Two firms produce a homogenous product. Let p denote the product's price. The output level of firm 1 is denoted by q1, and the output level of firm 2 by q2. The aggregate industry output is denoted by Q, Q = q1 + q2. The aggregate industry demand curve for this product is given by p = 200 – Q. a. Assuming that firms are homogeneous with cost function C(q1) = 2qi, derive the best response function for each firm. Show that Cournot-Nash equilibrium output for each firm is symmetric. Find the Cournot-Nash equilibrium aggregate output and price. Verify that given similar cost functions, equilibrium profits for each firm is symmetric as well.
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- Suppose market inverse demand function is p(y)=100-Yt where Yt is total production in the market. Assume that there are two firms with following marginal cost MC(firm 1)=Y1 MC(firm 2)=2*Y2+10 Assume that Yt=Y1+Y2 Set up profit function for both firms. What is the best response function of each firm by taking into account action of other firm? What output level is going to be produced by each firm in equilibrium? Assume that Firm 1 is leader in the market and going to act first. What will be the best response and output level of firm 2. What is difference between previous and new situation? Why? What is difference between Bertrand and previous competition? How would you like to find equilibrium price?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?Output 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)
- Suppose the market demand for a homogeneous product is given by Q = a - bP, where a and b are positive constants. The product is supplied by a dominant firm with a constant marginal cost c > 0 and n competitive fringe firms, each of which has a cost function ci(qi) = (qi^2)/(2ki) for i = 1, ... , n, where ki > 0 is a parameter. Suppose the dominant firm moves first by setting a price P, followed by competitive fringe rms setting their quantities, taking the price as given. a). Compute the equilibrium price and quantity level for each firm. b). How does the presence of competitive fringe firms affect the equilibrium price, as compared to the monopoly price by the dominant firm?The demand for home firm product is given by the inverse demand function: P = 120 −QD. The company’s costs are: T C = 20Q+ 200 and MC = $20.2. Suppose the home country open up to free trade and a foreign competitor enters the market. Assume thatthe foreign firm has the same cost structure as the home firm (the monopoly from the previous question).A) Derive the best response function for each firm (h-home and f-foreign)B) Find each firms’ output, the home market price, and each firms’ profit from the home marketSuppose Firm X is a dominant firm in a market where the market demand is Q = 1200 -2p. Once Firm X sets its price, those small competitors set their prices a little lower so that they can always sell up to their capacity. Assume the small firms’ combined capacity is 100 units. Further assume Firm X’s marginal cost is 50. Answer the following questions. Let Q^D be the quantity produced by the dominant firm. Write down the residual demand function faced by Firm X. (Hint: Think about how Q and Q^D are related.) Find Firm X’s profit-maximizing price.
- An industry contains two firms producing homogenous goods, one whose costfunction is C(Q1) = 30Q1 and another whose cost function is C(Q2) = 30Q2. The demandfunction for the market is given by:P = 65 - QT where QT = Q1 + Q2. a. Assuming firms are choosing quantities according to the Cournot model, what iseach firm’s reaction function?b. Graph each firm’s reaction curve (on same graph).c. How much does each firm produce in the Nash equilibrium of Cournot's model?Economics Consider a three-firm homogeneous product industry. The market demand function is X=1000-40P. The cost functions of the firms are: C1= 20X1, C2=13.5X2+0.075X22, and C3=16.3X3+0.005X32. Where, X=X1 + X2 + X3. 1. Explain the Firm's Cournot Behaviour. 2. Assuming the firms' practice on Cournot Behaviour, calculate the market price, outputs of the firms and their profitsAlpha 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…
- Let us consider a market where 10 firms I= {1,2,.,10} compete à la Cournot (quantity- setting competition). The inverse demand function is given by p( Q) =1200-18Q , where Q= Eiqi. The cost function is homogeneous and it is C( q ) =10q. 1.the profit functions of eachiEl is: 2.Derive the best reply functions for each firm 3.Derive the market price in the Nash equilibrium of the game. 4. The market price in the Nash equilibrium of the game is:wo firms A and B produce an identical product (Note: Industry Output = Q). The firms have to decide how much output qA and qB (Note: qA = Firm A Output; qB = Firm B Output) they must produce since they are the only two firms in the industry that manufacture this product. Their marginal cost (MC) is equal to their average cost (AC) and it is constant at MC = AC = X, for both firms. Market demand is given as Q = Y – 2P (where P = price and Q = quantity). Select any value for X between [21 – 69] and any value for Y between [501 – 999]. Using this information, calculate the Industry Price, Industry Output, Industry Profit, Consumer Surplus and Deadweight Loss under each of the following models: (a) Cournot Model error_outlineHomework solutions you need when you need them. Subscribe now.arrow_forward Question Two firms A and B produce an identical product (Note: Industry Output = Q). The firms have to decide how much output qA and qB (Note: qA =…1. Economies of scale Web Slinger is an Internet service provider. In the long run, Web Slinger can provide Internet service for 20,000 homes each month at a total cost of $600,000, Internet service for 30,000 homes at a total cost of $750,000, or Internet service for 40,000 homes at a total cost of $800,000. Use the purple points (diamond symbol) on this graph to plot points of the long-run average cost curve at outputs of 20,000, 30,000, and 40,000 homes. (? 50 Average cost 40 30 20 10 10 20 30 40 50 HOMES SERVED (Thousands) AVERAGE COST (Dollars per home per month)