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.