The Cournot model and the quantity leadership model are both oligopoly models that analyze the interaction between firms. In the Cournot model, firms simultaneously choose quantities, considering their competitors' quantities. In the quantity leadership model, one firm sets its quantity first, and other firms adjust their quantities accordingly. The main difference is the sequencing of quantity choices.
In the Cournot model, both firms simultaneously choose their quantities (Q1 and Q2). Let's assume the firms have identical costs, such that the cost of producing each unit is $10. Each firm aims to maximize its profit by considering the reaction function of the other firm. The reaction function specifies the optimal quantity of each firm based on the quantity chosen by the other firm. In this case, the reaction function for each firm would be:
Q1 = (100 - Q2 - P) / 2
Q2 = (100 - Q1 - P) / 2
Solving these equations simultaneously, we can determine the Cournot equilibrium quantities and price.
In the quantity leadership model, one firm, let's say Firm 1, acts as the quantity leader and chooses its quantity (Q1) first. Firm 2, the quantity follower, observes Firm 1's quantity and adjusts its own quantity (Q2) accordingly. Assuming Firm 1 is the leader, it would choose its quantity to maximize its profit, taking into account the anticipated response from Firm 2. Firm 2 would then choose its quantity based on Firm 1's choice.
Let's say Firm 1 chooses its quantity as 40. Firm 2, observing this quantity, decides to choose its quantity to maximize its profit. Assuming Firm 2 has perfect information and identical costs as Firm 1, it would choose its quantity to be (100 - 40 - P) / 2. The market price and equilibrium quantities can be determined based on these choices.
In summary, the key difference between the Cournot model and the quantity leadership model lies in the sequencing of quantity choices. In the Cournot model, firms choose quantities simultaneously, whereas in the quantity leadership model, one firm sets its quantity first, and the other firms adjust their quantities accordingly.