Consider Two Cournot Competitors Selling Complementary Goods with Demand Curves

Essay

Consider two Cournot competitors selling complementary goods with demand curves given by:
p₁ = 100 - q₁ + .5q₂
p₂ = 100 - q₂ + .5q₁
Suppose each firm has a marginal and average cost of $10.
a.What about the demand equations indicate that these goods are complements? How do they differ from the standard Cournot model?
b.Find the equilibrium prices and quantities.
c.Suppose the two firms merge.By doing so,the newly merged firm will act to maximize the joint profits ((q₁,q₂)= ₁(q₁,q₂)+ ₂(q₁,q₂)).Find the joint-profit maximizing price and quantities.
d.Are the combined profits greater or smaller from merging? That is,is merging profitable for the firms?
e.Are consumers better or worse off with the firms merging? How does this compare to the mergers of Cournot competitors selling substitutes? What does this imply about antitrust policy towards mergers of firms selling complementary goods (such as airplanes and engines,computers and processors,cars and tire companies,etc).