The (Inverse)demand in a Cournot Duopoly Is P = a -

Essay

The (inverse)demand in a Cournot duopoly is P = a - b (Q₁ + Q₂),and costs are C₁(Q₁)= c₁Q₁ and C₂(Q₂)= c₂Q₂.
Show that the Cournot equilibrium levels of output are $$Q _ { 1 } = \frac { a + c _ { 2 } - 2 c _ { 1 } } { 3 b }$$ and $Q _ { 2 } = \frac { a + c _ { 1 } - 2 c _ { 2 } } { 3 b }$ .