Quiz 8

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.