= Consider two firms, firm 1 and firm 2, facing the demand curve P = 24-2Q, where Q Q₁+Q₂. The firms' cost functions are C₁(Q₁) = Q and C₂ (Q₂) = 2Q². Derive the reaction functions if the firms behave non-cooperatively. a. b. C. d. What is each firm's Cournot-Nash-Equilibrium output and profit if they behave non-cooperatively? Draw the firms' reaction functions and show the equilibrium. Suppose that both firms have entered the industry as a cartel. What is the joint profit-maximising level of output? How much will each firm produce? How much is the profit of each firm?
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- QUESTION 10 Suppose there are two firms that produce an identical product. The demand curve for the product is given by P = 62 - Q where Q is the total quantity produced by the two firms. Both firms choose their individual quantities qı20 and q22 0 simultaneously. Each firm has a marginal cost of 37. What is the market price when both firms produce the quantities in the unique Nash equilibrium? Give your answer as a number to two decimal places.Consider the following normal form representation of the standard competition between firm A and firm B. Each firm can choose either standard A or standard B. Their payoffs are given as follows: Firm B A В A Firm A В 1 1 3 1 (1) (10 points) What's Nash equilibrium (NE) in this game? If there are more than one, find them all. But there is no NE, state that there is no NE. (2) (10 points) If you find a NE (or multiple Nash equilibria), is it (or are they) Pareto efficient?Three firms compete in the style of Cournot. The inverse demand is P(Q) = a - Q. Scenario 1: All three firms have the same constant marginal cost MC = c. Scenario 2: Firm 1 has MC = 0.5c, Firm 2 has MC = c, and Firm 3 has MC = 1.5c. Assume that a > 3c. Which of the following is correct? (Price means the price in Nash equilibrium.) O Price in scenario 1> Price in scenario 2 O Price in scenario 2> Price in scenario 1 O Price in scenario 1 = Price in scenario 2 O Any of the first three options is possible depending on the value of a O Any of the first three options is possible depending on the value of a and c.
- Duopoly and menu costs. (This is adapted from CaminaI 1987.) Consider two firms producing imperfect substitutes. Both firms can produce at zero marginal cost. The demand for the good produced by firm i is given by Now suppose that both firms enter the period with price p., which is the Nash equilibrium price for some value of a, a·. They know b and c. They each observe the value of a for the period, and each firm must independently quote a price for the period. If it wants to quote a price different from p*, it must pay a cost k. Otherwise, it pays nothing. Once prices are quoted, demand is allocated, demand determines produdion, and profits are realized. (b) Compute the set of values of a (around a*) for which not to adjust prices is a Nash equilibrium. (c) Compute the set of values of a (around a*) for which to adjust prices is a Nash equilibrium. (d) Check that all equilibria are symmetric and therefore that there are no other equilibria than the ones computed above.…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.Consider a market for crude oil production. There are two firms in the market. The marginal cost of firm 1 is 20, while that of firm 2 is 20. The marginal cost is assumed to be constant. The inverse demand for crude oil is P(Q)=200-Q, where Q is the total production in the market. These two firms are engaging in Cournot competition. Find the production quantity of firm 1 in Nash equilibrium. If necessary, round off two decimal places and answer up to one decimal place.
- 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.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=$_______________Suppose two firms, Firm A and Firm B, are competing by setting quantities (Cournot competition). Firm A has a constant marginal cost of $10 per unit; Firm B has a constant marginal cost of $15 per unit. Assume fixed costs are equal to 0 for both firms. Hint: since fixed costs are zero and the marginal cost is constant, MC = AC. The two firms choose between producing 50 units or 100 units. If the total output is 100 units, the price is $20 per unit; if total output is 150 units, the price is $15 per unit; if total output is 200 units, the price is $10 per unit. Based on the information provided, fill in the firms’ profits in the payoff matrix below with Firm A choosing the row and Firm B choosing the column. QB=100 QB=50 QA=100 , , QA=50 , , The resulting equilibrium is for Firm A to produce ____ (50 or 100)units and Firm B to produce_____ (50 or 100) units.
- 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.Question 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?Consider a Stackelberg duopoly:There are two firms in an industry with demand Q = 1 − Pd.The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF.Suppose now that the cost function is Ci(qi) = qi2 for i = L, F. (a) Find the subgame perfect equilibrium. (b) Compare the equilibrium you found with the Nash equilibrium if the game was simultaneous (i.e., Cournot competition). Is the Nash equilibrium of the Cournot game also a Nash equilibrium of the sequential game? Why or why not?