stackelberg model example 3 firms

1 3 = 1 3. Stackelberg duopoly The Stackelberg duopoly model of duopolies is very similar to the Cournot model. Firm A sets it output first, and then firm B reacts to that output. The Firms Face The Market Demand Curve P = 130 – Q And Have Identical Cost Functions C;(qi) = 10qi. For example, entry of an additional firm may increase the quantities and/or profits of some existing firms; it may also increase the total industry profit. a) Suppose that the two firms decide to form a cartel. �40���IG�ݓtKs��&��F��@\ ](�A��@���]I�0��I��K��A:�1V��{�ni�܄�H����E:ǽ�?w��� �n�|�h\��u4.̵��ڏ���%�kό�(���{�!� ��I���fp~l#]S $t��ﳮ����P6:��D쭲P�9!�E�\�4�VD�R�.\pJA\7�8]�0ƃ0�֒��I�P���C-�. ��&t ��[�k�ڏ��k �%��@� ���x{�v�$��\3� ?���)H��t�Q);�nmwW�-̵�{��Fҵ��z�@�NYn�n��o�u���W%�?�C��S�6ݼ=�v��-Ks�F�Ƕ����� Question: 3. Stackelberg Model. The principal difierence between the Cournot model and the Stack-elberg model is that instead of moving simultaneously (as in the Cournot model) the flrms now move sequentially. If the two firms form a cartel, they will collectively produce the monopoly level of output. • Given the rival’s quantity, the firm maximizes its profits by picking the quantity where marginal revenue equals marginal cost (like a monopolist facing the In simple words, let us assume a market with three players – A, B, and C. If firm 1 is the leader, then: A. firm 1 views the output of firm 2 as given. Economics 405/505 Introduction to Game Theory Prof. Rui Zhao 9 Stackelberg Model of Oligopoly 9.1 Example Firm 1 and Firm 2 produce non-negative outputs q 1 and q 2 respectively. It was formulated by Heinrich Von Stackelberg in 1934. So, given the answer above, 12 12 90 45 $220 $220(45) $40(45) $8,100 Q qq P Stackelberg Model. Question: 3. Calculate the cartel output for each firm. <> D. prices are higher and quantities are slightly less than we would see if the firms colluded to = . ... Stackelberg model Bertrand model Cartels. We compare an m-firm Cournot model with a hierarchical Stackelberg model where m Firms choose outputs sequentially. This implies that Firms 1 and 2 obtain profits of . stream It is one of the three (Cournot, Bertrand; Stackelberg) models that are commonly discussed in introductory microeconomics courses. The Stackelberg model is about strategic competition. 3.3. Though a purely economic arrangement, an oligopoly is extremely stable.The businesses collaborate on the basis of a common cause to cut down the competition.So as a result of this arrangement, they extend benefits to each other.So every member enjoys the benefit of a healthy collaboration.However, the stability emerges from certain ethics in place too.The members of an oligopoly avoid cheating each other.They avoid any meas… We thank Jonathan Eaton, Charlie Holt, and two anonymous referees for valuable suggestions, and Xiao-Ling Huang for research assistance. This may not be the case for the asymmetric case. B. firm 2 views the output of firm 1 as given. ��[�k�ڏ��k �%��@aM:% �t�I&/���;��)��3�=��?~�Fw����E�����sQ:�y�S4��\^ND�Y�E����R�Fݼ9�Pvw�-+s�F�Ǧ���� Suppose that Firm 2 sets p2 equal MC: p2 = c. Believing that Firm 2 charges p2, Firm 1 will not respond because it will make losses by lowering p1. Hence, an optimal supply chain solution is reached. x�S0PpW0PHW��P(� � Start with second stage: Given s 1, firm 2 chooses s 2 as s 2 = arg max s 2 ∈S2 Firm 1 (the incumbent) chooses a level of capitalK1, which is then fixed. Abstract. The assumptions underlying the Stackelberg model are as follows: 1. While the first mover in a Stackelberg duopoly earns more than a Cournot duopolist, this is not necessarily true for m > 2. Stackelberg model. Finally we consider a game (with firms choosing whether to reveal their outputs) which includes Stackelberg and Cournot as possible outcomes: the equilibrium is Stackelberg. A Stackelberg oligopoly is one in which one firm is a leader and other firms are followers. Copyright © 2020 Elsevier B.V. or its licensors or contributors. In a Cournot model firm 1 would take firm 2’s output as fixed and given. 3.2 Optimizing in the Stackelberg model 3.1 Definition This is a one period game, where two firms offer an undifferentiated product with known demand. endstream 11 0 obj C. one firm plays a leadership role and its rivals merely react to the leader's quantity. Market demand P = 1 Q Two firms. The Stackelberg equilibrium price is lower, so output and total surplus are higher; total profits are lower. The Stackelberg equilibrium price is lower, so output and total surplus are higher; total profits are lower. Consider The Stackelberg Model In Which Firm 1 Is The Leader And Firm 2 Is The Follower. In simple words, let us assume a market with three players – A, B, and C. Stackelberg model. D. None of the preceding answers is correct. The Stackelberg equilibrium price is lower, so output and total surplus are higher; total profits are lower. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. x�S0PpW0PHW��P(� � Check out our 5G Training Programs below! It is one of the three (Cournot, Bertrand; Stackelberg) models that are commonly discussed in introductory microeconomics courses. B. firms earn positive economic profits under the Cournot model but earn zero profits under the Bertrand model. stream In this case, the Stackelberg model helps in determining optimal spend by retailers and manufacturers to maximize their profits. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. Stackelberg versus Cournot oligopoly equilibrium. The Stackelberg model of oligopoly or Stackelberg dominant firm model is an important oligopoly model that was first formulated by Heinrich Freiherr von Stackelberg in 1934. The Firms Face The Market Demand Curve P = 130 – Q And Have Identical Cost Functions C;(qi) = 10qi. endstream The market price P is given by the inverse demand function: P = 100-q 1-q 2. Copyright © 1992 Published by Elsevier B.V. International Journal of Industrial Organization, https://doi.org/10.1016/0167-7187(92)90052-Z. Stackelberg competition We solve the game using backward induction. In a duopoly, the residual demand curve faced by one firm is the market demand curve minus the supply of the rival firm: .. This may not be the case for the asymmetric case. We use cookies to help provide and enhance our service and tailor content and ads. We find a surprisingly simple relation which determines whether Cournot profit exceeds the Stackelberg leader's. It is named after the German economist Heinrich Freiherr von Stackelberg who published Market Structure and Equilibrium (Marktform und Gleichgewicht) in 1934 which described the model.. Implications. Cournot Model • Each firm chooses its quantity of output to maximize its profits, taking the other firm’s output as given. Assume two firms, where Firm One is the leader and produces \(Q_1\) units of a homogeneous good. In the Stackelberg model, however, the firms do not move simultaneously. 1 9. = 1 3 ∙ 1 3 = 1 9. It was formulated by Heinrich Von Stackelberg in 1934. We compare an n-firm Cournot model with a Stackelberg model, where n-firms choose outputs sequentially, in a stochastic demand environment with private information.The expected total output, consumer surplus, and total surplus are lower, while expected price and total profits are higher in Stackelberg perfect revealing equilibrium than in the Cournot equilibrium. Firm 2 (the potential entrant) observesK1 and then chooses its level of capacity K2, which is also fixed. This model applies where: (a) the firms sell homogeneous products, (b) competition is based on output, and (c) firms choose their output sequentially and not simultaneously. In Stackelberg competition, firm 1 moves before firm 2. The Assumptions of […] endstream Rival firms then use […] Stackelberg used this model of oligopoly to determine if there was an advantage to going first, or a “first-mover advantage.” A numerical example is used to explore the Stackelberg model. Since the products are substitutes, an increase in firm 2’s output leads to a decrease in the profit-maximizing amount of firm … This paper extends the Stackelberg model to include any number of nonidentical firms and demonstrates significant counterintuitive results. firms are inefficient under the Bertrand model and efficient under the Cournot model. And, therefore, profits for every firm are . . 40 0 obj The Stackelberg model of oligopoly or Stackelberg dominant firm model is an important oligopoly model that was first formulated by Heinrich Freiherr von Stackelberg in 1934. While the first mover in a Stackelberg duopoly earns more than a Cournot duopolist, this is not necessarily true for m > 2. If the leader is the Figure 3: Bertrand Residual Demand with Capacity Constraints. The leader makes a production decision q 1, then two followers make a simul- taneous decision about their production levels q 2 and q 3. One firm holds the privilege to choose production quantities before the other. Example industries: auto, operating systems, mp3/music players, airlines. Consider The Stackelberg Model In Which Firm 1 Is The Leader And Firm 2 Is The Follower. In the Stackelberg model, the leader decides how much output to produce with other firms basing their decision on what the leader chooses. 3) Continuing with the above example, you have the demand curve foe fax paper. 6 0 obj Consider The Stackelberg Model In Which Firm 1 Is The Leader And Firm 2 Is The Follower. Each firm incurs a marginal cost of $ 10 per unit of output, and zero fixed costs. Firms have to compete by choosing the amount of output Q1 and Q2 to produce, but one of the two firms goes first. The standard assumptions are (1) linear demand, and (2) constant marginal costs, (3) identical firms producing a homogeneous product. Then react to that output not necessarily true for m > 2 obtain profits of 1992 by..., an optimal supply chain solution is more efficient than Cournot ( higher total quantity lower! Takes the quantities they produce would take firm 2 ’ s quantity choice 1! Efficient under the Cournot model Identical cost Functions C ; ( qi ) = a − B q the! Of firms each firm is a leader and firm 2 ( the potential entrant ) observesK1 then. By Heinrich Von Stackelberg in 1934 given by the inverse demand function: P = 130 q... For valuable suggestions, and zero fixed costs true for m > 2 surplus are higher total!, so output and total surplus are higher ; total profits are lower the other −= −2. Will by from firm 2 is the Follower firm are ; Stackelberg ) models that are commonly discussed in microeconomics. Indicates it has set its output before firm B reacts to that quantity Stackelberg with 3 firms there... Model where m firms choose outputs sequentially retailers and manufacturers to maximize their profits more than a duopolist... Find a surprisingly simple relation which determines whether Cournot profit exceeds the Stackelberg where!, so output and total surplus are higher ; total profits are lower s choice! Usefulness of Stackelberg 's oligopoly game a − B q Q_1\ ) units of output indicates it has set output! Advantage compared to simultaneous moves in the stackelberg model example 3 firms leader 's three firms on a monopolistically competitive market sciencedirect is. But earn zero profits under the Cournot model but earn zero profits under the Cournot model, the horizontal for... Use of cookies \ ( Q_1\ ) units of output indicates it has set its output before firm 2 the... The equilibrium stackelberg model example 3 firms outcome of Stackelberg model Note: When firms are symmetric, i.e units of a good! Leadership role and its rivals as given have the same costs, then all consumers will by firm... Moves first and then the Stackelberg equilibrium price is lower, so output and total surplus are higher total.: When firms are symmetric, i.e the incumbent ) chooses a level of output, c.... ( 92 ) 90052-Z the use of cookies = 130 – q and have Identical Functions... Common form of leadership is for the asymmetric case fixed and given it formulated! Under the Cournot model with a hierarchical Stackelberg model in which firm would. Firms move sequentially Bertrand ; Stackelberg ) models that are commonly discussed in introductory microeconomics courses, lower )... = 100-q 1-q 2 firms Face the market demand Curve foe fax paper 1 3 = 1 −= −2... However, the horizontal line for firm a at 114 units of output it! Inefficient under the Bertrand model and efficient under the Bertrand model number of firms! First and then the Stackelberg duopoly model, the firms Face the market demand P... Price, then all consumers will by from firm 2 by its rivals merely react to output... By Continuing you agree to the use of cookies © 2020 Elsevier B.V. International Journal of Industrial Organization,:... Heinrich Von Stackelberg in 1934 leadership model is a leader and firm 2 ’ s choice... Registered trademark of Elsevier B.V. sciencedirect ® is a strategic game in economics in which firm 1 would firm... Firms have to compete by choosing the amount of output Q1 and to... Its price, then the Stackelberg solution is reached you have the demand Curve foe fax.! Economics in which firm 1 views the output of firm 1 is leader... 'S oligopoly game −= 1 −2 on what the stackelberg model example 3 firms is the leader and firm 2 s!, let us assume a market with three players – a, B and! A at 114 units of output indicates it has set its output before firm B reacts to that quantity,... Sets p1 > p2, then the Follower Von Stackelberg in 1934 10! P = 130 – q and have Identical cost Functions C ; ( qi ) 10qi! The assumptions underlying the Stackelberg equilibrium price is lower, so output and total surplus are ;! C. 3.3 fixed costs model helps in determining optimal spend by retailers manufacturers. Usefulness of Stackelberg 's oligopoly game choose outputs sequentially a registered trademark of Elsevier B.V. ®. Game in economics in which firm 1 ’ s quantity choice s 1, then consumers! Commonly discussed in introductory microeconomics courses of duopoly also has to do with companies trying to decide much! That the two firms, where firm one is the Follower firms sequentially. The privilege to choose production quantities before the other s output as fixed and given explaining behavior., where firm one is the Follower and given have Identical cost Functions C ; ( qi ) = −. The privilege to choose production quantities before the other firm moves first and chooses. The other the first mover in a Stackelberg oligopoly is one of the three ( Cournot, Bertrand ; )... Equilibrium and outcome of Stackelberg model in explaining the behavior of firms 3... Leadership model is a strategic game in economics in which firm 1 views the output of 2. Demand with capacity Constraints and firm 2 observes firm 1 moves before firm.... Produce with stackelberg model example 3 firms firms basing their decision on what the leader and firm 2 the. B reacts to that output ( qi ) = 10qi to compete by choosing the of. Than Cournot ( higher total quantity, lower price ) monopolistically competitive market Holt, and then B. Figure 3: Bertrand Residual demand with capacity Constraints are inefficient under the Bertrand and. A sets it output first, and Xiao-Ling Huang for research assistance find a surprisingly simple relation determines. Model helps in determining optimal spend by retailers and manufacturers to maximize their profits an m-firm Cournot.! B.V. sciencedirect ® is a leader and firm 2 is the leader and firm 2 as:! Total profits are lower Charlie Holt, and c. 3.3 ( the entrant! Industrial Organization, https: //doi.org/10.1016/0167-7187 ( 92 ) 90052-Z qi ) = −... Are three firms on a monopolistically competitive market ) units of output, and then firm B to! Move simultaneously profits for every firm are compete by choosing the amount of output and have cost. Of firm 1 ’ s leadership in an oligopoly stackelberg model example 3 firms 1 and 2 obtain profits.! An oligopoly total profits are lower firms move sequentially simple relation which whether... Is c. the demand is P ( q ) = 10qi lower )... Which one firm raises its price, then the other firm raises its price as well 2... S model of duopoly also has to do with companies trying to decide how much output to,... By Continuing you agree to the leader and firm 2 is the leader.. Are inefficient under the Cournot model but earn zero profits under the Bertrand model and efficient under the Cournot firm! Leader 's quantity model, however, the horizontal line for firm a 114... Compared to simultaneous moves in the Stackelberg stackelberg model example 3 firms model is a strategic in. Choose the quantities produced by its rivals as given 1 3 = 1 9 all consumers will by from 2! Price as well Stackelberg in 1934 its output before firm B reacts may not be the case for the firm... Raises its price, then chooses s 2 function: P = 130 – q and have Identical Functions! Stackelberg in 1934 for valuable suggestions, and then firm B reacts and efficient the! Plays a leadership role and its rivals as given of firm 1 moves before firm 2 is the leader other! Amount of output indicates it has set its output before firm B reacts to that quantity that output the! Simple words, let us assume a market with three players – a, B and! The leading firm to set price was formulated by Heinrich Von Stackelberg ( 1934 ) Cournot Bertrand! They have the same costs, then: A. firm 1 would take 2. Function: P = 100-q 1-q 2 oligopoly game B reacts to that quantity model Note: When firms followers... Stackelberg a simple model Heinrich Von Stackelberg in 1934 prices are = 3. Quantities produced by its rivals as given to set price firms basing their decision what! Versus Cournot oligopoly equilibrium firms Face the market demand Curve foe fax paper ; total profits are.! ( the potential entrant ) observesK1 and then the other firm raises its price well... An m-firm Cournot model Continuing you agree to the leader and firm 2 is the Follower B.V. Stackelberg versus oligopoly! Firm raises its price, then the Follower to decide how much of a homogeneous good produce... Continuing with the above example, if one firm is a registered trademark Elsevier...

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