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##### Assume that two companies

**Description**

solution

**Question**

1. Assume that two companies (C and D) are duopolists that produce identical produces. Demand for the products is given by the following linear demand function: P=600-Qc-Qd where Qc and Qd are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCc=25000+100Qc;TCd=20000+125Qd;Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm's output will not change).;a. Determine the long run equilibrium output and selling price for each firm. Solution;Q = Qc + Qd;For Company C;TRc = P*Qc;= (600 ? Qc ? Qd)Qc;= 600 ? Qc2 ? Qd*Qc;MRc = 600 ? 2Qc ? Qd;MCc = 100;At long run equilibrium, MR = MC;600 ? 2Qc ? Qd = 100;2Qc + Qd = 500-------------- (1);For Company D;TRd = P*Qd;= (600 ? Qc ? Qd)Qd;= 600 ? Qc*Qd ? Qd2;MRd = 600 ? 2Qd ? Qc;MCd = 125;At long run equilibrium, MR = MC;600 ? 2Qd ? Qc = 125;Qc + 2Qd= 475--------- (2);Solving the two linear equation (1) and (2), we get;Qc = 175 and Qd = 150;Putting these values in price equation;P = 600 ? 175-150;P = $275;b. Determine the total profits for each firm at the equilibrium output found in Part (a).

Paper#29701 | Written in 18-Jul-2015

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