You are given the market demand function Q=2200-1000p, and that each duopoly firm's marginal cost is $0.07 per unit, which implies the cost function: C(qi) = 0.07gi, assuming no fixed costs for i = 1, 2. The Cournot equilibrium quantities are q₁ = and 92 = (enter your responses as whole numbers).
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- V5. You are the manager of Taurus Technologies, and your sole competitor is Spider Technologies. The two firms' products are viewed as identical by most consumers. The relevant cost functions are C(Qi) = 2Qi, and the inverse market demand curve for this unique product is given by P =290 - 3Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $500, Taurus Technologies can bring its product to market before Spyder finalizes production plans. (Assume Taurus Technologies is the leader in this scenario.) What are your profits if you do not make investment? What are your profits if you do make investment? Instructions: Do not include the investment of $500 as part of your profit calculation. Should you invest the $500? no or yesSuppose that Raleigh and Dawes are the only sellers of bicycles in the UK. The inverse market demand function for bicycles is ?(?)=200−2?. Both firms have the same total cost function: ??(?)=12? and the same marginal cost: ??(?)=12.Suppose this market is a Stackelberg oligopoly and Raleigh is the first mover.a) Write down a formula for the reaction function of Dawes.b) Calculate the equilibrium quantity that each firm produces and the equilibrium price in the market.c) At the Stackelberg equilibrium, how much profit does each firm make?Suppose now that the two firms decide to act like a single monopolist.a) What will the total quantity of bicycles sold in the market be and what will the equilibrium price be? Represent the profit maximisation problem on a graph and indicate the price and quantity at the equilibrium.b) Calculate the total profit made by the two firms when they act like a monopoly. Compare it with the total profit they were making in the Stackelberg oligopoly.c) For the…Three firms compete in the style of Cournot. All firms have a constant returns to scale technology: There are no fixed cost and each firm's marginal cost is constant. The market demand is given by Q(P) = 9 - P. Firm 1's marginal cost is MC1 = 1, firm 2's marginal cost is MC2 = 2. Let MC3 be the marginal cost of Firm 3. Which of the below is a necessary condition so that q > 0 for all three firms in a Nash equilibrium? a. MC3 < 1 b. MC3 < 4 c. MC3 < 3 d. MC3 > 1 e. MC3 < 2
- There are only two driveway paving companies in a small town, Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services is ?= 2040 ―20? where quantity is measured in pave jobs per month and price is measured in dollars per job. Assume Asphalt, Inc. has a marginal cost of $100 per driveway and Blacktop Bros. has a marginal cost of $150. Answer the following questions: Determine each firm’s reaction curve and graph it. How many paving jobs will each firm produce in Cournot equilibrium? What will the market price of a pave job be? How much profit does each firm earn?The inverse market demand curve for salmon is given by P(Y) = 100 – 2Y, and the total cost function for any firm in the industry is given by TC(y) = 4y. a. Suppose that two Cournot firms operated in the market. What would be the reaction function for Firm 1 and the reaction function of Firm 2? (Notes: The marginal cost is not zero). If the firms were operating at the Cournot equilibrium point, what would the industry output and price be? b. For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graphOutput is homogenous and the demand curve is P = 448 - Q. There are two firms with identical %3D costs given by C = q2 i where qi is the production of firm i. The marginal cost of firm i is Mci(qi) = 2qi . (a) Find the Cournot equilibrium firm outputs. (b)
- You are the manager of Taurus Technologies (T), and your sole competitor is Spyder Technologies (S). The two firms’ products are viewed as identical by most consumers. The relevant cost functions are C(QT) = 120 + 8QT and C(QS) = 120 + 10QS, and the market demand curve for this unique product is given by P = 160 – 2.5Q. Instructions: Use no decimals. Use the average cost to calculate monopoly profits. Do not round if values are used to complete other calculations. Complete the following table. Q1 Q2 P Profits T Profits S Duopoly competition 854 CollusionAlpha and Gamma are the only two phone handset manufacturers in the world. Each firm has a cost function given by: C(q) = cq + q?, where q is number of phones produced and c=70. The market demand for phones is represented by the inverse demand equation: P = a - bQ where Q = q1 + q2 is total output, a=250 and b=1. 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 Alpha and Gamma that they could do a lot better by colluding. If the two firms were to collude, 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 for…Suppose a market is served by two firms (a duopoly). The market demand function given by P = 1200 - Q_{1} - Q_{2} where Q_{1} is the output produced by firm and Q_{2} is the output produced by firm 2 . Firm cost of production is given by the function C(Q_{t}) = 120Q_{t} and firm 2's cost of production is given by the function C(Q_{2}) = 120Q_{2} The average cost of firm 1 is given by A*C_{1} = 120 and the average cost of firm 2 is given by A*C_{2} = 120 Marginal profit function for firm 1: Delta pi 1 Delta Q 1 equiv1080-2Q 1 -Q 2; (d*pi_{2})/(Delta*Q_{2}) = 1080 - Q_{1} - 2Q_{2} Marginal profit function for firm 2: What will be the equilibrium profit levels earned by the Stackelberg leader firm and the Stackelberg follower firm?
- Additional Problem 3: Assume two companies (C and D) are Cournot duopolists that produce identical products. Demand for the products is given by the following linear demand function: ? = 600 − ?C − ?D where ?C and ?D are the quantities sold by the respective firms and P is the price. Total cost functions for the two companies are ??C= 25,000 +100?C 2 ??D = 20,000 + 125?D c. Determine the equilibrium price and quantities sold by each firm. d.Determine the profits for the market as well as eachfirm.per pair You are the CEO of a company that advises clients on pricing strategies. Bilbo Baggins is a profit maximizing client who produces uniquely styled shoes and hires you for pricing advice. The graph shows the demand and marginal revenue (MR) curves faced by Bilbo's company for two different groups of consumers. Assume Bilbo can prevent the reselling of his shoes, faces constant marginal cost (MC) equal to $20/pair, can identify varying consumer groups, and has no fixed costs (so, MC ATC). Use the graph to answer the questions. = Price $100 90 80 70 60 50 40 B What price should Bilbo charge? He should charge the more elastic group $60/pair and the less elastic group $70/pair. 30 30 20 10 10 MR 2 Demand 2 He should shutdown in the short run because price is not greater than fixed costs. 0 100 200 300 40C He should price discriminate and produce where P = MC and charge $20/pair. He should produce where MR = MC and charge $70/pair.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…