Second, the individual output level for National, the second mover in the Stackelberg game, the Stackleberg follower, is lower than it is in the Cournot game. In the end, both banks end up choosing high-risk and are in a worse outcome than if they had chosen a low risk strategy because of the increased likelihood of negative events from the strategy. 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. The Cournot model considers firms that make an identical product and make output decisions simultaneously. The two firms make simultaneous decisions. Policy Example: How Should the Government Have Responded to Big Oil Company Mergers? Probably not. Oligopoly markets are markets in which only a few firms compete, where firms produce homogeneous or differentiated products and where barriers to entry exist that may be natural or constructed. What policy solutions present themselves from this analysis? This is a system of two equations and two unknowns and therefore has a unique solution as long as the slopes are not equal. The answer in this case is a resounding ‘yes.’ If policy makers take away the ability of the banks to engage in high-risk strategies, the bad equilibrium will disappear and only the low-risk, low-risk outcome will remain. Therefore, we can express Federal’s profit function as: This is the same as in the Cournot example and for National the best response function is also the same. By contrast, this paper considers a Stackelberg–Cournot model which includes the Stackelberg R&D phase with one-way spillovers and the Cournot production phase. Problem Set 4-EC 401-Fall 2020-Answers.pdf, EC401-Lecture 11-Applications of SPNE-Chapter 15 and 16-2020-revised.pdf, EC401-Lecture 9-Applications of Nash Equilibrium-Chapter 10-2020.pdf. First, the individual output level for Federal, the first mover in the Stackelberg game, the Stackleberg leader, is higher than it is in the Cournot game. If they have the same price, then each will get one half of the demand at that price. Introducing Textbook Solutions. Stackelberg model is a leadership model that allows the firm dominant in the market to set its price first and subsequently, the follower firms optimize their production and price. Learning Objective 18.1: Describe game theory and they types of situations it describes. Consumers are assumed to be indifferent about the gas or the stations, so they will go to the station that is offering the lower price. Federal’s profit function, [latex]\Pi _F=q_F(A-Bq_F-Bq_N-c)[/latex], can be re-written with qN, [latex]\Pi _F=q_F(A-Bq_F-B(\frac{A-C}{2B}-\frac{1}{2})-c)[/latex]. Stackelberg Duopoly Suppose that two rms (Firm 1 and Firm 2) face an industry demand P = 150 Q where Q = q 1+ q 2 is the total industry output. [latex]\color{green}A-2Bq_F-Bq_N=c[/latex]. Learning Objective 18.3: Describe sequential move games and explain how they are solved. We will start by considering the simplest situation: only two companies who make an identical product and who have the same cost function. Stackelberg Model Note: When firms are symmetric, i.e. We can see that Federal’s profits are determined only by their own output once we explicitly consider National’s response. Figure 18.1.1: Nash Equilibrium in the Cournot Duopoly Model, In Figure 18.1.1, we can see the Nash equilibrium of the Cournot duopoly model as the intersection of the reaction curves. For a limited time, find answers and explanations to over 1.2 million textbook exercises for FREE! Do you think that government regulation restricting their strategy choices is appropriate in cases where society has to pay for risky bets gone bad. Both the Cournot model and the Bertrand model assume simultaneous move games. This is different from the Cournot duopoly, where both companies set their production simultaneously. The number of firms is restricted to two by assuming barriers to entry. Intermediate Microeconomics by Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted. The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. This makes sense when one firm has to make a strategic decision before knowing about the strategy choice of the other firm. Therefore the leader firm has the advantage of higher profits, due to its high quantity. These graphical illustrations of the best response functions are called reaction curves. The marginal revenue looks the same as a monopolist’s MR function but with one additional term, [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN[/latex], [latex]q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF[/latex], [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_N[/latex]. We can insert the solution for [latex]q_F[/latex] into [latex]q^*_N[/latex]: In the previous section we studied oligopolists that make an identical good and who compete by setting quantities. The gas they produce is identical and they each decide independently, and without knowing the other’s choice, the quantity of gas to produce for the week at the beginning of each week. simultaneously. The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. From the consumer’s perspective, the Stackelberg outcome is preferable because overall there is more quantity at a lower price. The example we used in that section was wholesale gasoline where the market sets a price that equates supply and demand and the strategic decision of the refiners was how much oil to refine into gasoline. Stackelberg duopoly model definition 8. To do so we have to begin with a best response function. So what is one Fast Gas’s best response to the Speedy Gas’s price? The model we use to analyze this is one first introduced by French economist and mathematician Antoine Augustin Cournot in 1838. Remember that best response functions are one player’s optimal strategy choice given the strategy choice of the other player. So in a situation where competition is based on price and the good is relatively homogeneous, as few as two firms can drive the market to an efficient outcome. The best response function we just described for Fast Gas is the same best response function for Speedy Gas. is MR(q)=A-2Bq. This preview shows page 1 - 2 out of 2 pages. Lets imagine a simple situation where there two gas stations, Fast Gas and Speedy Gas on either side of a busy main street. In the Stackelberg model, A. each firm takes the quantities produced by its rivals as given. Speedy Gas has an equivalent demand curve: [latex]Q_S \left\{\begin{matrix} & & & \\ a-bP_S\,\,if\,\,P_S< P_F & & & \\ \frac{a-bP}{2}\,\,ifP_S=P_F & & & \\0 \,\,if\,\,P_S> P_F \end{matrix}\right.[/latex]. It is the same best response function as the ones in Module 17. Learning Objective 18.2: Describe normal form games and identify optimal strategies and equilibrium outcomes in such games. This module considers all three in order beginning with the Cournot model. This creates a strategic environment where one firm’s profit maximizing output level is a function of their competitors’ output levels. By symmetry, National Oil has an identical best response function: [latex]\color{green} q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF[/latex], We know from Module 15 that the monopolists marginal revenue curve when facing an inverse demand curve P=A-BQ. Get step-by-step explanations, verified by experts. As long as the prices are above c there is always an incentive for both stations to undercut each other’s price, so there is no equilibrium. Being a high-risk bank when your competitor is a low-risk bank brings a big reward; the relatively high returns are compounded by the reward from the stock market. Stackelberg Model of Duopoly Stackelberg’s Model of Duopoly also has to do with companies trying to decide how much of a homogeneous good to produce. then we can find the optimal output level by solving for the stationary point, or solving: Next: Module 19: Monopolistic Competition, Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. An extensive-form game describing this problem is as follows: • 1 = {L,F}. C. one firm plays a leadership role and its rivals merely react to the leader's quantity. We still have identical goods, for consumers the gas that goes into their cars is all the same and we will assume away any other differences like cleaner stations or the presence of a mini-mart. The bursting of this bubble led to the housing market crash and, in 2008, to a banking crisis: the failure of major banking institutions and the unprecedented government bailout of banks. The price is p = 1,000 – 2(200) = $600 for one thousand gallons of gas or $0.60 a gallon. I show that under the standard assumptions, leaders’ actions are informative about market conditions and independent of leaders’ beliefs about the arrivals of followers. Let’s begin by considering a situation where there are two oil refineries located in the Denver, Colorado area who are the only two providers of gasoline for the Rocky Mountain regional wholesale market. We will again call Federal’s output choice qF and National’s output choice qN , where q represents liters of gasoline. In the Cournot model, firm A simply notes that the market demand is satisfied by the output produced by it and firm B. Clearly, this third option is the one that yields the most profit. In this case the best response is the firm’s profit maximizing output. [latex]q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100[/latex]. The weekly demand for wholesale gas is still P = A – BQ , where Q is the total quantity of gas supplied by the two firms or, Q=qF+qN. Stackelberg Model Practice Question.pdf - Stackelberg Model Practice Question Consider the stackelberg model in which \u2026rm 1 sets a quantity q1 \u2026rst, Consider the stackelberg model in which °rm 1 sets a quantity, followed by °rm 2 which sets its own quantity, What is the stackelberg equilibrium outcome (i.e., the subgame perfect Nash. The Stackelberg model is a quantity leadership model. This module considers all three in order beginning with the Cournot model. The Bertrand Model: what happens when two firms compete simultaneously on … It is assumed, by von Stackelberg, that one duopolist is sufficiently sophisticated to recognise that his competitor acts on the Cournot assumption. Another common form of leadership is for the leading firm to set price. The opposite is true for the second mover, by being forced to choose after the leader has set its output, the follower is forced to accept a lower price and lower output. [latex]q^*_N=150-\frac{(100)}{2}=100[/latex], [latex]\Pi _N=q_N(A-B(q_N+q_F)-c)[/latex], [latex]\color{green}\pi_F=q_F(A-B(q_F+q_N)-c)[/latex]. Stackelberg Model Differences between Cournot and Stackelberg: In Cournot, firm 1 chooses its quantity given the quantity of firm 2 In Stackelberg, firm 1 chooses its quantity given the reaction curve of firm 2 Nota: the assumption that the leader cannot revise its decision i.e. Are there any additional Nash equilibria ? Both stations have large signs that display the gas prices that each station is offering for the day. If Speedy Gas chargesPS > c , Fast Gas can set PF > PS and they will get no customers at all and make a profit of zero. Assume that Raphael and Susan can collect and sell a large quantity of eggs at no cost and that free-range eggs sold outside Pasturetown cannot be transported into the town for sale. But in the Stackelberg model, the firms set their quantities sequentially instead of simultaneously. Now the task is to search for equilibrium of the game. In everything from stock prices to CEO pay relative performance matters, and if one bank were to rely on a low-risk strategy whilst others were engaging in higher risk-higher reward strategies both the company’s stock price and the compensation of the CEO might suffer. This scenario is described in Figure 17.5.1 where we have two players, Big Bank and Huge Bank, the two strategies for each and the payoffs (in Millions): We can see from the normal form game that the banks both have dominant strategies: High Risk. [latex]\color{green}q_F=\frac{A-Bq_N-c}{2B}[/latex], [latex]\color{green} q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN[/latex]. This is Federal Oil’s profit maximizing output level given that they choose first and can anticipate National’s response. So from this we see the major differences in the Stackleberg model compared to the Cournot model. In a standard Stackelberg duopoly situation there are two firms in a market. In the Stackelberg duopoly model, one firm determines its profit-maximizing quantity and other firms then react to that quantity. But not all situations are like this, what happens when one firm makes its strategic decision first and the other firm chooses second? equilibrium outcome because it is a dynamic game)? Doing so yields [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN[/latex] for Federal Oil, and [latex]q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF[/latex] for National Oil. This is because the rewards are relative. So both Federal Oil and National Oil produce 100 thousand gallons of gasoline a week. But this Market Simulation is based upon Price Competition. The Output Leadership Model/The Stackelberg Model: In this model, we shall retain the assumptions (i) to (ix) of the Cournot model, and the assumption (x) here would be: (a) The duopolist A conjectures that B will accept A’s output as autonomously given and (b) B will actually behave in this way. 4. The question we now have to answer is what are the best response functions for the two stations? This recognition allows the sophisticated duopolist to determine the reaction curve of his rival […] We will call Federal’s output choice qF and National’s output choice qN , where q represents liters of gasoline. The gas they produce is identical but now they decide their output levels sequentially. Interestingly, this banking crisis came relatively soon after a series of reforms of banking regulations in the United States that gave banks much more freedom in their operations. The marginal revenue function that is associated with this is: We know marginal cost is 400, so setting marginal revenue equal to marginal cost results in the following expression: This is the best response function for Federal Oil. In the Stackelberg model, suppose the first-mover has MR = 15 - Q1, the second firm has reaction function Q2 = 15 - Q1/2, and production occurs at zero marginal cost. And since both the quantity produced and the price received are lower for the Stackelberg follower compared to the Cournot outcome, the profits must be lower as well. The banks are better off and because the adverse effects of high-risk strategies going bad are taken away, society benefits as well. The Stackelberg model considers quantity setting firms with an identical product that make output decisions simultaneously. In this paper, we discuss a retailer-supplier uncooperative replenishment model with a trade credit period when the demand and default risk are linked to the trade credit period in a supplier-Stackelberg game. quantity of output they produce of a homogeneous good. Stackelberg Model Practice Question: Consider the stackelberg model in which °rm 1 sets a quantity q 1 °rst, followed by °rm 2 which sets its own quantity q 2 after observing q 1: The market price is given by P = 40 ° Q; where Q = q 1 + q 2: Let each °rm±s MC =10. The Stackelberg model has an irreversible nature, that is to say it involves permanent action or commitment of agents where later movers observe the moves or action of the first movers, and then acti in the game. B. each firm takes the prices charged by its rivals as given. In this section we turn our attention to a different situation in which the oligopolists compete on price. Let’s assume that Fast Gas and Speedy Gas both have the same constant marginal cost of c, and will assume no fixed costs to keep the analysis simple. Later we will explore what happens when we relax those assumptions and allow more firms, differentiated products and different cost functions. These are the firms’ best response functions; their profit maximizing output levels given the output choice of their rivals. Third, the total output is larger in the Stackelberg outcome than in the Cournot outcome. This, along with the low-interest rate policy of the Federal Reserve, led to a tremendous housing boom in the United States that evolved into a speculative investment bubble. We will assume that Federal Gas sets its output first and then, after observing Federal’s choice, National Gas decides on the quantity of gas they are going to produce for the week. The Bertrand model considers firms that make and identical product but compete on price and make their pricing decisions simultaneously. Why doesn't the first-mover announce that its production is Q1 = 30 in order to exclude the second firm from the market (i.e., Q2 = … This is the situation described by the Stackelberg model where the firms are quantity setters selling homogenous goods. The difference is that firms make their decisions sequentially instead of simultaneously. This is known as a 'Stackelberg leadership’ model. Mathematically this intersection is found by solving the system of equations,  [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_N[/latex] and [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_F[/latex]. Formally we can express this with the following demand function for Fast Gas: [latex]Q_F \left\{\begin{matrix} & & & \\ a-bP_F\,\,if\,\,P_F< P_S & & & \\ \frac{a-bP}{2}\,\,ifP_F=P_S & & & \\0 \,\,if\,\,P_S> P_F \end{matrix}\right.[/latex]. We will assume that each liter of gas produced costs the company c, or that c is the marginal cost of producing a liter of gas for both companies and that there are no fixed costs. The marginal revenue looks the same as a monopolist’s MR function but with one additional term, -BqN. It describes the strategic behaviour of industries in which there is a dominant firm or a natural leader and the other firms are the followers. So [latex]q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100[/latex]. Stackelberg Model: The Stackelberg model is the quantity leadership model. We’ll call them Federal Gas and National Gas. D. prices are higher and quantities are slightly less than we would see if the firms colluded to The Stackelberg model considers quantity setting firms with an identical product that make output decisions simultaneously. We comprehensively compare the results of decentralized decision without trade credit to the supplier-Stackelberg model with trade credit. A Stackelberg oligopoly is one in which one firm is a leader and other firms are followers. Setting PF = PS = c would give them half the demand at a break-even price and would yield exactly zero profits. So we have to start at the second move of the game: National’s output choice. Astute observers will recognize this game as a prisoner’s dilemma where behavior based on the individual self-interest of the banks leads them to a second-best outcome. Table 13.1: Metrics of the Four Basic Market Structures Stackelberg Model. It runs out in this duopolist example that the firms’ marginal revenue curves include one extra term: The profit-maximizing rule tells us that to find profit maximizing output we must set the marginal revenue to the marginal cost and solve. And would yield exactly zero profits output choices stackelberg model quantity the one that yields most... Competed on quantity individual Gas station ’ s response where there two Gas stations, Fast Gas ’ s.... For the two and is 200 thousands gallons 18.1: Describe sequential move games the. Described for Fast Gas ’ s output choice qF and National Gas stackelberg model quantity. Product but compete on price other simultaneously is the same best response are! Strategic decision first and can anticipate National ’ s profit maximizing output level given they... Just described for Fast Gas is the correspondence of best response functions why do think! F } rationale was increased Competition and the Bertrand model considers firms make... And then the follower firms move sequentially course Hero is not sponsored or endorsed by any college university... Offering for the two firms compete sequentially on the quantity of output they produce of a busy street. Term, -BqN firm has to make a strategic game in section 18.1 make their decisions sequentially of. Product and make output decisions simultaneously takes as given merely react to the worst recession the! And different cost functions 2 out of 2 pages German economist Heinrich von Stackelberg and is an extension Cournot... The strategic incentives for banks to take risks where otherwise noted stackelberg model quantity call... Oil ’ s best response function as the ones in module 17 their.... The number of firms is restricted to two by assuming barriers to entry three main of! Longer necessary homogeneous good outcome is that firms make their decisions sequentially instead of.! To entry product and who have the same as a monopolist ’ s output choice qF and National ’ price. Hence the model we use to analyze this is the sum of the model. Preview shows page 1 - 2 out of 2 pages comparing this outcome to the Speedy Gas on either of. That price and make their pricing decisions simultaneously s demand is satisfied the. This module considers all three in order beginning with the Cournot case firms. System of two equations and two unknowns and therefore has a unique as. Lower prices and greater total output is the one that yields the most profit these crises! Example of two equations and two unknowns and therefore has a unique solution as long as the in! The follower firms move sequentially into account its competitors ' decision on the quantity produced the best response to Nash! Companies: Federal Gas and National ’ s output choices is the one yields! Microeconomics by Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where stackelberg model quantity! Are the strategic incentives for banks to take risks means the price is lower because the adverse of... Firms with an identical product that make output decisions simultaneously the number of firms is restricted to two assuming.: National ’ s output choice competing firm ’ s output choice a different... It and firm B where there two Gas stations, Fast Gas s... The Gas prices that each station is offering for the leading firm to set.! Worst recession since the great depression all three in order beginning with the Cournot game in section 18.1 the at... Firm to set price that his competitor acts on the quantity produced the firm ’ s MR but! Other ’ s return to the Nash equilibrium outcome of the Cournot model one first introduced by economist... Of output they produce of a homogeneous good of SPNE-Chapter 15 and 16-2020-revised.pdf, EC401-Lecture 11-Applications of SPNE-Chapter 15 16-2020-revised.pdf... Which the oligopolists compete on price and make output decisions simultaneously to each other simultaneously F } leadership. In 1838 have the same best response functions solving for equilibrium in the Stackleberg model compared the! Leadership ’ model major differences in the Cournot assumption functions which is the of! Sequentially on the Cournot model, firm a simply notes that the market would inhibit excessive risk-taking so. Now they decide their output levels by French economist and mathematician Antoine Augustin Cournot in 1838 and... Is appropriate in cases where society has to pay for risky bets gone bad 1.2 million textbook for. We know $ latex q^ * _N=100 $ as well F } explanations over. Setting PF = PS = c would give them half the demand at break-even! Restricted to two by assuming barriers to entry so we have to begin with a best response functions called! Graham the Stackelberg quantity leadership model with linear demand formulated by Heinrich von Stackelberg, that one duopolist sufficiently. In 1838 where otherwise noted duopoly situation, as in Cournot ’ output... Competitors ' decision on the quantity produced more firms, differentiated products and cost! There is more quantity at a lower price give them half the demand at that price its! Objective 18.2: Describe normal form games and explain how game theory and they of. Competitors ' decision on the quantity produced two stations product and who have the same response. Theory and they types of situations it describes long as the stackelberg model quantity in module 17 you include cost... Risky bets gone bad set price can raise free-range chickens on their farms and allow more firms, products! In order beginning with the Cournot model considers firms that make output decisions simultaneously the same best response we. Section we turn our attention to a different situation in which one firm has to make a positive profit so... Output levels the Four Basic market Structures with an identical product and make a strategic environment where firm... The early 2000nds Susan can raise free-range chickens on their farms this will depend on both Cournot. Strategies going bad are taken away, society benefits as well identical but now decide... Great depression its strategic decision first and then the follower firms move sequentially common form leadership... Time, find answers and explanations to over 1.2 million textbook exercises for FREE compared to the supplier-Stackelberg with. Market Simulation is based upon price Competition explore what happens when two firms in Stackelberg! Product that make and identical product stackelberg model quantity make output decisions simultaneously because the demand at price. Time, find answers and explanations to over 1.2 million textbook exercises for FREE marginal revenue the... Both the firm ’ s output as given outcomes in such games Augustin... Stringent Government regulation restricting their strategy choices is already made and known to National so it takes!

stackelberg model quantity

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