Quiz 8

Q: Market demand is given by P=85-2Q. If there are two firms each
with TC=q^{2}+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 (85-2q_{1}-2q_{2})*q_{1}.
Thus the MR for firm 1 is 85-4q_{1}-2q_{2}. Taking into
account the symmetry in the problem q_{1}=q_{2}. Thus
setting MR =MC gives 2q_{1}+5= 85-4q_{1}-2q_{1} or
80= 8q_{1 }or q_{1}=10=q_{2}. Since Q=20, P=45.
TR for a firm is 10*45=450 and TC=10^{2}+5(10)=150 so profit is 300.