find the optimal price for OLD A new firm, called NEW, is considering to enter this market. It is selling an identical product to OLD, has the same cost per unit as OLD. In addition, it has an entry cost. b) Explain in words why the nature of competition after entry can be decisive for whether it is profitable to enter or not (hint: Cournot vs Bertrand competition) Let us now assume that if entry then those two firms compete a la Cournot, and only in one period. The entry cost is 50, and this is a cost that firm NEW must incur before it enters the market and that is sunk (irreversible). c) Draw the game on extensive form d) Find the optimal choices for firm NEW, both its entry or not in period 1 and quantity sold in period 2 if entry (Hint: Find Subgame Perfect Nash Equilibrium of the game using backward induction) However, firm NEW realizes that if entry, they can be active forever in this market. They expect to compete a la Cournot if competition in each period. However, NEW states the following to a newspaper (which is public information that firm OLD also read): We think it is important for the consumers with a choice. At the same time, the prices must be sustainable in the long run. Our strategy is to set the same price as OLD are offering today when we enter the market, so that we serve half the market each. But if OLD decides to kill the market by lowering price (by selling a large quantity), then we will of course also start competing in the market. But then we must all expect to compete for infinity, which is not good for our business. Assume that the demand in each period is the one shown above, and that the actual discount factor is equal to 0.95 for both firms. Firm OLD had in the previous period sold a quantity such that the price is the one you calculated in a). e) If you were firm OLD, how much would you then sell in this period, the period NEW enters the market? (Hint: Assume that NEW has already paid the entry costs and OLD expect them to follow the strategy outlined above) However, it turns out that NEW had not yet made the entry decision. So OLD is still alone in the market until NEW eventually enters. Then OLD is considering to make an investment in new technology that lowers its marginal costs to zero. It can make such a sunk investment prior to NEWs decision to enter or not. f) Discuss in words and with graphs how such an investment will affect the equilibrium outcome in the market if they compete a la Cournot. Explain why it will make entry less profitable g) Calculate the competitive outcome if OLD undertakes such an investment and NEW enters the market, and show that entry is still profitable even if there is a competitive outcome (Note, the two firms now have different marginal costs. Note also that you must assume that it is an infinitely repeated game) h) Discuss more generally, with verbal reasoning, how such an investment in technology can affect the potential for a collusive outcome i) Do the calculus to check whether the collusive outcome described above is sustainable