Consider a situation where two firms with differentiated products behave as a duopoly in a market. The inverse demand functions for firms 1 and 2 are as follows: P1 = 200 ' Ch " 0-532 P2 = 200 ' 0-5q1 ' Q2 and both firms face constant marginal costs of c = 60. a. (5 points) Suppose that each firm set their output level simultaneously. Find the equilibrium quantity for each firm. (Hint: Symmetry can be invoked here.) b. (5 points) Suppose now that firm 1 was able to set their output level first, then firm 2 observed firm 1's output level and set their own. Find the equilibrium quantity for each firm. (Hint: Symmetry cannot be invoked here.) c. (5 points) If the products were identical, we would have that q'} = 70 and q\"'2 = 35 if the firms competed sequentially. Compare this result to your results from part (b). Explain why the quantities in part (b) are closer to one another (or farther away)