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?
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- Consider a market that only includes two large firms. The (inverse) market demand is P = 100 – Q. 3q2. Firm 1 has a cost function of C, = 2q1, and firm 2 has a cost function of C2 Use a Cournot model to calculate the Nash equilibrium outputs q, and q2 of the two firms. and 92 (a) Give each firm's profit as a function of (b) Compute the Nash equilibrium q, and q2.QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)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.
- Consider that Firm 1 and Firm 2 are involved in price competition. The demand for each firm is given as follows, where Xj denotes the demand for firm i=1,2 and Pi denotes the price that firm i=1,2 chooses. X1=465-3P1+P2 X2=465-3P2+P1 For each firm, it costs 5 to produce a product. At the Nash equilibrium, the price of Firm 1 is Blank 1. Calculate the answer by read surrounding text. , and the price of Firm 2 is Blank 2. Please answer Blank 1 and Blank2.The market demand function is Q=10,000-1,000p. Each firm has a marginal cost of m=$0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. Compare your solution to the Cournot-Nash equilibrium. The Stackelberg-Nash equilibrium quantities are: q1=___________ units and q2=____________units The Stackelberg-Nash equilibrium price is: p=$_____________ Profits for the firms are profit1=$_______________ and profit2=$_______________ The Cournot-Nash equilibrium quantities are: q1=______________units and q2=______________units The Cournot-Nash equilibrium price is: p=$______________ Profits for the firms are profit1=$_____________ and profit2=$_______________2. An industry contains two firms that have identical cost functions C(q)=10+2q. The inverse demand function for the market is P=50-2Q where Q is the total industry output. Assuming the firms compete in quantities: Find the firms' best response functions. b. Solve for the Cournot Nash Equilibrium of the game. What is the total industry output in equilibrium? What is the equilibrium price? с. i. If both firms could collude, what would the industry output and price be? Suppose they decide that each firm produces half of the industry output found in part (i). Is this agreement self-enforcing? Explain. ii. a.
- 1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.Consider a market in which there are two firms: A and B. Each firm produces a differentiated product and chooses its price Assume that each firm can set price equal to $60 or $70. The payoffs associated with each set of prices are shown If the firms choose price simultaneously, then the Nash equilibrium price for firm A If firm A chooses price first and can commit to that price, then firm A will Firm B's Price is set its price equal to $00 $70 OA. $60, $60 OB. $70, $70 $2700 $2475 $60 OC 570, $60 OD. $60, $70 $2700 $3375 Firm A's Price $3375 $3300 $70 $2475 $3300Question 1: Suppose Southwest (S) and JetBlue (J) choose a number of flights, qs and qj respectively, from Chicago to New York. They both have the same constant marginal cost of 12. For Q = qs + qj, the market demand function for flights is p = 60 – 2Q (1) Suppose the airlines choose quantity simultaneously. Find the Cournot Nash Equilibrium quantities. (2) Suppose the airlines choose price simultaneously. Find the Bertrand Nash Equilibrium. (3) Suppose Southwest and JetBlue collude in the quantities they choose to obtain monopoly profits. Assuming they split the market evenly, what quantity does each firm choose? (4) Suppose Southwest and JetBlue agree in principle to the collusion in Part (4), but Southwest decides to cheat. What quantity will Southwest choose?
- Suppose the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(q) - 40g Assume that the demand curve for the industry is given by P= 190 -Q and that each firm expects the other to behave as a Cournot compedtor. Calculate the Coumot-Nash equilibrium for each firm, assuming that each chooses the output level that maximizes as profes when taking its rival's output as given. What are the profits of each firm? (Round all quantities and dollar amounts to two decimal places) When competing, each firm will produce units of output. In tum, each firm will earn profit of $. What would be the equilibrium quantity if Texas Air had constant marginal and average costs of $10 and American had corntant marginal and average costs of S407 It Texas Air had constant marginal and average costs of $10 and American had constant marginal and average costs of S40, American would produceunits and Texas Air Corp. would produce units. In…uppose that the market demand for a certain product is given by P=370−2QP=370−2Q, where QQ is total industry output. There are only two firms F1,F2 that manufacture that product. The two firms have the following marginal costs: c1=24 and c2=26 a) Determine the output levels that will be produced in a Cournot-Nash equilibrium q1= q2= the price level in such an equilibrium P= and the profit levels u1= u2= b) Determine the output levels that will be produced in a Stackelberg-Nash equilibrium (consider F1F1 is the leader and F2F2 is the follower) q1S= q2S= the price level in such an equilibrium PS= and the profit levels uS1= uS2=* Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q, and that of firm 2 is denoted by q Each firm faces a constant marginal cost of 3. Let Q denote total output. Le Q-q+42 The inverse demand curve in the market is given by (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) If the firms could collude, what would be the total output in the mar ket? Assuming each firm produces half of the collusive output, what is the profit of each firm? (c) Suppose each firm produces half of the collusive output identified in part (b). Firm 1 considers a deviation from this arrangement. What would be the best deviating output of firm 1 and its deviation profit? (d) Suppose firms interact repeatedly over an infinite horizon, and firms have a common discount factor & € (0,1) Specify a trigger strategy for each firm to sustain the collusive arrangement as an equilibrium outcome Cal- culate…