(a) Describe the concept of a (pure strategy) Nash equilibrium; provide an illustrative example. Describe the concept of a mixed-strategy Nash equilibrium; provide an illustrative example. Within the context of oligopoly, discuss the differences between a Cournot-Nash equilibrium and a Bertrand-Nash equilibrium. (b) In terms of output, price, consumer surplus, profits and societal welfare, contrast the monopoly equilibrium with the perfectly competitive equilibrium. Describe how the introduction of: (i) perfect price discrimination; and, (ii) increasing returns to scale (i.e. a downward sloping average cost curve) would impact on this comparison?!

(a) Describe the concept of a (pure strategy) Nash equilibrium; provide an illustrative example. Describe the concept of a mixed-strategy Nash equilibrium; provide an illustrative example. Within the context of oligopoly, discuss the differences between a Cournot-Nash equilibrium and a Bertrand-Nash equilibrium. (b) In terms of output, price, consumer surplus, profits and societal welfare, contrast the monopoly equilibrium with the perfectly competitive equilibrium. Describe how the introduction of: (i) perfect price discrimination; and, (ii) increasing returns to scale (i.e. a downward sloping average cost curve) would impact on this comparison?!

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

See similar textbooks

Similar questions

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
. OPEC, the Organization of Petroleum Exporting Countries, was founded in 1969. Their original objective was to form a cartel to increase the price that they receive for their oil exports. Create a prisoner’s dilemma type game for two large members of OPEC (e.g. Saudi Arabia and Indonesia). Create numbers, where payoffs are total annual oil export revenues for each of these two countries. Verbally explain how you got your numbers. Find the Nash equilibrium. Based on this model, what strategy is in the oil exporters’ best interest (Nash or otherwise)? How do they make it happen? Create another prisoner’s dilemmamodel for all of OPEC on one side, and all non OPEC oil exporting nations on the other side. Create numbers, where payoffs are total annual oil export revenues for each of the two sides. Verbally explain how you created your numbers. Also create your numbers applying the fact that OPEC’s total production capacity is greater than total non OPEC exports…
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.
Duopoly: 1. Consider a duopoly game with 2 firms. The market inverse demand curve is given by P(Q) = 120-Q, where Q = 9₁ +9₂ and q; is the quantity produced by firm i. The firm's long run total costs are given by C₁(9₁)=2q₁ and C₂(92)=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? Graph these best response functions in on the same graph. Compute the associated payoffs for each firm. Game Th
(b) Compare and contrast the non-cooperative and cooperative outcomes when duopolists are involved in quantity competition. (c) Does the Nash equilibrium outcome of a one-shot game have to be unique? Provide an example to illustrate your point.
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.
5) The following set of (extensive form) games represent two firms who are attempting to form a cartel. The firms are called "A" and "B". The moves each can make are "Increase output" (1 ) and "don't increase output"(X). The first game (shown below) represents their behavior in a single period where they act simultaneously, unaware of what their opponent is doing. Nash Equilibrium (NE) A: В: A A: 3 A: 1 A: 4 A: 2 B: 3 B: 4 B: 1 B: 2 a. Solve the game by the Rollback (backward induction) method by identifying the dominant strategies (the ones that the players choose), and circle the Nash Equilibrium (for the entire game) and write it above the starting node.
Suppose OPEC has only two producers, Saudi Arabia and Nigeria, Saudi Arabia has far more oil reserves and is the lower-cost producer compared to Nigeria. The payoff matrix in the table to the right shows the profits earned per day by each country. "Low output" corresponds to producing the OPEC assigned quota and "high output" corresponds to producing the maximum capacity beyond the assigned quota Which of the following statements is true? OA. The Nash equilibrium is a cooperative equilibrium. OB. The Nash equilibrium is a noncooperative, dominant strategy equilibrium OC. The Nash equilibrium is a collusive equilibrium. D. There is no Nash equilibrium in this game because each party. pursues its dominant strategy. Low output Nigeria High output Low output Nigeria earns $20 million Saudi Arabia Nigeria earns $30 million Saudi Arabia earns $100 million Saudi Arabia earns $80 million High output Nigeria earns $12 million Saudi Arabia earns $75 million Nigeria earns $20 million Saudi Arabia…
This is a Microeconomics problem. Two firms A and B operating in the same market must choose between a collude price and a cheat price. Answer the following questions in order. (a) Does Firm A have a dominant strategy? Explain your answer. (b) Does Firm B have a dominant strategy? Explain your answer. (c) Is there an equilibrium solution to the above game? (d) Is this equilibrium solution to the game the most "ideal" outcome for the players? Explain clearly why or why not.
Question 1 (40 points) Consider a homogeneous duopoly market where two firms compete in prices. Demand is given by D 8-2p, where p is price. Marginal cost of production is 2. a)lf the individual capacity of both firms is 2, is there an equilibrium in pure strategies? If so, what are the equilibrium prices? If not, provide a proof. b) Consider then that a third firm enters the market and that all three firms have a capacity of 2. Does an equilibrium in pure strategies exist? If so, what are the equilibrium prices? If not, why not? c) Does you answer under b) change if the firms' capacities are respectively equal to 1, 2 and 3?.
5) Use a supply and demand diagram like in the slide titled "From monopoly to Cournot duopoly" to explain conceptually the supply decision that leads to a Cournot Nash equilibrium, and why it has lower price and total profits than the collusive (monopoly) supply. Optionally you can also use precise numbers: assume market demand behaves like P=36-3Q, (Q=Q1 +Q2), and the constant marginal cost is MC=18, then solve for price and profits, both under collusion and Cournot competition. Hint: you will need to solve for each oligopolist's supply decision contingent on that of the other, so-called best-response functions. You may consult the Perloff excerpt for the individual steps.
2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ = [0, 1], and the strategy s₁ of Firm 1 corresponds to the amount of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S2 = [0, 1], and the strategy s2 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1 — 81 — 82, the utility of Firm 1 would be their profit, u₁ (81, 82) = (1-81-82 - c)81, and the utility of Firm 2 would be their profit, u2($1, $2) = (1-81-82-c)s2, where 0 ≤ c< 1 is the marginal cost of production for both firms. (a) Find the pure-strategy Nash equilibria of this game. (b) Are there other Nash equilibria in this game.