Final answer:
In a Cournot duopoly market, two firms decide on their production levels simultaneously, and each firm's decision affects the market price and the other's production. They determine their equilibrium production levels by using their reaction functions, and the point where these functions intersect is the Cournot equilibrium, where both firms produce such that marginal cost equals marginal revenue.
Step-by-step explanation:
In a Cournot duopoly market with two firms, Firm 1 and Firm 2 make simultaneous decisions on how much quantity (q1 and q2 respectively) to produce. The demand curve is given by p = 36 - (q1 + q2). Each firm's production decision impacts the market price, which in turn affects the quantity produced by the other firm. The firms are interdependent because each firm's profit depends not only on its own output decision, but also on the output decision of the other firm.
To find the equilibrium in such a market, we determine the reaction functions of each firm, which express the quantity produced by one firm in terms of the quantity produced by the other firm. Each firm selects the level of output that maximizes its own profit given the output level of the competitor. Once both firms have no incentive to unilaterally deviate from their chosen production levels, Cournot equilibrium is achieved. In equilibrium, both firms charge the same price and produce an equilibrium quantity such that marginal cost equals marginal revenue.
For instance, if Firm 1 believes Firm 2 will produce q2 units, then Firm 1 chooses its optimal q1 to maximize its profit considering the demand curve. This leads to a reaction function for Firm 1, and conversely, Firm 2 will have its own reaction function based on Firm 1's output. The point where these two reaction functions intersect gives the Cournot equilibrium quantities for both firms. The equilibrium price is then determined by substituting these quantities into the demand function.