Extension of the Cournot Mode1

Extension of the Cournot Mode1 - simplicity's sake, let's...

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Extension of the Cournot Model We now extend the Cournot Model of duopolies to an oligopoly where n firms exist. Assume the following: 1. Each firm chooses a quantity to produce. 2. All firms make this choice simultaneously. 3. The model is restricted to a one-stage game. Firms choose their quantities only once. 4. All information is public. Recall that in the Cournot model, the strategic variable is the output quantity. Each firm decides how much of a good to produce. All firms know the market demand curve, and each firm knows the cost structures of the other firms. The essence of the model: each firm takes the other firms' choice of output level as fixed and then sets its own production quantities. Let's walk through an example. Assume all firms face a single market demand curve as follows: Q = 100 - P where P is the single market price and Q is the total quantity of output in the market. For
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Unformatted text preview: simplicity's sake, let's assume that all firms face the same cost structure as follows: MC_i = 10 for all firms I Given this market demand curve and cost structure, we want to find the reaction curve for Firm 1. In the Cournot model, we assume Q i is fixed for all firms i not equal to 1. Firm 1's reaction curve will satisfy its profit maximizing condition, MR 1 = MC 1 . In order to find Firm 1's marginal revenue, we first determine its total revenue, which can be described as follows Total Revenue = P * Q1 = (100 - Q) * Q1 = (100 - (Q1 + Q2 +. ..+ Qn)) * Q1 = 100 * Q1 - Q1 ^ 2 - (Q2 +. ..+ Qn)* Q1 The marginal revenue is simply the first derivative of the total revenue with respect to Q 1 (recall that we assume Q i for i not equal to 1 is fixed). The marginal revenue for firm 1 is thus: MR1 = 100 - 2 * Q1 - (Q2 +. ..+ Qn)...
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