Answer Key. q C. Firm i s profit-maximization problem (PMP) is given by. }{{} i + γ(a q i q j c)q Firm j s profit
|
|
- Wesley Walsh
- 5 years ago
- Views:
Transcription
1 Homework #5 - Econ 57 (Due on /30) Answer Key. Consider a Cournot duopoly with linear inverse demand curve p(q) = a q, where q denotes aggregate output. Both firms have a common constant marginal cost c > 0, and where a > c. Assume that firms do an equity swap of γ, i.e., each firm i receives a share 0 < γ in firm j s profits, where j i. (a) Find the Cournot equilbrium output, (q C, q C ). Firm i s profit-maximization problem (PMP) is given by max q i ( γ)(a q i q j c)q }{{} i + γ(a q i q j c)q }{{} j Firm i s profit Firm j s profit Taking first-order conditions with respect to q i yields ( γ)(a q i q j c) ( γ)q i γq j = 0 In a symmetric equilibrium q C i = q C j = q C, which lets us simplify the above expression as follows ( γ)(a q C c) ( γ)q C γq C = 0 which, solving for q C yields q C = ( γ)(a c) 3 γ (b) Evaluate equilibrium output q C i at γ = 0 and γ =. Interpret. When firms do not benefit from each other s profits, γ = 0, equilibrium output q C becomes a c, thus coinciding with that under the standard Cournot model 3 with linear inverse demand curve p(q) = a q. In contrast, when firms fully share their profits, γ = /, equilibrium output q C becomes a c 4, thus coinciding with half of monopoly output (or cartel output). (c) Determine if q C i increases or decreases in γ. Differentiating q C with respect to share γ yields q C γ = a c 3 γ + ( γ)(a c) (3 γ)
2 which simplifies to a c (3 γ) which is clearly negative since a > c by definition. Intuitively, as firms share more of each other s profits, their individual PMP resembles the joint PMP in a cartel, leading each of them to reduce its production. For illustrative purpose, figure depicts q C as a function of the profit share γ. For simplicity, we consider a = and c = 0 which yields a output q C = γ 3 γ. (d) Find equilibrium profits, π C, and determine whether they increase or decrease in γ. Equilibrium profits are π C = ( γ)(a c) (3 γ) which increase in γ since π C γ = ( γ)(a c) (3 γ) 3 is positive given that γ by definition. Intuitively, as firms take more into account each other s profits, their individual profits approach those they would obtain under a cartel agreement, which are larger than under a standard Cournot model.. Consider a homogeneous good industry with two potential firms. Market demand is given by Q = ( p), where is the market size and Q is the industry output. Firms have zero constant marginal costs but incur a fixed cost k ( 0, 9 ) if they are active. The time structure of the game is as follows: First, they decide wether or not to enter. Then, they compete in the product market. For the following three different forms of competition, find equilibrium quantities, prices, profits, consumer surplus and welfare: (a) Firms independently and simultaneously choose quantities (Cournot competition).
3 To analyze the case of quantity competition, we first find the inverse demand function (solving for p), which is p = Q. A firm i chooses q i to maximize π i = The first-oder conditions are [ q ] i + q j q i k π i q i = q i q j = 0 At the symmetric equilibrium q i = q j = q the solution will be given by q C = 3. Equilibrium prices and individual profits will be p C = 3 and πc = 9 k > 0. It is easy to find consumer surplus and total welfare as C C = ( p)( ( ( p) = ) 3) 3 = and W C = C C + π C = 4 k. 9 9 (b) Firms non-cooperatively choose prices (Bertrand competition); Given that products are homogeneous, competition would bring about zero (short-run) profits, which would not allow both firms to cover fixed costs. Therefore, at the (long-run) equilibrium in pure strategies only one firm will be active in this market. This firm will choose Q so as to maximize monopoly profits π i = [ Q ] Q k Taking first-oder conditions with respect to Q, we find that equilibrium output, price and profits will be Q B =, pb =, and πb = [ ] k = k > 0. Consumer surplus and total welfare are 4 CB = ( p)( p) = ( ) ( ) = and W B = C B + π B = 3 k. (c) Firms set quantities (or prices, it is equivalent) so as to jointly maximize their profits (cartel). Firms will set outputs q and q so as to maximize the joint profits π + π = [ q ] + q (q + q ) k Clearly, this gives rise to the same solution as in the Bertrand case (where a single firm sets aggregate output Q as a monopolist) but with duplication in the fixed costs. Consumer surplus and total welfare are C M = ( p)( p) = ( ) ( ) = 3
4 and W M = C M + π M = 3 k. (d) Compare the social welfare resulting from the three forms of competition analyzed in parts (a)-(c). Comparing W C and W B, we find that W C W B if and only if 4 k k, or if k satisfies k, as depicted in the upper region of figure 3. 7 (Note that, by definition, k.) 9 In addition, note that the cartel (or monopoly) yields the lowest social welfare since W M < W C and W M < W B. Indeed W M < W C since 3 k < 4 9 k for all k > 5 7 (which holds by definition since k > 0), while W M < W B given that 3 k < 3 k for all values of k. 3. Consider an industry with n identical firms competing a la Cournot. uppose that the inverse demenad function is P (Q) = a bq, where Q is total industry output, and a, b > 0. Each firm has a marginal costs, c, where c < a, and no fixed costs. (a) (no merger) Find the equilibrium output that each firm produces at the symmetric Cournot equilibrium, What is the aggregate output and the equilibrium price? What are the profits that every firm obtains in the Cournot equilibrium? What is the equilibrium social welfare? at the symmetric equilibrium with n firms, we have that each firm i maximizes max (a bq i bq i ) q i cqi () where Q i q j denotes the aggregate production of all other j i firms. taking F.O.C. with respect to q i, we obtain a bq i bq i c = 0 () An at the symmetric equilibrium Q i = (n )q i. Hence, the above FOCs become a b(n )qi q i bqi q i c = 0 or a c = b(n + )qi. olving for q i, we find that the individual output level in equilibrium is q i = a c (n + )b (3) Hence, aggregate output level in equilibrium is Q = nqi q i = n n+ 4 a c; while the b
5 equilibrium price is p = a+cn and equilibrium profits are n+ π i = (a c). b(n+) Q The level of social welfare with n firms, Wn, is defined by W n = [a bq] dq cq. Calculating the integral, i.e., yields Q [a bq] dq cq = aq b Q, and substituting for Q 0 W n = n(n + )(a c) n(n + ) (4) 0 (b) (Merger) Now let m out of n firms merge. how that the merger is profitable if and only if it involves a sufficiently large number of firms. Assume that m out of n firms merge. While before the merger there are n firms in this industry,, after there are n m +. In order to examine whether the merger is profitable for the m mergerd firms, we need to show that the profit after the merger, π n m+, satisfies π n m+ mπ n.that is (a c) m(a c)(n + ) (5) (n m + ) solving for n, we obtain that n < m m, note that this condition is compatible with the fact that the merger must involve a subset of all firms, i.e., m n. alternative interpretation of the condition can be found by first solving for m, which yields m > n n m; and, second, finding the market share that this minimal number of firms represents, i.e., α = m n = 3+n 5+4n n (c) Are the profits of the nonmerged firms larger when m of their competitors merge than when they do not? The number of firms producing the Cournot output decreases (since the merged firms produce a smaller output), implying that each of the nonmerged firms earns larger profits after the merger. This condition holds for mergers of any size, i.e., both when condition n < m m and otherwise. This surprising result is often referred as the merger paradox as it is the nonmerged firms the ones seeing their profits increase for all paremeters values. 4. Consider a tackelberg duopoly model with the following timing: () firm chooses a quantity q 0; () firm observes q and then chooses a quantity q 0; (3) the payoff to firm i is given by the profit function π i (q i, q j ) = q i [P (Q) c], An 5
6 where P (Q) = a Q is the market-clearing price when the aggregate quantity on the market is Q = q + q. (a) Use backward induction to find the production levels as a function of the marginal cost to the firms of c and of parameter a. Using backwards-induction, firm s profit maximization is max q [a q q c] (6) with FOC a q q c = 0 (7) solving for q, we obtain firm s best response function q (q ) = a c q () Moving to the first period, firm s maximization problem is max q [a c q q(q )] c] (9) with FOC a c q = 0 or q = a c and substituting into firm s best response function q = a c 4. (b) olve for each firm s profit levels π and π, in the backwards-induction outcome, when Firm moves first. Give the sign for and interpret π i c i = {, }. for every firm The equilibrium price is p = a+3c 4 and profits are π = (a c) and π = (a c) 6. Differentiating both firms profits with respect to c, π c = a c < 0 4 (0) π c = a c < 0 () whivh indicates that as costs rise, the profits for both firms fall, with the profit for firm falling at twice the rate as the profit for firm. (c) Consider now the following variation in the tackelberg game: Firm is given the following choice before either firm chooses production levels. For some set value of K > 0, it is told that if it pays K, it will get to be the first-mover in the tackelberg game. If it does not pay K, it will be the tackelberg follower. 6
7 . As a function of c and a, solve for the highest K, K, that Firm would pay for the first-move advantage. Firm would be willing to pay any K, such that its profits as the leader are weekly higher than its profits as the follower, i.e., (a c) K (a c) 6 () olving for K, firm would be willing to pay any K such that K (a c). 6. Comparative statics. olve for and give an interpretation of K K and. c a olving for the two derivatives K c = a c < 0 (3) K a = a c > 0 (4) The first derivative implies that as cots go up, firm would be willing to pay less in order to be tackelberg leader, which is consistent with our results from the last part as the profits for the leader fall faster than the profits for the follower. The second derivative implies that as the size of the market increases, firm is willing to pay more to be the tackelberg leader as its profit level will increase more as the stackelberg leader than as the follower. 7
Exercises Solutions: Oligopoly
Exercises Solutions: Oligopoly Exercise - Quantity competition 1 Take firm 1 s perspective Total revenue is R(q 1 = (4 q 1 q q 1 and, hence, marginal revenue is MR 1 (q 1 = 4 q 1 q Marginal cost is MC
More informationNoncooperative Oligopoly
Noncooperative Oligopoly Oligopoly: interaction among small number of firms Conflict of interest: Each firm maximizes its own profits, but... Firm j s actions affect firm i s profits Example: price war
More informationEcon 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
More informationEconS 424 Strategy and Game Theory. Homework #5 Answer Key
EconS 44 Strategy and Game Theory Homework #5 Answer Key Exercise #1 Collusion among N doctors Consider an infinitely repeated game, in which there are nn 3 doctors, who have created a partnership. In
More informationCournot with N rms (revisited)
Cournot with N rms (revisited) Cournot model with N symmetric rms, constant unit variable cost c, and inverse demand function P(Q) = a bq where Q = N i=1 q i The results: q = a c b (1 + N) p = a + Nc 1
More informationDUOPOLY. MICROECONOMICS Principles and Analysis Frank Cowell. July 2017 Frank Cowell: Duopoly. Almost essential Monopoly
Prerequisites Almost essential Monopoly Useful, but optional Game Theory: Strategy and Equilibrium DUOPOLY MICROECONOMICS Principles and Analysis Frank Cowell 1 Overview Duopoly Background How the basic
More informationLecture 9: Basic Oligopoly Models
Lecture 9: Basic Oligopoly Models Managerial Economics November 16, 2012 Prof. Dr. Sebastian Rausch Centre for Energy Policy and Economics Department of Management, Technology and Economics ETH Zürich
More informationOligopoly (contd.) Chapter 27
Oligopoly (contd.) Chapter 7 February 11, 010 Oligopoly Considerations: Do firms compete on price or quantity? Do firms act sequentially (leader/followers) or simultaneously (equilibrium) Stackelberg models:
More informationMICROECONOMICS AND POLICY ANALYSIS - U8213 Professor Rajeev H. Dehejia Class Notes - Spring 2001
MICROECONOMICS AND POLICY ANALYSIS - U813 Professor Rajeev H. Dehejia Class Notes - Spring 001 Imperfect Competition Wednesday, March 1 st Reading: Pindyck/Rubinfeld Chapter 1 Strategic Interaction figure
More informationECO410H: Practice Questions 2 SOLUTIONS
ECO410H: Practice Questions SOLUTIONS 1. (a) The unique Nash equilibrium strategy profile is s = (M, M). (b) The unique Nash equilibrium strategy profile is s = (R4, C3). (c) The two Nash equilibria are
More informationHorizontal Mergers. Chapter 11: Horizontal Mergers 1
Horizontal Mergers Chapter 11: Horizontal Mergers 1 Introduction Merger mania of 1990s disappeared after 9/11/2001 But now appears to be returning Oracle/PeopleSoft AT&T/Cingular Bank of America/Fleet
More informationEC 202. Lecture notes 14 Oligopoly I. George Symeonidis
EC 202 Lecture notes 14 Oligopoly I George Symeonidis Oligopoly When only a small number of firms compete in the same market, each firm has some market power. Moreover, their interactions cannot be ignored.
More informationStrategic Production Game 1
Lec5-6.doc Strategic Production Game Consider two firms, which have to make production decisions without knowing what the other is doing. For simplicity we shall suppose that the product is essentially
More informationEcon 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
More informationCUR 412: Game Theory and its Applications, Lecture 9
CUR 412: Game Theory and its Applications, Lecture 9 Prof. Ronaldo CARPIO May 22, 2015 Announcements HW #3 is due next week. Ch. 6.1: Ultimatum Game This is a simple game that can model a very simplified
More informationLecture Note 3. Oligopoly
Lecture Note 3. Oligopoly 1. Competition by Quantity? Or by Price? By what do firms compete with each other? Competition by price seems more reasonable. However, the Bertrand model (by price) does not
More informationMKTG 555: Marketing Models
MKTG 555: Marketing Models A Brief Introduction to Game Theory for Marketing February 14-21, 2017 1 Basic Definitions Game: A situation or context in which players (e.g., consumers, firms) make strategic
More informationEcon 302 Assignment 3 Solution. a 2bQ c = 0, which is the monopolist s optimal quantity; the associated price is. P (Q) = a b
Econ 302 Assignment 3 Solution. (a) The monopolist solves: The first order condition is max Π(Q) = Q(a bq) cq. Q a Q c = 0, or equivalently, Q = a c, which is the monopolist s optimal quantity; the associated
More informationSolution Problem Set 2
ECON 282, Intro Game Theory, (Fall 2008) Christoph Luelfesmann, SFU Solution Problem Set 2 Due at the beginning of class on Tuesday, Oct. 7. Please let me know if you have problems to understand one of
More informationEconS Oligopoly - Part 3
EconS 305 - Oligopoly - Part 3 Eric Dunaway Washington State University eric.dunaway@wsu.edu December 1, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 33 December 1, 2015 1 / 49 Introduction Yesterday, we
More informationEcon 101A Final exam Th 15 December. Do not turn the page until instructed to.
Econ 101A Final exam Th 15 December. Do not turn the page until instructed to. 1 Econ 101A Final Exam Th 15 December. Please solve Problem 1, 2, and 3 in the first blue book and Problems 4 and 5 in the
More informationEconS 424 Strategy and Game Theory. Homework #5 Answer Key
EconS 44 Strategy and Game Theory Homework #5 Answer Key Exercise #1 Collusion among N doctors Consider an infinitely repeated game, in which there are nn 3 doctors, who have created a partnership. In
More informationStatic Games and Cournot. Competition
Static Games and Cournot Introduction In the majority of markets firms interact with few competitors oligopoly market Each firm has to consider rival s actions strategic interaction in prices, outputs,
More informationECON/MGMT 115. Industrial Organization
ECON/MGMT 115 Industrial Organization 1. Cournot Model, reprised 2. Bertrand Model of Oligopoly 3. Cournot & Bertrand First Hour Reviewing the Cournot Duopoloy Equilibria Cournot vs. competitive markets
More informationGS/ECON 5010 Answers to Assignment 3 November 2005
GS/ECON 5010 Answers to Assignment November 005 Q1. What are the market price, and aggregate quantity sold, in long run equilibrium in a perfectly competitive market for which the demand function has the
More informationDUOPOLY MODELS. Dr. Sumon Bhaumik (http://www.sumonbhaumik.net) December 29, 2008
DUOPOLY MODELS Dr. Sumon Bhaumik (http://www.sumonbhaumik.net) December 29, 2008 Contents 1. Collusion in Duopoly 2. Cournot Competition 3. Cournot Competition when One Firm is Subsidized 4. Stackelberg
More informationResearch Article Welfare Comparison of Leader-Follower Models in a Mixed Duopoly
Applied Mathematics Volume 03 Article ID 307 7 pages http://dx.doi.org/0.55/03/307 Research Article Welfare Comparison of Leader-Follower Models in a Mixed Duopoly Aiyuan Tao Yingjun Zhu and Xiangqing
More informationEstimating Market Power in Differentiated Product Markets
Estimating Market Power in Differentiated Product Markets Metin Cakir Purdue University December 6, 2010 Metin Cakir (Purdue) Market Equilibrium Models December 6, 2010 1 / 28 Outline Outline Estimating
More informationECON106P: Pricing and Strategy
ECON106P: Pricing and Strategy Yangbo Song Economics Department, UCLA June 30, 2014 Yangbo Song UCLA June 30, 2014 1 / 31 Game theory Game theory is a methodology used to analyze strategic situations in
More informationis the best response of firm 1 to the quantity chosen by firm 2. Firm 2 s problem: Max Π 2 = q 2 (a b(q 1 + q 2 )) cq 2
Econ 37 Solution: Problem Set # Fall 00 Page Oligopoly Market demand is p a bq Q q + q.. Cournot General description of this game: Players: firm and firm. Firm and firm are identical. Firm s strategies:
More informationElements of Economic Analysis II Lecture XI: Oligopoly: Cournot and Bertrand Competition
Elements of Economic Analysis II Lecture XI: Oligopoly: Cournot and Bertrand Competition Kai Hao Yang /2/207 In this lecture, we will apply the concepts in game theory to study oligopoly. In short, unlike
More informationAnswers to Microeconomics Prelim of August 24, In practice, firms often price their products by marking up a fixed percentage over (average)
Answers to Microeconomics Prelim of August 24, 2016 1. In practice, firms often price their products by marking up a fixed percentage over (average) cost. To investigate the consequences of markup pricing,
More informationMicroeconomics III. Oligopoly prefacetogametheory (Mar 11, 2012) School of Economics The Interdisciplinary Center (IDC), Herzliya
Microeconomics III Oligopoly prefacetogametheory (Mar 11, 01) School of Economics The Interdisciplinary Center (IDC), Herzliya Oligopoly is a market in which only a few firms compete with one another,
More informationHomework # 8 - [Due on Wednesday November 1st, 2017]
Homework # 8 - [Due on Wednesday November 1st, 2017] 1. A tax is to be levied on a commodity bought and sold in a competitive market. Two possible forms of tax may be used: In one case, a per unit tax
More informationMS&E HW #1 Solutions
MS&E 341 - HW #1 Solutions 1) a) Because supply and demand are smooth, the supply curve for one competitive firm is determined by equality between marginal production costs and price. Hence, C y p y p.
More informationA monopoly is an industry consisting a single. A duopoly is an industry consisting of two. An oligopoly is an industry consisting of a few
27 Oligopoly Oligopoly A monopoly is an industry consisting a single firm. A duopoly is an industry consisting of two firms. An oligopoly is an industry consisting of a few firms. Particularly, l each
More informationUC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 201A) Fall 2012
UC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 01A) Fall 01 Oligopolistic markets (PR 1.-1.5) Lectures 11-1 Sep., 01 Oligopoly (preface to game theory) Another form
More informationProblem 3,a. ds 1 (s 2 ) ds 2 < 0. = (1+t)
Problem Set 3. Pay-off functions are given for the following continuous games, where the players simultaneously choose strategies s and s. Find the players best-response functions and graph them. Find
More informationECONS 424 STRATEGY AND GAME THEORY MIDTERM EXAM #2 ANSWER KEY
ECONS 44 STRATEGY AND GAE THEORY IDTER EXA # ANSWER KEY Exercise #1. Hawk-Dove game. Consider the following payoff matrix representing the Hawk-Dove game. Intuitively, Players 1 and compete for a resource,
More informationIntroduction to Industrial Organization Professor: Caixia Shen Fall 2014 Lecture Note 5 Games and Strategy (Ch. 4)
Introduction to Industrial Organization Professor: Caixia Shen Fall 2014 Lecture Note 5 Games and Strategy (Ch. 4) Outline: Modeling by means of games Normal form games Dominant strategies; dominated strategies,
More informationStrategic Pre-Commitment
Strategic Pre-Commitment Felix Munoz-Garcia EconS 424 - Strategy and Game Theory Washington State University Strategic Commitment Limiting our own future options does not seem like a good idea. However,
More informationName: Midterm #1 EconS 425 (February 20 th, 2015)
Name: Midterm # EconS 425 (February 20 th, 205) Question # [25 Points] Player 2 L R Player L (9,9) (0,8) R (8,0) (7,7) a) By inspection, what are the pure strategy Nash equilibria? b) Find the additional
More informationMath 152: Applicable Mathematics and Computing
Math 152: Applicable Mathematics and Computing May 22, 2017 May 22, 2017 1 / 19 Bertrand Duopoly: Undifferentiated Products Game (Bertrand) Firm and Firm produce identical products. Each firm simultaneously
More informationEconS Micro Theory I 1 Recitation #9 - Monopoly
EconS 50 - Micro Theory I Recitation #9 - Monopoly Exercise A monopolist faces a market demand curve given by: Q = 70 p. (a) If the monopolist can produce at constant average and marginal costs of AC =
More informationMicroeconomics I - Seminar #9, April 17, Suggested Solution
Microeconomics I - Seminar #9, April 17, 009 - Suggested Solution Problem 1: (Bertrand competition). Total cost function of two firms selling computers is T C 1 = T C = 15q. If these two firms compete
More informationSOLVING COURNOT, STACKELBERG AND COLLUSION GAMES USING R
SOLVING COURNOT, STACKELBERG AND COLLUSION GAMES USING R GIACOMO FRANCHINI AND MATTEO BONFANTI 1. Introduction The issue we would like to cover in this brief guide is how to run Cournot, Stackelberg Games
More informationEconS Industrial Organization Assignment 6 Homework Solutions
EconS 45 - Industrial Organization Assignment 6 Homework Solutions Assignment 6-1 Return to our vertical integration example we looked at in class today. Suppose now that the downstream rm requires two
More informationLECTURE NOTES ON GAME THEORY. Player 2 Cooperate Defect Cooperate (10,10) (-1,11) Defect (11,-1) (0,0)
LECTURE NOTES ON GAME THEORY September 11, 01 Introduction: So far we have considered models of perfect competition and monopoly which are the two polar extreme cases of market outcome. In models of monopoly,
More informationChapter 11: Dynamic Games and First and Second Movers
Chapter : Dynamic Games and First and Second Movers Learning Objectives Students should learn to:. Extend the reaction function ideas developed in the Cournot duopoly model to a model of sequential behavior
More informationStatic Games and Cournot. Competition
Static Games and Cournot Competition Lecture 3: Static Games and Cournot Competition 1 Introduction In the majority of markets firms interact with few competitors oligopoly market Each firm has to consider
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationGame Theory with Applications to Finance and Marketing, I
Game Theory with Applications to Finance and Marketing, I Homework 1, due in recitation on 10/18/2018. 1. Consider the following strategic game: player 1/player 2 L R U 1,1 0,0 D 0,0 3,2 Any NE can be
More informationBusiness Strategy in Oligopoly Markets
Chapter 5 Business Strategy in Oligopoly Markets Introduction In the majority of markets firms interact with few competitors In determining strategy each firm has to consider rival s reactions strategic
More informationEcon 815 Dominant Firm Analysis and Limit Pricing
Econ 815 Dominant Firm Analysis and imit Pricing I. Dominant Firm Model A. Conceptual Issues 1. Pure monopoly is relatively rare. There are, however, many industries supplied by a large irm and a ringe
More informationNoncooperative Market Games in Normal Form
Chapter 6 Noncooperative Market Games in Normal Form 1 Market game: one seller and one buyer 2 players, a buyer and a seller Buyer receives red card Ace=11, King = Queen = Jack = 10, 9,, 2 Number represents
More informationHW Consider the following game:
HW 1 1. Consider the following game: 2. HW 2 Suppose a parent and child play the following game, first analyzed by Becker (1974). First child takes the action, A 0, that produces income for the child,
More informationDuopoly models Multistage games with observed actions Subgame perfect equilibrium Extensive form of a game Two-stage prisoner s dilemma
Recap Last class (September 20, 2016) Duopoly models Multistage games with observed actions Subgame perfect equilibrium Extensive form of a game Two-stage prisoner s dilemma Today (October 13, 2016) Finitely
More informationMICROECONOMICS II. Author: Gergely K hegyi. Supervised by Gergely K hegyi. February 2011
MICROECONOMICS II. Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics, Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE) Department
More informationTable 10.1: Elimination and equilibrium. 1. Is there a dominant strategy for either of the two agents?
Chapter 10 Strategic Behaviour Exercise 10.1 Table 10.1 is the strategic form representation of a simultaneous move game in which strategies are actions. s b 1 s b 2 s b 3 s a 1 0, 2 3, 1 4, 3 s a 2 2,
More informationEconomics Honors Exam 2008 Solutions Question 1
Economics Honors Exam 2008 Solutions Question 1 (a) (2 points) The steel firm's profit-maximization problem is max p s s c s (s, x) = p s s αs 2 + βx γx 2 s,x 0.5 points: for realizing that profit is revenue
More informationThese notes essentially correspond to chapter 13 of the text.
These notes essentially correspond to chapter 13 of the text. 1 Oligopoly The key feature of the oligopoly (and to some extent, the monopolistically competitive market) market structure is that one rm
More informationTitle: The Relative-Profit-Maximization Objective of Private Firms and Endogenous Timing in a Mixed Oligopoly
Working Paper Series No. 09007(Econ) China Economics and Management Academy China Institute for Advanced Study Central University of Finance and Economics Title: The Relative-Profit-Maximization Objective
More informationAnswer Key: Problem Set 4
Answer Key: Problem Set 4 Econ 409 018 Fall A reminder: An equilibrium is characterized by a set of strategies. As emphasized in the class, a strategy is a complete contingency plan (for every hypothetical
More informationWhen one firm considers changing its price or output level, it must make assumptions about the reactions of its rivals.
Chapter 3 Oligopoly Oligopoly is an industry where there are relatively few sellers. The product may be standardized (steel) or differentiated (automobiles). The firms have a high degree of interdependence.
More informationAdvertisement Competition in a Differentiated Mixed Duopoly: Bertrand vs. Cournot
Advertisement Competition in a Differentiated Mixed Duopoly: Bertrand vs. Cournot Sang-Ho Lee* 1, Dmitriy Li, and Chul-Hi Park Department of Economics, Chonnam National University Abstract We examine the
More informationStrategic export policy, monopoly carrier, and product differentiation
MPRA Munich Personal RePEc Archive Strategic export policy, monopoly carrier, and product differentiation Kazuhiro Takauchi Faculty of Business and Commerce, Kansai University 7 August 2015 Online at https://mpra.ub.uni-muenchen.de/66003/
More informationEcon 101A Final Exam We May 9, 2012.
Econ 101A Final Exam We May 9, 2012. You have 3 hours to answer the questions in the final exam. We will collect the exams at 2.30 sharp. Show your work, and good luck! Problem 1. Utility Maximization.
More informationVolume 29, Issue 1. Second-mover advantage under strategic subsidy policy in a third market model
Volume 29 Issue 1 Second-mover advantage under strategic subsidy policy in a third market model Kojun Hamada Faculty of Economics Niigata University Abstract This paper examines which of the Stackelberg
More informationUC Berkeley Haas School of Business Game Theory (EMBA 296 & EWMBA 211) Summer 2016
UC Berkeley Haas School of Business Game Theory (EMBA 296 & EWMBA 211) Summer 2016 More on strategic games and extensive games with perfect information Block 2 Jun 11, 2017 Auctions results Histogram of
More informationAS/ECON 2350 S2 N Answers to Mid term Exam July time : 1 hour. Do all 4 questions. All count equally.
AS/ECON 2350 S2 N Answers to Mid term Exam July 2017 time : 1 hour Do all 4 questions. All count equally. Q1. Monopoly is inefficient because the monopoly s owner makes high profits, and the monopoly s
More informationOligopoly. Johan Stennek
Oligopoly Johan Stennek 1 Oligopoly Example: Zocord Reduces cholesterol Produced by Merck & Co Patent expired in April 2003 (in Sweden) Other companies started to sell perfect copies (= containing exactly
More informationThe Timing of Endogenous Wage Setting under Bertrand Competition in a Unionized Mixed Duopoly
MPRA Munich Personal RePEc Archive The Timing of Endogenous Wage Setting under Bertrand Competition in a Unionized Mixed Duopoly Choi, Kangsik 22. January 2010 Online at http://mpra.ub.uni-muenchen.de/20205/
More informationCompetitive Markets. Market supply Competitive equilibrium Total surplus and efficiency Taxes and subsidies Price maintenance Application: Imports
Competitive Markets Market supply Competitive equilibrium Total surplus and efficiency Taxes and subsidies Price maintenance Application: Imports Three fundamental characteristics 1) Price taking behaviour:
More informationGame Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati.
Game Theory and Economics Prof. Dr. Debarshi Das Department of Humanities and Social Sciences Indian Institute of Technology, Guwahati. Module No. # 06 Illustrations of Extensive Games and Nash Equilibrium
More informationMicroeconomic Theory August 2013 Applied Economics. Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY. Applied Economics Graduate Program
Ph.D. PRELIMINARY EXAMINATION MICROECONOMIC THEORY Applied Economics Graduate Program August 2013 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationIMPERFECT COMPETITION AND TRADE POLICY
IMPERFECT COMPETITION AND TRADE POLICY Once there is imperfect competition in trade models, what happens if trade policies are introduced? A literature has grown up around this, often described as strategic
More informationMicroeconomics II. CIDE, MsC Economics. List of Problems
Microeconomics II CIDE, MsC Economics List of Problems 1. There are three people, Amy (A), Bart (B) and Chris (C): A and B have hats. These three people are arranged in a room so that B can see everything
More informationM.Phil. Game theory: Problem set II. These problems are designed for discussions in the classes of Week 8 of Michaelmas term. 1
M.Phil. Game theory: Problem set II These problems are designed for discussions in the classes of Week 8 of Michaelmas term.. Private Provision of Public Good. Consider the following public good game:
More informationEconS Micro Theory I 1 Recitation #7 - Competitive Markets
EconS 50 - Micro Theory I Recitation #7 - Competitive Markets Exercise. Exercise.5, NS: Suppose that the demand for stilts is given by Q = ; 500 50P and that the long-run total operating costs of each
More informationFee versus royalty licensing in a Cournot duopoly model
Economics Letters 60 (998) 55 6 Fee versus royalty licensing in a Cournot duopoly model X. Henry Wang* Department of Economics, University of Missouri, Columbia, MO 65, USA Received 6 February 997; accepted
More informationI. Introduction and definitions
Economics 335 March 7, 1999 Notes 7: Noncooperative Oligopoly Models I. Introduction and definitions A. Definition A noncooperative oligopoly is a market where a small number of firms act independently,
More informationAdvanced Microeconomic Theory EC104
Advanced Microeconomic Theory EC104 Problem Set 1 1. Each of n farmers can costlessly produce as much wheat as she chooses. Suppose that the kth farmer produces W k, so that the total amount of what produced
More informationAnswers to June 11, 2012 Microeconomics Prelim
Answers to June, Microeconomics Prelim. Consider an economy with two consumers, and. Each consumer consumes only grapes and wine and can use grapes as an input to produce wine. Grapes used as input cannot
More informationIn Class Exercises. Problem 1
In Class Exercises Problem 1 A group of n students go to a restaurant. Each person will simultaneously choose his own meal but the total bill will be shared amongst all the students. If a student chooses
More informationAdvanced Microeconomics
Advanced Microeconomics Price and quantity competition Harald Wiese University of Leipzig Harald Wiese (University of Leipzig) Advanced Microeconomics 1 / 92 Part C. Games and industrial organization 1
More informationCredibility and Subgame Perfect Equilibrium
Chapter 7 Credibility and Subgame Perfect Equilibrium 1 Subgames and their equilibria The concept of subgames Equilibrium of a subgame Credibility problems: threats you have no incentives to carry out
More informationFIRST PUBLIC EXAMINATION
A10282W1 FIRST PUBLIC EXAMINATION Preliminary Examination for Philosophy, Politics and Economics Preliminary Examination for Economics and Management Preliminary Examination for History and Economics SECOND
More informationGS/ECON 5010 section B Answers to Assignment 3 November 2012
GS/ECON 5010 section B Answers to Assignment 3 November 01 Q1. What is the profit function, and the long run supply function, f a perfectly competitive firm with a production function f(x 1, x ) = ln x
More informationEcon 101A Final exam Mo 18 May, 2009.
Econ 101A Final exam Mo 18 May, 2009. Do not turn the page until instructed to. Do not forget to write Problems 1 and 2 in the first Blue Book and Problems 3 and 4 in the second Blue Book. 1 Econ 101A
More informationSHORTER PAPERS. Tariffs versus Quotas under Market Price Uncertainty. Hung-Yi Chen and Hong Hwang. 1 Introduction
SHORTER PAPERS Tariffs versus Quotas under Market Price Uncertainty Hung-Yi Chen and Hong Hwang Soochow University, Taipei; National Taiwan University and Academia Sinica, Taipei Abstract: This paper compares
More informationAnalysis of a highly migratory fish stocks fishery: a game theoretic approach
Analysis of a highly migratory fish stocks fishery: a game theoretic approach Toyokazu Naito and Stephen Polasky* Oregon State University Address: Department of Agricultural and Resource Economics Oregon
More informationLicense and Entry Decisions for a Firm with a Cost Advantage in an International Duopoly under Convex Cost Functions
Journal of Economics and Management, 2018, Vol. 14, No. 1, 1-31 License and Entry Decisions for a Firm with a Cost Advantage in an International Duopoly under Convex Cost Functions Masahiko Hattori Faculty
More informationPrice discrimination in asymmetric Cournot oligopoly
Price discrimination in asymmetric Cournot oligopoly Barna Bakó Corvinus University of Budapest e-mail: Department of Microeconomics Fővám tér 8 H-1085 Budapest, Hungary, barna.bako@uni-corvinus.hu Abstract
More informationMohammad Hossein Manshaei 1394
Mohammad Hossein Manshaei manshaei@gmail.com 1394 Let s play sequentially! 1. Sequential vs Simultaneous Moves. Extensive Forms (Trees) 3. Analyzing Dynamic Games: Backward Induction 4. Moral Hazard 5.
More informationOnline Appendix to R&D and the Incentives from Merger and Acquisition Activity *
Online Appendix to R&D and the Incentives from Merger and Acquisition Activity * Index Section 1: High bargaining power of the small firm Page 1 Section 2: Analysis of Multiple Small Firms and 1 Large
More informationOn supply function competition in a mixed oligopoly
MPRA Munich Personal RePEc Archive On supply function competition in a mixed oligopoly Carlos Gutiérrez-Hita and José Vicente-Pérez University of Alicante 7 January 2018 Online at https://mpra.ub.uni-muenchen.de/83792/
More informationProfitable Mergers. in Cournot and Stackelberg Markets:
Working Paper Series No.79, Faculty of Economics, Niigata University Profitable Mergers in Cournot and Stackelberg Markets: 80 Percent Share Rule Revisited Kojun Hamada and Yasuhiro Takarada Series No.79
More informationTrade Liberalization and Labor Unions
Open economies review 14: 5 9, 2003 c 2003 Kluwer Academic Publishers. Printed in The Netherlands. Trade Liberalization and Labor Unions TORU KIKUCHI kikuchi@econ.kobe-u.ac.jp Graduate School of Economics,
More informationPublic Schemes for Efficiency in Oligopolistic Markets
経済研究 ( 明治学院大学 ) 第 155 号 2018 年 Public Schemes for Efficiency in Oligopolistic Markets Jinryo TAKASAKI I Introduction Many governments have been attempting to make public sectors more efficient. Some socialistic
More informationInternational Economics B 6. Applications of international oligopoly models
.. International Economics B 6. Applications of international oligopoly models Akihiko Yanase (Graduate School of Economics) November 24, 2016 1 / 24 Applications of international oligopoly models Strategic
More information