2.7 In a homogeneous-good Cournot duopoly where both firms have a constant marginal cost m and the inverse market demand function is p = a - bQ, show that the Nash-Cournot equilibrium output of a typical firm is q = (a - m)/3b. Show that the corresponding equilibrium price is p = (a + 2m)/3.

(Hint: See Appendix 11A.) C