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# Question 2. [20 points] Consider Stackelberg's duopoly game in the

case that the inverse demand function is defined by P(Q) = a = Q for Q ≤ a (and P(Q) = 0 if Q &gt; a) and the cost function of firm i is C(qi) = ciqi with 0 &lt; c1&lt;α and 0 &lt; c2&lt;α

1. [8 points] Find the subgame perfect equilibrium. Be sure to specify the firms' equilibrium strategies..

2. [4 points] How much output does each firm produce in the subgame perfect equilibrium? 3. [8 points] Does the extensive game have a Nash equilibrium in which firm 1's output is zero? If it does, fully describe the firms' equilibrium strategies in this equilibrium. If it does not, argue why not.

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