A Patent Race (Dutta) [This question is harder. It looks at a patent race under very different assumptions to the 'duel' we played in class.] Two firms, A and B, are each considering trying to develop a new widget. Whichever firm is first to develop the new widget wins a patent worth $20 million plus a penny. Developing a new widget involves several 'steps'. The firms alternate moves, with A moving first, until one of them wins the patent. All moves are observed. In each turn, a firm can choose whether to take 0, 1, or 2 development 'steps'. Taking 0 steps in a turn costs that firm $0. Taking 1 step in a turn costs $4 million. And taking 2 steps in a turn costs $11 million. For simplicity, assume a zero discount rate. Initially, each firm is 4 steps away from completing development. (a) Describe and explain carefully what will happen in this patent race and why. [Hint: it may help to read Dutta ch 12 (but notice I changed the numbers).] (b) Very briefly explain what is the economic rationale for granting 'intel