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3) Assuming both firms behave as Bertrand duopolists, solve for p1 and p2. Show all work. Graph the reaction functions.
Demand for firm 1’s product: Q1 = 160 – p1 +(1/2)p2
Demand for firm 2’s product: Q2 = 160 – p2 + (1/2)p1
And TC1 = 20Q1; TC2 = 20Q2
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- Consider a duopoly market with 2 firms. Aggregate demand in this market is given by Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B. Assume the firms compete a la Cournot. Find the inverse demand in this market. Note that marginal revenue for both firms is given by MRA=500-2QA-QB, MRB=500-QA-2QB. Describe what a best-response curve is and how to find it. Derive the best-response function for each firm. What are the equilibrium quantities? What is the total quantity supplied on this market? What is the equilibrium price in this market?Consider a duopoly market with 2 firms. Aggregate demand in this market is given by Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B. Assume the firms compete a la Cournot. Find the inverse demand in this market. Note that marginal revenue for both firms is given by MRA=500-2QA-QB, MRB=500-QA-2QB. 2.Describe what a best-response curve is and how to find it. 3. Derive the best-response function for each firm. 4. What are the equilibrium quantities? 5. What is the total quantity supplied on this market? 6. What is the equilibrium price in this market?Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P=200-Qa-Qb where QAQA and QBQB, are the quantities sold by the respective firms and P is the selling price. The total cost functions for the two companies are TCa=1,500+55Qa+Qa2 TCb=1,200+20Qb+2Qb2 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). For Company A, the long-run equilibrium output is and the selling price is $ . For Company B, the long-run equilibrium output is , and selling price is $ . At the equilibrium output, Company A earns total profits of $ and Company B earns total profits of $ . Therefore, the total industry profits are $ .
