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Two firms sell differentiated products. The demand for firm 1's product is Q1(p1, p2) = 1 - 2p1 + p2 and the demand for firm 2's is Q2(p1, p2) = 1 + 2p1 - 3p2, where p1 denotes firm 1's price and p2 firm 2's. Marginal cost for each firm is 0. Each firm's objective function is its own profit.

  1. Suppose firms choose prices simultaneously. Calculate the Nash equilibrium prices.
  2. Suppose firm 1 chooses its price first, knowing that this choice will be observed by firm 2 before firm 2 chooses its price. Determine the equilibrium choice of prices.
  3. In a reaction function diagram, draw each firm's reaction function and draw iso-profit contours through the equilibrium prices in the parts (a) and (b), being sure to say which curves correspond to which firm. (The figure does not need to be to scale, but the orientation of the curves should be correct.)

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