Suppose that the market for microprocessors is dominated by just two firms. All microprocessors produced are sold at the market-clearing price which depends on TOTAL industry output. The market demand was estimated to be P = 30 - Q_{TOTAL ,}where Q_TOTALis the combined output of two firms in million.

The only decision variable for each firm is how many microprocessors to produce. Each firm must decide whether to build a plant suited to produce high volume, low volume, or to produce no microprocessors at all. Once the output decision is made, it is final. Regardless of the volume of production, each microprocessor costs a firm $7 to produce.

High and low volumes are 10 million and 5 million microprocessors, respectively.

a.Suppose the game is played simultaneously. Present the game in the normal form, using the table below and expressing payoffs in TOTAL PROFIT amounts.

(Consider, for example, the case when Firm 1 produces 5 mln units and firm 2 produces 10 mln units. The total industry output is 15 million. According to the demand equation, the market price will be P = 30 - 15 = $15.

The profit margin is then (P-ATC) = 15 - 7 = $8 per microprocessor. Finally, the profits of the two firms are 85=$40mln and 810=$80mln, respectively... and so on.)

Firm 2

Volume=10mln

Volume=5mln

Volume=0mln

Firm 1

Volume=10mln

Volume=5mln

40,80

Volume=0mln

b.Does any of the firms have a dominant strategy? If so, state what those are.

c. Does any of the firms have a secure strategy? If so, state what those are.

d. 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.

Next, suppose one of the firms is able to commit to a certain plant size first and make it known to the other firm.

e. (4 pts) Present this game in the extensive form (a tree). Make sure all the nodes, branches, and payoffs are properly labeled!

f. (4 pts) Identify the most likely outcome of the game presented in part e.

Does changing the rules of the game change your prediction about the most likely outcome? Comment briefly.