Suppose the airline industry consists of only two airlines, Jumbo jet and Kenya airways. Let the two firms have identical costs C(Q,) = 40Q, where i = 1,2. Assume that the demand curve for the industry is given by P=100-Q a) Calculate the Cournot-Nash equilibrium for each firm: equilibrium price, output and profit
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- 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 < 2Consider two firms that produce the same good and competesetting quantities. The firms face a linear demand curve given by P(Q) =1 − Q, where the Q is the total quantity offered by the firms. The costfunction for each of the firms is c(qi) = cqi, where 0 < c < 1 and qiis the quantity offered by the firm i = 1, 2. Find the Nash equilibriumoutput choices of the firms, as well as the total output and the price, andcalculate the output and the welfare loss compared to the competitiveoutcome. How would the answer change if the firms compete settingprices? What can we conclude about the relationship between competitionand the number of firms?Two firms with differentiated products are competing in price. Firm A and B face thefollowing demand curves: Q_A = 70 − 2P_A + P_B and Q_B = 120 − 2P_B + P_Arespectively. Assume production is costless.a. Give equations for and graph each firm’s reaction curve.b. If both firms set their prices at the same time, what is the Nash equilibriumprice, quantity, and profit for each firm?c. Suppose A sets its price first and then B responds. What price and quantitydoes each firm set now? Is it advantageous to move first?d. Compare the profits from part b and c. Which firm benefits more from thesequential price choosing? (Please do b-d, thanks :))
- Let ci be the constant marginal and average cost for firm i (so that firms may have different marginal costs). Suppose demand is given by P=1-Q. Calculate the Nash equilibrium quantities assuming there are two firms in a Cournot market. Also compute market output, market price, firm profits, industry prof- its, consumer surplus, and total welfare. Represent the Nash equilibrium on a best-response function diagram. Show how a reduction in firm 1’s cost would change the equilibrium. Draw a representative isoprofit for firm 1.Suppose that two firms produce mountain spring water and the market demand for mountain spring water is given as follows: P= 254 - 91 - 92 Firm 1 and Firm 2 have a MC = 50 a) Find the Cournot-Nash equilibrium price and quantity of each firm. b) Assume now that firm 1 becomes the Stackelberg leader. What will be the market price, output by each firm? Compared to part a, who gains? c) If Firm 1 chooses a quantity, then Firm 2 chooses a quantity (having observed Firm 1's quantity), then Firm 1 has an opportunity to revise its quantity (having observed Firm 2's quantity), then payoffs are determined, does either firm stand to gain relative to the case of simultaneous quantity choice? Why or why not? (hint: there is no need to do any calculation here).Consider a Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given byT Ci = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?(c) Find the Nash equilibrium quantities (Q∗1, Q∗2)?(d) What is the equilibrium price? Just help with c and d here please
- Two identical firms are engaged in Cournot competition, with cost functionsTCA(QA) = 10 QA and TCB(QB) = 10 QB. The market demand is given by P = 610 –2Q.a) Plot the best response functions and report the Cournot-Nash equilibrium quantities, price and profits.b) What are the prices, quantities, and profits for the firms if they decide to collude and share profits equally? c) Show that firms have an incentive the deviate from the collusive outcome.d) Find the Stackelberg equilibrium if A leads and B follows.e) Show the equilibria in the previous parts on the inverse demand function. Calculate and identify consumer surplus and deadweight loss in each equilibrium..Firms A and B operate in a market with inverse demand given by p = 160 - (q_{A} + q_{B}) Their total cost functions are C_{A}(q_{A}) = q_{A} ^ 2 / 2 and C_{B}(q_{B}) = q_{B} ^ 2 / 2 , respectively. The firms compete in quantities (Cournot competition). Denote by q_{A} ^ C and q_{B} ^ C the Nash equilibrium quantities in this game. What are q_{A} ^ C and q_{B} ^ C Hint: Again, note that I gave you the total cost function for each firm, not the marginal costs. (a) q_{A} ^ C = 24 q_{B} ^ C = 24 (b) q_{A} ^ C = 60 q_{B} ^ C = 30 (c) q_{A} ^ C = 40 q_{B} ^ C = 40 (d) q_{A} ^ C = 20 q_{B} ^ C = 20 (e) q_{A} ^ C = 30 q_{B} ^ C = 30Consider a market with two identical firms, Firm A and Firm B. The market demand is:1P = 100 — —2Qwhere Q = QA + QB . The cost conditions are MCA = MC, = ACA = AC, = 24. (Hint: Round your solutions to 2 decimal places.)Assume this market has a Stackelberg leader, Firm A. Solve for the quantity, price and profit for each firm. Explain your calculations.How does this compare to the Cournot-Nash equilibrium quantity, price and profit? Explain your calculations.
- Consider the following statements about the Stackelberg game from the slides, assuming both firms are identical: (I) Denote by qC the Cournot equilibrium quantity produced by each firm, and by qPC the competitive quantity defined by P(qPC) = c (price equals marginal cost). Let s2 denote a strategy where firm 2 plays q2 = qC if it observes q 1 = qC, and plays q2 = qPC otherwise. Let s 1 denote a strategy where firm 1 plays q1 = qC. Then, (s1,s2) is a Nash equilibrium of the Stackelberg game, but it’s not a subgame perfect Nash equilibrium. (II) The first firm is allowed to change its quantity after observing firm 2’s quantity chosen at the second stage. (III) Consumers are worse off in the Stackelberg game compared with the Cournot outcome given the same parameters. Group of answer choices: a. Only II is correct b. Only I is correct. c. All options are incorrect. d. Only III is correct e. More than one option is correct.Assume a Nash-Cournot equilibrium. How much output does firm 1 produce? Assume a Nash-Cournot equilibrium and no fixed cost. How much profit does firm 2 make? Now assume a collusive equilibrium. What is firm 1's output?(Cournot competition with different marginal costs) Our best estimate for total marketdemand in a given market is P 1000-2Q. Two firms (1 and 2) are competing in this market in quantities, choosing Q1 and Q2 simultaneously. Firm 1 has marginalcost equal to c1 = 100 and Firm 2 produces at marginal cost c2 = 200. (a) Write down the profits of both firms and and their best response functions. (b) Find the Cournot - Nash equilibrium in quantities, and calculate equilibrium profits for both firms. (c) Suppose that each firm has the option, at a previous stage, to invest in an R&D project that will reduce its marginal cost of production by 50% if successful. What is the value of this innovation to each firm? Given that R&D costs and successprobabilities are equal, which one has greater incentives to invest in R&D ? You can think in terms of per - period profits to set aside timing issues.