4 Two Cournot duopoly firms facing a demand PaD 90a g simu

4. Two Cournot duopoly firms, facing a demand P(a+D) = 90-(a + g), simultaneously choose their levels of output to maximize profit. Suppose both firms have the same unit cost 6. Show that successive elimination of strictly dominated strategies yields a unique prediction (q,g) = (28,28) in this game.

Solution

P = 90 - (q1+q2)

MC = 6

Competitive market equilibrium

P = MC

90 - Q = 6

Q = 84

Cournot Equilibrium = (2/3) Competitive Output

= (2/3)*84

= 56

Each firm produces 28 units