Suppose that the market for batteries installed in electric vehicles is dominated by just two firms. Further let us assume that all batteries produced are sold at the market-clearing price which depends on the TOTAL industry output. The market demand was estimated to be P-27-QOTAL where P is the market price in thousands of dollars and QroTAL is the combined output of two firms in millions of units. The only decision variable for each firm is how many batteries to produce. Each firm must decide whether to build a plant suited to produce high volume, low volume, or to produce no batteries at all. Once the output decision is made, it is final. Regardless of the volume of production, each battery costs a firm 6 thousand dollars to produce. High and low volumes are 10 million and 5 million, respectively. a (4 pts) Suppose the game is played simultaneously. Present the game in the normal form, using the table below and expressing payoffs in TOTAL PROFIT amounts. (Hint: Consider, for example, the case when Firm 1 produces 5 min units and firm 2 produces 10 min. units. The total industry output is 15 million. According to the demand equation, the market price will be P 27-15 $12 (remember these are thousands dollars). The profit margin is then (P-AC) 12-6-$6 (thousand) per battery. Finally, the profits of the two firms are 6.5-$30 billion and 6-10-$60 billion, respectively... and so on.) Firm 2 Volume Omln Volume 5mln Volume=10min Volume Omln Firm 1 Volume 5min 30 60 Volume-10mln b. (2 pts) Do any of the firms have a dominant strategy? If so, state what those are. c. (2 pts) Do any of the firms have a secure strategy? If so, state what those are. d. (3 pts) You are Firm 1, and you are concerned only with your own profit. According to the textbook and the lecture, which strategy should you play? Explain your choice carefully.