Duopoly: 1. Consider a duopoly game with 2 firms. The market inverse demand curve is given by P(Q) = 120-Q, where Q=q₁ + q₂ and q, is the quantity produced by firm qi i. The firm's long run total costs are given by C₁(q₁)=2q₁ and C₂(q2)=92, respectively. a. Determine the Nash Equilibrium for Cournot competition, in which firms compete based on quantity. What is each firm's best response as a function of the other firm's output? Graph these best response functions in on the same graph. Compute the associated payoffs for each firm. b. Determine the Nash Equilibrium for Bertrand competition, in which firms compete based on price and stand ready to meet market demand at that price. What is each firm's best response as a function of the other firm's price? Granh these bort rom

Duopoly: 1. Consider a duopoly game with 2 firms. The market inverse demand curve is given by P(Q) = 120-Q, where Q=q₁ + q₂ and q, is the quantity produced by firm qi i. The firm's long run total costs are given by C₁(q₁)=2q₁ and C₂(q2)=92, respectively. a. Determine the Nash Equilibrium for Cournot competition, in which firms compete based on quantity. What is each firm's best response as a function of the other firm's output? Graph these best response functions in on the same graph. Compute the associated payoffs for each firm. b. Determine the Nash Equilibrium for Bertrand competition, in which firms compete based on price and stand ready to meet market demand at that price. What is each firm's best response as a function of the other firm's price? Granh these bort rom

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

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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
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. In class, we showed that in a Cournot duopoly with demand p: ab(91 +92) and marginal costs of c₁ for firm 1 and c2 for firm two, the firms' best response functions were as follows: a C1 92 2b 91 a-c2 92 - 2b 91 822 and (a) Find equilibrium expressions for q₁ and q in terms of a, b, C1, and C2 only. (b) Show that the equilibrium price will be p": = a + c1 + €2 3
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?
Do question number 14 from the Oligopoly and Game Theory chapter. This is the first challenge question (at least for me) and starts out "The French economist Antoine Cournot developed an interesting model of competition....." Picture below. For the graph note that both reaction functions should be on the same graph. This graph should have Firm X quantity on one axis and Firm Y quantity on the other. One curve gives you the quantity of firm X for every given quantity of firm Y and the other curve gives the quantity of firm Y for any given quantity by firm X. In other words, even though they are the same function, there should be two different lines on the graph. Your submission should include the table, the graph and the answer to the question at the end with description. Please try to think carefully about the description. It shouldn't be long but there is a key idea I want to be sure that you get. One sentence should be enough if you get the thing.
What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q= 1,800 - 1,000p. and each firm's marginal cost is $0.28 per unit? The Cournot-Nash equilibrium occurs where q, equals and 92 equals (Enter numenic responses using real numbers rounded to two decimai places.) Furthermore, the equilibrium occurs at a price of $ (Round your answer to the nearest penny.)
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?
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.
How do I determine values for Y that have dominant strategy? What is the Nash equilibirum? If the Market demand for two companies is P=120-Q and marginal cost is 20. How will the payoff matrix with strategies for each that show cournot equilibirum quantity/half of the monopoly quantity look? How do i solve for the nash equilibrium?
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?
3. Consider a model of Cournot duopoly. Two firms produce an identical product. The inverse demand function for the product is given by p = 60-y, where y = y₁ + y2 is the sum of the quantity produced by the two firms. Production costs are zero for both firms. a) Find the quantity produced by each firm in the Nash equilibrium of this game. Find the price of the product and the profit of each firm. b) Now say that marketing guru Jim has a proposal for firm 1. He would be able to convince people that the two firms' products were in fact slightly different from each other, so that the amount produced by each firm would not impact the price of the other's product as much as it did before. The inverse demand function for each product would become P₁ = 60-9₁-92 and p2 = 60 - 92 - -9₁. What is the most that firm 1 would be willing to pay Jim to do this? Show your work and explain in a few sentences what you did to find your answer.
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