Q: Market demand is given by P=85-2Q. If there are two firms each with TC=q2+5q that compete according to the Cournot model, what profit will each firm earn?
A: The MC of a firm is 2q+5. TR for firm 1 is (85-2q1-2q2)*q1. Thus the MR for firm 1 is 85-4q1-2q2. Taking into account the symmetry in the problem q1=q2. Thus setting MR =MC gives 2q1+5= 85-4q1-2q1 or 80= 8q1 or q1=10=q2. Since Q=20, P=45. TR for a firm is 10*45=450 and TC=102+5(10)=150 so profit is 300.