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 - q₁ - 0.5q₂

p₂ = 200 - 0.5 q₁ - q₂

and both firms face constant marginal costs of c = 60.

Suppose that each firm set their output level simultaneously. Find the equilibrium quantity for each firm. (Hint: Symmetry can be invoked here.)

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.)

(5 points) If the products were identical, we would have that q^*₁ = 70and 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).