1. Suppose the duopolists producing homogeneous products face the following market demand curve and total cost functions. P=100 –2Q Where Q=9,+92 TC,=10q, And TC,=20q; Determine the equilibrium quantity, price and profit for each firm assuming firm 1 is the leader and firm 2 is the follower
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- Assume that the market demand and the costs of the duopolists are: P=120-0.4(QA + QB) TCA=5QA TCB= 0.2Q2B Also assume that firm B is the sophisticated leader, Determine: a. The reaction curve of A ,the reaction curve of B and the profit function of A b. Stackelberg equilibrium output level for firm A and Stackelberg equilibrium output level for firm B c. The market price3) 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 = 20Q22. Suppose there are two duopolists that have fixed costs of $ 60, variable costs of $ 10, and have the same demand curves:Q1 = 36 - 2P1 + P2Q2 = 36 - 2P2 + P1P1 and P2 = PQ1 and Q2 = Q Each company chooses its own price and takes the competitor's price as fixed a. Determine the profit equation and the profit valueb. Calculate the reaction curves for firm 1 and firm 2c. Perform the Nash equilibrium determined in the competition model with differentiated products.
- 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…Consider two firms, i = 1; 2, producing differentiated products and engaged in Cournot a. Given the market demands, what are the best-response functions of the two firms? b. Draw the best-response functions both for complements (d 0). c. Compute the Cournot equilibrium quantities and prices in this market. d. Compare the outcome between substitutes and complements goods. e. What are the profit-maximizing quantities and prices if firm i is a monopolist in this market? Compare with part c.Suppose that the market demand for mountain spring water is given as follows: P = 1200 - Q Mountain spring water can be produced at no cost. Determine the level of output produced and price charged by each firm in a Cournot duopoly. A monopolist faces a demand with constant elasticity of -2.0.It has a constant marginal cost of R20 per unit and sets a price to maximise its profit. If marginal cost should increase by 25 percent, would the price charged also rise by 25 percent? Provide a brief explanation.
- A monopolist can produce at a constant average and marginal cost of ATC = MC = $5. It faces a market demand curve given by Q = 53 - P. Suppose there are N firms in the industry, all with the same constant MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also show that as N becomes large, the market price approaches the price that would prevail under perfect competition. (Hint: your answers will be functions of N)(BONUS)QUESTION THREE The market demand faced by duopolists is given by P=100-0.4Q and their respective cost functions are C1=5Q1,and C2=0.1Q22 where, Q1 and Q2 are quantities produced and supplied by duopolists 1 and 2 respectively so that Q= Q1+Q2 Derive the reaction equations Calculate quantity of the leader duopolist, Firm 1 Calculate quantity of the followerConsider 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. 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 byQ = 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. 1. 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 byQ = 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. a)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. b)Describe what a best-response curve is and how to find it. c)Derive the best-response function for each firm. hi, can you answer part a.b,c please. If possible, please answer this question in typing as i can't read hand -written answers, thanksIn the mobile phone market, Samsung and Apple constitute a duopoly in the production of devices.The American firm has the following demand q_a = 10 - p_a + 0.25p_s, and the Korean firm, q_s = 20 -p_s+ 0.5p_a. Because both firms assembly their devices in China, their cost structure is the same andequal to ?(q) = 10q, answer the following questions.a) What would be the equilibrium (quantity, price, and profit) in this market, and interpret youranswer.b) If they decide to form a cartel, what are the new quantities, prices, and profits?
