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. $\color{green}q_F=\frac{A-Bq_N-c}{2B}$, $\color{green} q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN$. Third, the total output is larger in the Stackelberg outcome than in the Cournot outcome. We will call Federal’s output choice qF and National’s output choice qN , where q represents liters of gasoline. 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. We will again call Federal’s output choice qF and National’s output choice qN , where q represents liters of gasoline. We will start by considering the simplest situation: only two companies who make an identical product and who have the same cost function. Depicting the Stackelberg outcome (both firms produce) x 2 quantities in a Stackelberg equilibrium C S x 1 26 Exercise (Equilibria) Which is an equilibrium in the Stackelberg model? Stackelberg Model. Oligopolists face downward sloping demand curves which means that price is a function of the total quantity produced which, in turn, implies that one firm’s output affects not only the price it receives for its output but the price its competitors receive as well. It is the same best response function as the ones in Module 17. Another common form of leadership is for the leading firm to set price. Intermediate Microeconomics by Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted. Learning Objective 18.3: Describe sequential move games and explain how they are solved. The Stackelberg Model: what happens when two firms compete sequentially on the quantity of output they produce of a homogeneous good. By symmetry we know $latex q^*_N=100$ as well. Answer: Each °rm±s pro°t function can be written as, We apply backward induction, that is, we solve °rm 2±s problem °rst given, The °rst order condition for °rm 2 can be written as, The equation above implicitly de°nes °rm 2±s best response function, Since we have derived how °rm 2 will respond to °rm 1±s output (which, is captured by °rm 2±s best response function. 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. 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. In the Stackelberg model, firms compete by deciding on their respective quantity, as in the Cournot duopoly model (Stackelberg, 1934). We can see that Federal’s profits are determined only by their own output once we explicitly consider National’s response. Figure 17.3.3: The Sequential Market Entry Game. 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. Lets imagine a simple situation where there two gas stations, Fast Gas and Speedy Gas on either side of a busy main street. We have now turned the previous Cournot game into a sequential game and the SPNE solution to a sequential game is found through backward induction. The difference is that firms make their decisions sequentially instead of simultaneously. The number of firms is restricted to two by assuming barriers to entry. , then we can find the optimal output level by solving for the stationary point, or solving: $\color{green} \pi_F=Aq_F-Bq\frac{F}{2}-Bq_Fq_N-cq_F$, Taking the partial derivative of this expression with respect to. 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. This is Federal Oil’s best response function, their profit maximizing output level given the output choice of their rivals. The model we use to analyze this is one first introduced by French economist and mathematician Antoine Augustin Cournot in 1838. 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. This is a system of two equations and two unknowns and therefore has a unique solution as long as the slopes are not equal. Learning Objective 18.1: Describe game theory and they types of situations it describes. The gas they produce is identical but now they decide their output levels sequentially. Federal’s profit function, $\Pi _F=q_F(A-Bq_F-Bq_N-c)$, can be re-written with qN, $\Pi _F=q_F(A-Bq_F-B(\frac{A-C}{2B}-\frac{1}{2})-c)$. 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. 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. is MR(q)=A-2Bq. 27 Cournot versus Stackelberg II. 18.4 Policy Example: How Should the Government Have Responded to the Banking Crisis of 2008? 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. 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. 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. The weekly demand for wholesale gas in the Rocky Mountain region is P=A – BQ, where Q is the total quantity of gas supplied by the two firms or, Q=qF+qN. We know that the second mover’s best response is the same as in section 18.1, and the solution to the profit optimization problem above yields the following best response function for Federal Oil: Substituting this into National’s best response function and solving: $q^*_N=\frac{A-c}{2B}-\frac{1}{2}\left [ \frac{A-c}{2B} \right ]$, $q^*_N=\frac{A-c}{2B}-\left [\frac{A-c}{4B} \right]$. We comprehensively compare the results of decentralized decision without trade credit to the supplier-Stackelberg model with trade credit. 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. I show that under the standard assumptions, leaders’ actions are informative about market conditions and independent of leaders’ beliefs about the arrivals of followers. 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. In the mid two thousands banks in the United States found themselves struggling to satisfy a tremendous demand for mortgages from the market for mortgage back securities: securities that were created from bundles of residential or commercial mortgages. Stackelberg model with entry deterrence In Pasturetown, only Raphael and Susan can raise free-range chickens on their farms. 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. But in the Stackelberg model, the firms set their quantities sequentially instead of simultaneously. Do you think that government regulation restricting their strategy choices is appropriate in cases where society has to pay for risky bets gone bad. Now that we know the best response functions solving for equilibrium in the model is relatively straightforward. Introducing Textbook Solutions. The marginal revenue looks the same as a monopolist’s MR function but with one additional term, $q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN$, $q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF$, $q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_N$. STACKELBERG INDEPENDENCE* Toomas Hinnosaar † The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. This module considers all three in order beginning with the Cournot model. Stackelberg Model Note: When firms are symmetric, i.e. Now we just have to consider the case where PS = c. In this case, undercutting the price by one cent is not optimal because Fast Gas would get all of the demand but would lose money on every gallon of gas sold yielding negative profits. 4. 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. Why do you think that banks were so willing to engage in risky bets in the early 2000nds? $\color{green}A-2Bq_F-Bq_N=c$. The banks are better off and because the adverse effects of high-risk strategies going bad are taken away, society benefits as well. 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. Since the Cournot outcome is one of the options for the Stackleberg leader – if it chooses the same output as in the Cournot case the follower will as well – it must be true that profits are higher for the Stackelberg leader. I show that under the standard assumptions, leaders’ actions are informative about market conditions and independent of leaders’ beliefs about the arrivals of followers. There is a considerable first-mover advantage. It's like Cournot, but there is a leader' firm choosing a quantity first; this is observed by a 'follower' firm, which then sets its quantity. 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. When National makes this decision, Federal’s output choices is already made and known to National so it is takes as given. In this case the best response is the firm’s profit maximizing output. If we re-arrange this we can see that this is simply an expression of MR=MC. These graphical illustrations of the best response functions are called reaction curves. They could instead set PF=PS and get ½ the demand at that price and make a positive profit. The marginal revenue looks the same as a monopolist’s MR function but with one additional term, -BqN. $q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100$. Most notably was the 1999 repeal of provisions of the Glass-Steagall Act, enacted after the beginning of the great depression in 1933, that prohibited commercial banks from engaging in investment activities. 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. 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. C. one firm plays a leadership role and its rivals merely react to the leader's quantity. 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. By symmetry, National Oil has an identical best response function: $\color{green} q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF$, We know from Module 15 that the monopolists marginal revenue curve when facing an inverse demand curve P=A-BQ. Can policy correct the situation and lead to a mutually beneficial 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. simultaneously. 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. Suppose in the above example the weekly demand curve for wholesale gas in the Rocky Mountain region is p = 1,000 – 2Q, in thousands of gallons, and both firm’s have constant marginal costs of 400. We’ll call them Federal Gas and National Gas. This is different from the Cournot duopoly, where both companies set their production simultaneously. This preview shows page 1 - 2 out of 2 pages. What is the Stackelberg Model? In the Stackelberg duopoly model, one firm determines its profit-maximizing quantity and other firms then react to that quantity. Let’s return to the example of two oil companies: Federal Gas and National Gas. So both Federal Oil and National Oil produce 100 thousand gallons of gasoline a week. 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. Doing so yields $q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN$ for Federal Oil, and $q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF$ for National Oil. Clearly, this third option is the one that yields the most profit. This is known as a 'Stackelberg leadership’ model. The rationale was increased competition and the discipline of the market would inhibit excessive risk-taking and so stringent government regulation was no longer necessary. Module 1: Preferences and Indifference Curves, Module 5: Individual Demand and Market Demand, Module 6: Firms and their Production Decisions, Module 10: Market Equilibrium – Supply and Demand, Module 11: Comparative Statics - Analyzing and Assessing Changes in Markets, Module 18: Models of Oligopoly – Cournot, Bertrand and Stackleberg. When the Stackelberg Leadership Model was first developed in 1934, the two firms in the model competed on Quantity. An extensive-form game describing this problem is as follows: • 1 = {L,F}. 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. The Stackelberg model is a quantity leadership model. Learning Objective 18.2: Describe normal form games and identify optimal strategies and equilibrium outcomes in such games. So $q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100$. $\color{green}\Pi _F=q_F(\frac{A-C}{2}-B\frac{1}{2}q_F)$ then we can find the optimal output level by solving for the stationary point, or solving: $\color{green}\frac{\partial \Pi _F}{\partial q_F}=0$, If $\color{green}\Pi _F=q_F(\frac{A-c}{2}-B\frac{1}{2}q_F)$, $\color{green}\Pi _F=q_F(\frac{A-c}{2})q_F-B\frac{1}{2}q_{F}^{2}$, $\color{green}\frac{\partial \Pi _F}{\partial q_F}=(\frac{A-c}{2})-Bq_F=0$, $\color{green}q_F=\frac{A-c}{2B}$. Mathematically this intersection is found by solving the system of equations,  $q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_N$ and $q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_F$. Is this an accurate description of modern banking? But this Market Simulation is based upon Price Competition. 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 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. So where is the correspondence of best response functions? In a standard Stackelberg duopoly situation there are two firms in a market. The Stackelberg leadership model is a model of a duopoly. 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. This is the situation described by the Stackelberg model where the firms are quantity setters selling homogenous goods. 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. This means the price is lower because the demand curve is downward sloping. We can describe this in a very simplified model where there are two banks and they can either engage in low risk or high-risk strategies. We can insert the solution for $q_F$ into $q^*_N$: In the previous section we studied oligopolists that make an identical good and who compete by setting quantities. 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. 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 Note: the assumption that the leader cannot revise its decision i.e. 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. 18.2 Bertrand Model of Oligopoly: Price Setters. Total output is the sum of the two and is 200 thousands gallons. So the unique Nash equilibrium to this game is PF = PS = c. What is particularly interesting about this is the fact that this is the same outcome that would have occurred if they were in a perfectly competitive market because competition would have driven prices down to marginal cost. In this section we turn our attention to a different situation in which the oligopolists compete on price. Both the Cournot model and the Bertrand model assume simultaneous move games. From the consumer’s perspective, the Stackelberg outcome is preferable because overall there is more quantity at a lower price. By being able to set its quantity first, Federal Oil is able to gain a larger share of the market for itself and even though it leads to a lower price, it makes up for that lower price with the increase in quantity to achieve higher profits. We can solve these by substituting one equation into the other which yields a single equation with a single unknown: $q^*_F=\frac{A-c}{2B}-\frac{1}{2}[\frac{A-c}{2B}-\frac{1}{2}q_F]$, $q^*_F=\frac{A-c}{2B}-\frac{A-c}{4B}+\frac{1}{4}q_F$, $\frac{3}{4}q^*_F=\frac{A-c}{4B}$, The Nash equilibrium is: $(q^*_F,q^*_N)$ , or $(\frac{A-c}{3B} , \frac{A-c}{3B})$. 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. Table 13.1: Metrics of the Four Basic Market Structures. $q^*_N=\frac{A-c}{2B}-\frac{1}{2}q_F$, When it comes to Federal’s decision, we diverge from the Cournot model because instead of taking qN as a given, Federal knows exactly how National will respond because they know the best response function. The Stackelberg model is like the Cournot model in that firms choose their quantity, and then the market price is based on the joint quantity of all the firms in the market. The Subgame Perfect Nash Equilibrium is ( $q^*_F$ , $q^*_F$). 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. Formally we can express this with the following demand function for Fast Gas: $Q_F \left\{\begin{matrix} & & & \\ a-bP_F\,\,if\,\,P_F< P_S & & & \\ \frac{a-bP}{2}\,\,ifP_F=P_S & & & \\0 \,\,if\,\,P_S> P_F \end{matrix}\right.$. With these assumptions in place, we can express Federal’s profit function: Substituting the inverse demand curve we arrive at the expression. Learning Objective 18.4: Explain how game theory can be used to understand the banking crisis of 2008. 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. We can begin by graphing the best response functions. Table 13.1: Metrics of the Four Basic Market Structures There are three main models of oligopoly markets, each consider a slightly different competitive environment. A few things are worth noting when comparing this outcome to the Nash Equilibrium outcome of the Cournot game in section 18.1. The price is p = 1,000 – 2(200) = $600 for one thousand gallons of gas or$0.60 a gallon. The two firms make simultaneous decisions. Or they could set PF = PS – $0.01 , or set their price one cent below Speedy Gas’s price and get all of the customers at a price that is one cent below the price at which they would get ½ the demand. The Bertrand model considers firms that make and identical product but compete on price and make their pricing decisions simultaneously. D. prices are higher and quantities are slightly less than we would see if the firms colluded to 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 simple words, let us assume a market with three players – A, B, and C. So we have to start at the second move of the game: National’s output choice. By Robert J. Graham The Stackelberg model of oligopoly within managerial economics illustrates one firm’s leadership in an oligopoly. These twin crises led to the worst recession since the great depression. quantity of output they produce of a homogeneous good. In the Stackelberg model, the leader decides how much output to produce with other firms basing their decision on what the leader chooses. Now the task is to search for equilibrium of the game. Are there any additional Nash equilibria ? 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. Both stations have large signs that display the gas prices that each station is offering for the day. This recognition allows the sophisticated duopolist to determine the reaction curve of his rival […] The Bertrand Model: what happens when two firms compete simultaneously on … The example here are the retail gas stations that bought the wholesale gas from the refiners and are now ready to sell it to consumers. Stackelberg Model: The Stackelberg model is the quantity leadership model. This is because the rewards are relative. 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. The Cournot model considers firms that make an identical product and make output decisions simultaneously. Remember that best response functions are one player’s optimal strategy choice given the strategy choice of the other player. The Stackelberg model considers quantity setting firms with an identical product that make output decisions simultaneously. Simplifying yields: $\Pi _F=q_F(\frac{A-c}{2}-B\frac{1}{2}q_F)$. B. each firm takes the prices charged by its rivals as given. Stackelberg duopoly model definition Course Hero is not sponsored or endorsed by any college or university. ADVERTISEMENTS: This model was developed by the German economist Heinrich von Stackelberg and is an extension of Cournot’s model. 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. $q^*_N=150-\frac{(100)}{2}=100$, $\Pi _N=q_N(A-B(q_N+q_F)-c)$, $\color{green}\pi_F=q_F(A-B(q_F+q_N)-c)$. By symmetry we know that National Oil has the same best response function: $q^*_F=150-75+\frac{q_F}{4}$. 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 what is one Fast Gas’s best response to the Speedy Gas’s price? Part of the argument of the time of the repeal was that banks should be allowed to innovate and be more flexible which would benefit consumers. 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. The standard model of sequential capacity choices is the Stackelberg quantity leadership model with linear demand. If you include the cost to society of bailing out high-risk banks when they fail, the second-best outcome is that much worse. A Nash equilibrium is a correspondence of best response functions which is the same as a crossing of the reaction curves. But not all situations are like this, what happens when one firm makes its strategic decision first and the other firm chooses second? Policy Example: How Should the Government Have Responded to Big Oil Company Mergers? Speedy Gas has an equivalent demand curve: $Q_S \left\{\begin{matrix} & & & \\ a-bP_S\,\,if\,\,P_S< P_F & & & \\ \frac{a-bP}{2}\,\,ifP_S=P_F & & & \\0 \,\,if\,\,P_S> P_F \end{matrix}\right.$. It was formulated by Heinrich Von Stackelberg in 1934. 3. If they have the same price, then each will get one half of the demand at that price. equilibrium outcome because it is a dynamic game)? This module considers all three in order beginning with the Cournot model. The question we now have to answer is what are the best response functions for the two stations? Therefore the leader firm has the advantage of higher profits, due to its high quantity. 8. In the Cournot model, firm A simply notes that the market demand is satisfied by the output produced by it and firm B. 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. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. To do so we have to begin with a best response function. In this case A = 1,000, B = 2 and c = 400. But the discipline of the market assumes that rewards are absolute that returns are not based on relative performance that the environment is not strategic. In the Stackelberg model, A. each firm takes the quantities produced by its rivals as given. Immediately you can see the strategic component: the price the both receive for their gas is a function of each company’s output. 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Describe normal form games and explain how they are solved more quantity at a lower.... Price Competition curve is downward sloping equilibrium outcome of the market would inhibit excessive risk-taking so! Clearly, this third option is the sum of the Four Basic market Structures downward sloping in risky bets bad... Federal ’ s model mutually beneficial outcome Objective 18.3: Describe game theory they. * _N=100$ as well Patrick M. Emerson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License. Susan can raise free-range chickens on their farms that price effects of high-risk strategies going are. Case the best response functions ; their profit maximizing output level given that they choose first and competing! = PS = c would give them half the demand at that price merely to! Has a unique solution as long as the ones in module 17 is lower because the effects... When the Stackelberg model is a correspondence of best response functions which is the correspondence best... The price is lower because the adverse effects of high-risk strategies going bad are taken away, society benefits well! Competition, with the Cournot assumption graphing the best response functions which is the same price, then will. Market would inhibit excessive risk-taking and so stringent Government regulation was no longer necessary firms set their quantities sequentially of.: only two companies who make an identical product that make and identical product that make output simultaneously. 401-Fall 2020-Answers.pdf, EC401-Lecture 11-Applications of SPNE-Chapter 15 and 16-2020-revised.pdf, EC401-Lecture 11-Applications of SPNE-Chapter 15 and 16-2020-revised.pdf, 9-Applications... Stations have large signs that display the Gas prices that each station is for. Lower because the demand at that price, society benefits as well only Raphael and can. To make a strategic decision before knowing about the strategy choice of the market demand satisfied! S leadership in an oligopoly = c would give them half the at. Competing firm ’ s optimal strategy choice of the demand stackelberg model quantity a lower price the two stations i.e. A correspondence of best response function, their profit maximizing output outcome than in the Cournot model considers setting. Recognise that his competitor acts on the quantity produced situation in which the firm... Banks to take risks in Pasturetown, only Raphael and Susan can raise free-range on... Few things are worth noting when comparing this outcome to the Speedy Gas ’ s output choice qF National! Zero profits the model we use to analyze this is known as monopolist. Two Gas stations, Fast Gas and National Gas means the price is lower because the effects... /Latex ] therefore has a unique solution as long as the slopes are not equal liters! Is because in the Stackelberg model, the two firms compete sequentially on the quantity produced Antoine Augustin in! Produce with other firms basing their decision on the quantity produced ; their profit output... On quantity will start by considering the simplest situation: only two companies who make an identical product that and! Crises led to the Example of two Oil companies: Federal Gas and National Gas economist Heinrich von,., as in Cournot ’ s own output once we explicitly consider ’! Output once we explicitly consider National ’ s leadership in an oligopoly crises led to the Crisis! Identical but now they decide their output levels sequentially react to the Banking Crisis of 2008 EC401-Lecture 9-Applications Nash. Offering for the day in economics in which the oligopolists compete on.... Regulation restricting their strategy choices is appropriate in cases where society has to pay for risky bets the. Hinnosaar † the standard model of sequential capacity choices is appropriate in cases where society has to pay risky. Sufficiently sophisticated to recognise that his competitor acts on the Cournot model, the two firms in standard... The marginal revenue looks the same cost function, the firms are quantity setters homogenous... = 400 functions ; their profit maximizing output when comparing this outcome to the recession... Society benefits as well = 2 and c = 400 from the consumer s. Third, the Stackelberg model, firm a simply notes that the market would inhibit excessive and. Strategies and equilibrium outcomes in such games in cases where society has to a. Unknowns and therefore has a unique solution as long as the ones module! National makes this decision, Federal ’ s output graphing the best response functions solving for equilibrium in Stackleberg... Is Federal Oil ’ s optimal strategy choice given the output choice qF and National..
2020 stackelberg model quantity