Cournot and Bertrand equilibria are the same under certain market conditions. Specifically, when firms are identical and market demand is linear, the Cournot and Bertrand models result in the same equilibrium outcomes as firms will produce the same efficient quantity. In Cournot, firms choose quantities assuming rivals' quantities are fixed, while in Bertrand firms choose prices assuming rivals' prices are fixed. However, with identical firms and linear demand, these assumptions lead to the same equilibrium.

1. Under what conditions are cournot and bertrand equilibria the same? You may assume the
market demand is p = a ? bQ. Consider when firms are identical and different. If not, please
explain why.
Solution
Both are oligopoly models in which firms produce a homogeneous good. In the Cournot model,
each firm assumes its rivals will not change the quantity produced. In the Bertrand model, each
firm assumes its rivals will not change the price they charge. In both models, each firm takes
some aspect of its rivals behavior (either quantity or price) as fixed when making its own
decision.
The firms are taken identical because with the same degree of power influence over price and
output, the completion between the two will result in efficient level of production.