consider two firms who are acting as cournot duopolists. the inverse demand function is represented by P=100-(q1+q2). here p is the price. q1 and q2 are the output levels of firms 1 and 2 marginal cost mc functions of the two firms are mc1=5 mc2= 15 find the profit of two firms
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consider two firms who are acting as cournot duopolists. the inverse demand function is represented by P=100-(q1+q2). here p is the price. q1 and q2 are the output levels of firms 1 and 2
marginal cost mc functions of the two firms are
mc1=5
mc2= 15
find the profit of two firms
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- 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=400−QA−QBP=400−QA−QB where QAQA and QBQB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCA=1,500+110QA+QA2TCA=1,500+110QA+QA2 TCB=1,200+40QB+2QB2TCB=1,200+40QB+2QB2 Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce units and sell at .Similarly, Company B will produce units and sell at . At the optimum output levels, Company A earns total profits of and Company B earns total profits of . Therefore, the total industry profits are . At the optimum output levels, the marginal cost of Company A is and the marginal cost of Company B is . The following table shows the long-run equilibrium if the firms act independently, as in…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−QBP=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+QA2TCA=1,500+55QA+QA2 TCB=1,200+20QB+2QB2TCB=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 the 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 .Suppose the inverse demand function for two Cournot duopolists is given by P = 10 −(Q1+ Q2) and their costs are zero. 1. What is each firm’s marginal revenue? 2. What are the reaction functions for the two firms? 3. What are the Cournot equilibrium outputs? 4. What is the equilibrium price?
- The market demand curve for a pair of duopolists is given as P = 21 − 2Q, where Q = Q1 + Q2. The constant per unit marginal cost is $9 for each duopolist. Find the equilibrium price, total quantity and profit for each firm, assuming the firms act as a Stackelberg leader and follower, with firm 1 as the leader.Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function: P=600−QC−QD�=600−��−�� 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=25,000+100QCTC�=25,000+100�� TCD=20,000+125QDTC�=20,000+125�� 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 C, the long-run equilibrium output is , and the selling price is . For Company D, the long-run equilibrium output is , and the selling price is . At the equilibrium output, Company C earns total profits of , and Company D earns total profits ofIf a duopolist has a linear demand curve of the form Q=400 – P. Assuming each firm has total cost (TC=3000+100Q). Calculate the profit-maximizing price-quantity combinations using the following four oligopoly pricing models listed below demonstrating that: a. Under the Quasi-competitive model, the firm will make a loss equivalent to fixed cost. b. Under the Stackelberg’s model the leader will earn more than twice the profit of the follower and that total industry profits will be lower than under both Cournot and Cartel models. Explain why this is would be the case.
- Consider a Bertrand duopoly. Both firms produce an identical good at the same constant marginal cost of $0.80. Demand is given by Q=100−P. If the two firms charge the same price, they share market demand equally. The firms are located in Singapore, where the smallest currency denomination is $0.05. The firms thus can only choose prices in increments of $0.05. a) Suppose that both firms choose the same price, P. What is the profit of a firm as a function of P? b) Now suppose that one firm unilaterally deviates from the arrangement in (a) by charging a price $0.05 lower than P. What is that firm’s profit as a function of P? c) A Nash equilibrium occurs when no firm has an incentive to deviate by lowering its price. Using your answers in (a) and (b), set up an inequality that characterizes the Nash equilibrium. Then solve for the Nash equilibria in this game. (Hint: there are three equilibria)Consider two Cournot oligopolists, firm 1 and firm 2, in a homogenous product market. The market demand is P = 100 – 3Q and each firm has a constant marginal cost MC=10. The Cournot equilibrium quantity for each firm is: a. 7.5 b. 10 c. 5 d.15Suppose the inverse demand function for two Cournot duopolists is given by P = 10 – (Q1 + Q2) and their costs are zero. What is each firm’s marginal revenue and reaction functions? Determine the Cournot equilibrium outputs and equilibrium price. What is the implication of this model?
- Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function given by: C(q) = 10+20q + q^2, where q is number of widgets produced. The market demand for widgets is represented by the inverse demand equation: P = 200 - 2Q where Q = q1 + q2 is total output. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm__ price__ profit__ b) It occurs to the managers of Gamma and Zeta that they could do a lot better by colluding. If the two firms were to collude in a symmetric equilibrium, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm__ price__ profit__ c) What minimum discount factor is required…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. Total cost functions for the two companies are TCa=1,500+55Qa+Qa2 TCb=1,200+20Qb+2Qb2 Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce units and sell at $ . Similarly, Company B will produce units and sell at $ . At the optimum output levels, Company A earns total profits of $ and the marginal cost of Company B earns total profits of $ . Therefore, the total industry profits are $ . At the optimum output levels, the marginal cost of Company A is $ and the marginal…Suppose the inverse demand function for two Cournot duopolists is given by P = 10 – (Q1 + Q2) and their costs are zero. A. What is each firm’s marginal revenue and reaction functions? B. Determine the Cournot equilibrium outputs and equilibrium price. What is the implication of this model?
