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: а. Find the firms' best response functions. Solve for the Cournot Nash Equilibrium of the game. What is the total industry output in equilibrium? What is the equilibrium price? b. с. 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. 2.
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- 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 1.1. 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.
- 4. In 2056, there are two mining firms operating on the moon, extracting Helium 3. Once both firms have entered the market, they compete a la Cournot. The market inverse demand function is given by P(Q) = 8 – Q. Assume that both firms have the total cost functions = 2+ 2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which C(q): of the following statements is true? (a) qi = 4 = 4 (b) qi > qž (c) p* = 6 (d) nj < T (e) Tỉ = = 2 5. Assume the same demand and cost structures as in question 4, but now firm 1 enters the market first and firm 2 follows, as in the Stackelberg model from lecture (both firms are guar- anteed to enter; the only choice is quantities produced). Which of the following statements regarding the equilibrium outcome is FALSE? (a) The first mover produces a greater quantity than the second mover (b) Total market output is Q* = 4.5 (c) The second mover will receive a negative profit (d) The first mover will receive a greater profit than the…1. Best responses in a Cournot Oligopoly Firm A and Firm B sell identical goods Total market demand for the good is: The inverse demand function is therefore 1 P(QM) = 780 -Q=780 -0.02222QM 45 QM is total market production (i.e., combined production of firm's A and B. That is: Q(P) = 35, 100- 45P 2M = A +QB As a result, the inverse demand curve for each firm is: P(QA, QB) = 780- -1/32₁-752 45 Unlike the example in class, the two firms have different costs. = 4000A TCA (QA) TCB (QB) = 260QB = 780 -0.022220A -0.02222QB a. Using the demand function and the cost functions above, what is firm A's profit function. b. Using the profit function above and assuming that firm B produces Qg, calculate what firm A's best response is to firm B’s decision to produce QB- Note: Firm A's best response should be a function of BThree 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.
- 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?* 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…Give typing answer with explanation and conclusion Suppose two firms produce identical good. The inverse demand curve for the good is: P = 240-Q, where Q is the total quantity produced by the two firms. Each firm has a constant marginal cost 20 of producing the good and fixed cost = 100. Find the Cournot Nash equilibrium of this game. What quantity will each firm produce? what will be the market price? What would be the profits of each firm?
- 12. Two firms with differentiated products are competing in price. Firm A and B face the following demand curves: QA = 90 – 2PĄ + Pg and QB = 140 – 2Pg + PA respectively. 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 equilibrium price, quantity, and profit for each firm? c. Suppose A sets its price first and then B responds. What price and quantity does each firm set now? Is it advantageous to move first? d. Compare the profits from part b and c. Which firm benefits more from the sequential price choosing?4. In 2056, there are two mining firms operating on the moon, extracting Helium 3. Once both firms have entered the market, they compete a la Cournot. The market inverse demand function is given by P(Q) = 8 - Q. Assume that both firms have the total cost functions C(q) =2+2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which of the following statements is true? (a) q₁ =q2 = 4 (b) qt > 92 (c) p* = 6 (d) π₁ < π₂ (e) T₁ = π = 2 the C1. 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?