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Between Competition and Monopoly - Cournot Duopoly

Between Competition and Monopoly - Cournot Duopoly -...

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UNC-Wilmington ECN321 Department of Economics and Finance Dr. Chris Dumas Cournot Model of Duopoly Example Problem: Suppose there are only two producers of product Q, firm 1 and firm 2. The producers make production decisions at the same time / simultaneously (or, equivalently, they are myopic). Firm 1 produces Q 1 units of output at a cost of $c 1 per unit. Firm 2 produces Q 2 units of output at a cost of $c 2 per unit. Consumer demand for product Q is given by P Q = a - bQ, where a and b are constants, and Q = Q 1 +Q 2 is total quantity sold to consumers. Determine each firm's reaction function, then determine each firm's profit-maximizing output level Q 1 * and Q 2 * (the superscript "*" is used to denote the "Cournot model solution"). Next, determine the resulting market price, P Q * . Finally, determine each firm's profit level (Profit 1 * and Profit 2 * ). Solution: Let's solve firm 1's problem first. Firm 1 wants to maximize profit, taking into account his per unit cost of production, c, the level of demand in the market P Q = a - bQ, and the fact that the total supply on the market will be the total of firm 1's production plus firm 2's production, Q = Q 1
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