Q: Two firms each have MC=5 compete according to the Cournot model. If the market demand is given by P=485-2Q, how many units should each firm produce?
A: For firm 1 TR=P*q1=(485-2q1-2q2)q1 since Q= q1+q2. Since TR= 485q1-2q12-2q2q1, MR=485-4q1-2q2. Setting MR=MC gives 485-4q1-2q2 = 5. By symmetry we know that q1=q2 so we can rewrite this as 485-4q1-2q1 = 5 or 480=6q1 or q1= 80 = q2.