8. Suppose there are two identical firms in an industry who compete by settingquantities. The output of firm 1 is denoted by q1 and that of firm 2 is denotedby q2. Each firm faces a constant marginal cost of 3. Let Q denote total output,1.e. Qq1 +42. The inverse demand curve in the market is given byP-15-Q(d) Suppose firms interact repeatedly over an infinite horizon, and firms havea common discount factor & € (0,1). Specify a trigger strategy for eachfirm to sustain the collusive arrangement as an equilibrium outcome. Cal-culate the minimum value of & for which such a trigger strategycollusion as an equilibrium in the repeated interaction.ain

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 the minimum value of & for which such a trigger strategy collusion as an equilibrium in the repeated interaction. air

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 the minimum value of & for which such a trigger strategy collusion as an equilibrium in the repeated interaction. air

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

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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. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Q-91 +42. The inverse demand curve in the market is given by P-15-Q (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 ket? Assuming each firm produces half of the collusive output, the profit of each firm? the mar- what is (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…
8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Qq1 +42. The inverse demand curve in the market is given by P-15-Q (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?
3. Consider a duopoly with a demand curve given by P = a -bQ, where a and b are positive constants and Q is the total production by the two firms. Firms sell identical goods and have an identical constant marginal cost of production c. Fixed costs are equal to zero. We assume firms choose quantities simultaneously (Cournot competition). a. Obtain the first order condition of profit maximization for each firm. Use graphical analysis and economic intuition to explain what they represent. b. Obtain the profit maximizing quantity for each firm. Explain what they represent using game theory concepts c. Demonstrate using relevant graphical analysis and economic intuition that the results obtained in b are not a Pareto Optimum for the firms involved. d. How would the graphical analysis in part a change if Firm A had a fixed cost of production
Please no written by hand solution Considerthe following problem. There are five firms producing a homogenous good and competing in quantities simultaneously. The demand function for this good is given by D(p) = 100−p, where p denotes price. The marginal cost is the same for all firms and equals 40 Answer the following questions. (a) Compute the equilibrium quantities and profits of each firm. (b) Now suppose that two of these firms (say firms 1 and 2) want to merge. (The remaining firms stay unchanged.) Merging, however, is costly. To merge, each merging firm has to pay a fixed cost F. Determine the highest fixed cost F that the two firms would be willing to pay in order to proceed with the merger.
Q² 4 PROBLEM (4) Firm A and Firm B with identical total costs TCA (QA) related goods and competing in prices (Bertrand competition), with demands: QA = 510 - 2PA + pв and Qв= 510 - 2pв+ pa, respectively. = and TCB (QB) Q² 4 are producing (a) Calculate the Bertrand-Nash equilibrium prices. (b) Calculate the prices they charge when A is the leader and sets its price first, anticipating B's best response and taking it into account (like in Stackelberg competition). (c) Calculate the prices they charge when they collude, in order to maximize sum of their profits.
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 C
7. Suppose the market demand for a homogeneous product is given by P = a - bQ, where a and b are positive constants. There are n firms, with constant marginal costs, 0 ≤ c₁ ≤ C₂ ≤ ... ≤ Cn
2. Suppose that two firms with zero marginal costs are facing the inverse demand P=240-Q. Show that it is more advantageous to be the leader and announce your output decision first.
2. An industry contains two firms and the inverse demand function for the firms' output is P-180-30, where Q is the total output Suppose that firm I's cost and marginal cost functions are C(q)- 30q; and MC(q)-30, while firm 2's cost and marginal cost functions are C(q)-q² and MC(q)-2q2 a. Determine each firm's Nash equilibrium output. b. Determine each firm's profit at the Nash equilibrium output.
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 B