1. A Patent Race (Dutta) [This question looks at a patent race under very different  assump-
tions 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 briey  explain what is the economic rationale for granting `intellectual propertyrights' such as patents. What are some disadvantages for society of granting such rights?