Problem 3 Consider the infinitely repeated game with the discount factor 8 € (0, 1) of the following Cournot duopoly model with inverse demand function P(Q) :{ = a- 0 where Q = 91 +92 and cost functions Ci(qi) given by = Q if Q ≤ a if Q > a cqi, i 1,2. The profit function of firm i is Ti (91, 92) = qiP(q₁ +92) - cqi. Consider the following grim-trigger strategy. Produce half the monopoly output in the first period and as long as everybody has produced that amount so far. Otherwise produce the Cournot output. Verify that this is a subgame perfect equilibrium.
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- Consider a homogeneous-product Cournot ollgopoly of 3 firms with cost functions TC(a) = 24, Sup- pose that the Inverse demand function Is P(Q) = 30 - Q. (a) Solve for Cournot-Nash equilibrlum. (b) Firm 1 and Firm 2 merge Into Firm A. Solve for the new Cournot-Nash equilibrlum. Provide an Intultive explanation for the decrease In the combined profit of the merged firms.In the aeronautical market, Boing and Airbus constitute a duopoly in the production of large airplanes. The American firm has the following cost structure C(qa) = 20 + 39a + qả, and the European firm, C(qe) 150 – P, answer the following questions. = 50 + qe + q?. If the market demand for large airplanes is given by Qp = 9a + qe = a) Interpret the cost structures of both firms b) What would be the equilibrium (quantity, price, and profit) if firms compete by quantity as in Cournot and interpret your answer. c) If they decide to form a cartel, what are the new quantities, prices, and profits? Interpret your answer using the Game Theory insights. d) Calculate now what would happen if Airbus is the leader (Stackelberg model) in terms of quantity, price, and profit and interpret your outcomes.Questions: A) How much less do each of these firms earn in the Nash equilibrium than if they jointly maximize profits? Please provide me with the correct answer, complete with a detailed explanation and calculations; otherwise, I will give multiple downvotes.Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.
- 1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB). a. Assume firm A chooses quantity first. Frim B observes this choice and then chooses its own quantity. What is Frim B's profit as a function of QA and QB? b. Firm B has MRB = 220 – 2QB – QA. What is firm B’s best response to an arbitrary QA selected by firm A? c. Given that firm A expects firm B’s best response, what is firm A’s profit as a function of QA? (Hint: the only unknown variable in the profit function should be QA) d. Firm A has MRA = 150 – 4QA/3. What are the equilibrium QA and QB selected in this game? e. What is the equilibrium price, and how much profit does each firm collect?8)Consider a market in which 5 companies operate, whose marginal and average costs are equal to c. The demand function is given by P(Q)= 1-Q, where P is the price and Q indicates the total quantity. Assume that companies compete with Cournot in choosing production levels. Assume that the game is repeated an infinite number of periods, that companies adopt trigger strategies and that the punishment is represented by Nash Reversion. 1)What is the value of the discount factor that allows companies to sustain tacit collusion in a balanced situation? 2) Assume now that companies are able to discover the defection of a rival company with K periods of delay. What do you think the effect on the sustainability of collusion can be? 3) Do you think that in this market collusion would be more easily sustainable if the companies compete with Bertrand? 4) If in a price-competitive market (Bertrand) N symmetrical companies operate, what would be the critical value of the discount factor that would…Consider a duopoly market, where two firms sell differentiated prod- ucts, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices pi and p2 simultaneously. The derived demand functions for the two firms are: D1 (p1, P2) and D2 (p1, P2) = + 2, where S > 0 and the parameter t > 0 을 + S + P2-P1 2t 2t measures the degree of product differentiation. Both firms have constant marginal cost c > 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profits of the two firms.
- The inverse demand for a homogenerous-product STakelberg duopoly is P=18,000-5Q. The cost structures for the leader and the follower, respectively, are CL(QL=2,000QLand CF(QF)=4000Qf. What is the follower's reaction function? Determine equilibrium output level for both leader and follower. Determine the equilibrium market price. Determin the profits of the leader and the follower. Please answer correct please asap please Don't answer by pen paper plz1. Return to our Cournot competition model with two firms. Suppose now that the products aren't quite identical. In fact, both firms face different demand functions, a – b(q1 + dq2) a – b(dqn + 42) Pi = P2 = where d is some umber between 0 and 1 that specifies how similar the products are. Everything else about the model remains the same. (a) Calculate the best response functions for each firm. How does the slope of those best responses change with d? What happens when d = 0 or d = 1? (b) Calculate the equilibrium prices and quantities in this market. (Note: the firms are not identical).Additional Problem 3: Assume that two companies (C and D) are Cournot duopolists that produce identical products. Demand for the products is given by the following linear demand function: P = 600 – Qc - QD where Qc and Qp are the quantities sold by the respective firms and P is the price. Total cost functions for the two companies are TC = 25,000 + 100QC TCp = 20,000 + 125QD %3! %3D a. Determine the profit functions for both firms. b. Given the cost functions, which firm will produce more in an equilibrium? c. Determine the equilibrium price and quantities sold by each firm. d. Determine the profits for the market as well as each firm.
- Consider the following 2-firm (firm 1 and 2) model of Bertrand duopoly with differen- tiated products. Demand for firm i is q:(Pi, P;) = a – Pi – bi.Pj costs are zero for both firms. The sensitivity of firm i's demand to firm j's price is measured by bị. (a) First suppose b1 # b2. Find the equilibrium prices p1 and p2. (b) Deduce that if the two firms are identical, they choose the same price p = 216) where b = b1 = b2. аDiscuss Many electronics stores like EMAX, and Jumbo have low-price guaranteepolicies. At a minimum, these guarantees promise to match a rival’s price, and somepromise to beat the lowest advertised price by a given percentage. Do these types ofpricing strategies result in cutthroat competition and zero economic profits? If not, whynot? If so, suggest an alternative pricing strategy that will permit these firms to earnpositive economic profits.Suppose you are employed at a monopolistic company as a research (pricing) economist and you are deriving the behavior of two markets based on demand curves given by: Di(P1) 3 50 — Pі D:(p>) — 50 — 2р2 Assume that the marginal cost is constant at $8 a unit. (a) If it can price discriminate, what price should it charge in each market in order to maximize profits? (b) If it can't price discriminate, what price should it charge?