If an industry is composed of only two giant firms, each selling identical products and having half of the total market, there is every likelihood of collusion between the two firms. In some cases, competition in terms of price changes seems more logical than quantity competition, especially in the short run. Industrial organizationmatilde machado stackelberg model 15 3. Consider a stackleberg duopoly consisting of two identical firms leader and follower subscripted i 1, 2, respectively each with the cost function cq cq where c 4.
Games and economic behavior 2, 2946 1990 endogenous timing in duopoly games. Duopoly analysis by economists dates back to the 19th century. So if the firms are firm a and firm b, then the residual demand curves for each. The inverse demand for a homogeneousproduct stackelberg duopoly is p 10,000 4q. When it comes to a stackelberg equilibrium in di erential games, it is natural to consider an openloop and a feedback stackelberg equilibria. This paper considers a twostage quantitysetting duopoly model. Consider a cournot duopoly with the following inverse demand function. Obviously a duopoly is the simplest sort of oligopoly, and many of the concepts and results that we will describe can be extended to the case of an oligopoly with more than two. When firm 1 enjoys a firstmover advantage in a stackelberg duopoly, it will produce. Some of the central concepts of duopoly analysis have to do with strategic behavior, and the. Besides, one of the assumptions of cournots duopoly model is that firms supply a homogeneous product. The classical stackelberg game is extended to boundedly rational price stackelberg game, and the dynamic duopoly game model is described in detail.
The leader in a stackelberg duopoly earns at least as much profit as it would in a cournot duopoly. Comparing cournot and stackelberg duopoly hitotsubashi. Thus, if firm a makes its decision first, firm a is the industry. A profit maximization calculator for cournot duopoly, stackelberg duopoly, symmetric cartel, and folk theorem. The firms may agree on a price, or divide the market, or assign quota, or merge themselves into one unit and fo. However, such a task is extremely di cult since at least four di erential equations arise. Stackelberg duopoly with heterogeneous costs consider a. Osborne in a previous paper 1971 i studied the following problem. Considering bertrands model from a game theory perspective, it can be analysed as a. View notes stackelberg duopoly from econ 451 at purdue university. It was developed in 1934 by heinrich stackelberg in his market structure and equilibrium and represented a breaking point in the study of market structure, particularly the analysis of duopolies since it was a model based on different starting assumptions and. Stackelberg duopoly with heterogeneous costs consider a stackelberg duopoly with both firms producing a homogeneous good and facing linear demand of the form. We analyze the stability of the fixed points by numerical simulation.
Cournot calculation help needed related articles alevel business studies help a revision tips for business students gcse business studies help eight things you should be getting from a good business degree. When firms choose output quantities, there is a firstmover advantage and when firms choose prices, there is a secondmover advantage. Slutsky department of economics, university of florida, gainesville, florida 3261. Firms face a strategic setting in oligopoly markets. I have changed the values and need the model to plug my numbers in. Take the case where inverse demand is given by p12. Stackelberg model of duopoly stackelbergs model of duopoly also has to do with companies trying to decide how much of a homogeneous good to produce. Ii stacklebergs models 4 consider a stackleberg duopoly. Consider a cournot duopoly with the following inverse. Stackelberg duopoly stackelberg duopoly practice problems 1. In the simple model im using for these examples, the market demand is q 500 p and the firm both firms in this duopoly case have no fixed costs and a constant marginal cost of 150.
By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied. In the stackelberg duopoly firm a is allowed to move first and firm b can observe firm as move before making its own choice. This is a homework question, but resources online are exceedingly complicated, so i was hoping there was a fast, efficient way of solving the following question. Oligopoly chapter 27 ucsbs department of economics.
Unfortunately, neither the text files nor the pictures were successfully uploaded into here. The inverse demand curve for a stackelberg duopoly is p 5,000 3q. Oligopoly is a kind of market structure, like monopoly or perfect competition an oligopolistic industry is an industry consisting of a few rms duopoly two rms example industries. Based on this information, the stackelberg leaders reaction function is. A duopoly is the most basic form of oligopoly, a market dominated by a. A stackelberg classroom experiment abstract the timing of moves can dramatically affect firm profits and market outcomes.
Stackelbergs duopoly model with diagram article shared by trisha. Price competition in static oligopoly models we have seen how price and output are determined in perfectly competitive and monopoly markets. A duopoly or twinstick, referring to stick as jargon for a radio tower is a situation in television and radio broadcasting in which two or more stations in the same city or community share common ownership. Can someone help me with this cournot duopoly questions. The result of the model creates a paradox, known as bertrands paradox. All treatments in our experiment are based on the same stackelberg duopoly game as in huck et al. A slight increase in the marginal cost of a firm definitely leads to a reduction in its output if the firm competes in the. The stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. Pdf reciprocal strategies and aspiration levels in a. In section 5, we exerted control on the duopoly stackelberg game model. Cournot competition with two firms wolfram demonstrations. Changing the assumptions of how firms react to one another changes the decisionmaking process. Filippini 2005 looked into the optimal licensing contract for an inside.
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 stackelberg equilibrium price is lower, so output and total surplus are higher. Most markets are oligopolistic, however, where more than one but less than many firms compete for consumer business. In this sheet we set up a basic stackelberg duopoly with linear demands and constant marginal costs. Comparison of cournot, stackelberg and cartel duopoly.
Received december, 1988 simultaneous versus sequential play is studied in an extended game. And some comparisons with bertrand game with bounded rationality are also performed. To find the solution to this duopoly problem, the concept of subgame perfect equilibrium or backwards induction is needed. The firms marginal costs are identical and are given by mc i 2. Sep 29, 2011 the stackelberg leader output for firm a this time is 205. Two profitmaximizing firms, producing identical products at constant marginal cost, play a noncooperative game of perfect information all past and current outputs known complete information all costs. His model differs from cournots in that he assumes that each firm expects that the rival will keep its price constant, irrespective of its own decision about pricing. Uc berkeley economic analysis for business decisions.
The equilibrium does not hold with asymmetric cost functions since the firm with the lowest marginal cost would. In stackelberg oligopoly among the competitive companies there is a company that brings the first decision for increase or increase in output. Based on this information firm 1 and 2s reaction functions are a. Pricing and output determination under duopoly definition. The inverse demand for a homogeneousproduct stackelberg duopoly is p 16,000 4q. The horizontal axis represents and the vertical one represents.
The purpose of this paper is to take a small step for it. Consider a stackelberg duopoly with the following inverse demand function. While the first mover in a stackelberg duopoly earns more than a cournot duopolist, this is not necessarily true for m 2. The cost structures for the leader and the follower, respectively, are c l q l 3,000q l and c f q f 4,000q f a.
In the first stage, each firm independently announces its output. The inverse demand for a homogeneous product stackelberg. For these lower output levels, the profit of each firm would increase from 64 to 72. Stackelberg duopoly, also called stackelberg competition, is a model of imperfect competition based on a noncooperative game. Firms are identical and produce an homogenous product. Each firm can discount its announced output but cannot raise it. In a duopoly, the residual demand curve faced by one firm is the market demand curve minus the supply of the rival firm.
As the industry leader, the firm is able to implement its decision before its rivals. Cournot reaction functions, the cournot equilibrium at their intersection, and the two stackelberg equilbria, stackel x with the. A duopoly is a situation in which two companies own all or nearly all of the market for a given product or service. Analysis of price stackelberg duopoly game with bounded. Replying is easier on our app click here to download for free.
Each firm knows its own total cost of production, the total cost of production of the competitor and the industry demand. Cournot or stackelberg kazuhiro ohnishi institute for basic economic science, japan. Secondmover advantage and price leadership in bertrand. Download wolfram player this demonstration illustrates a simple cournot competition in which there are only two firms, and the inverse function is. In the stackelberg model of duopoly, one firm serves as the industry leader. Stackelberg equilibrium in a dynamic duopoly model. As nouns the difference between duopoly and oligopoly is that duopoly is economics a market situation in which two companies exclusively provide a particular product or service while oligopoly is an economic condition in which a small number of sellers exert control over the market of a commodity. A dynamic stackelberg duopoly model with different strategies. The cost structures for the leader and the follower, respectively, are clql 4,000ql and cf qf 6,000qf. Some of the close examples of duopoly in the present day are microsoft vs macintosh computer operations system android vs ios smartphone operating system visa vs master card payment mehods coca cola vs pepsi soft dinks making companies boei. Considering this, bertrand proposed an alternative to cournot. Consider a stackelberg duopoly with the following inverse.
Stackelberg model differences between cournot and stackelberg. Determine the equilibrium output level for both the leader and the follower. If inverse demand curve for a stackelberg duopoly is p. So if the firms are firm a and firm b, then the residual demand curves. Thus each firm is faced by the same market demand, and aims at the maximization of its own profit. The firms marginal cost are identical and given by mciqi 2qi.
The inverse demand for a homogeneous product stackelberg duopoly is p 16,000 4q. Bertrand stackelberg cartels midterm 2 bring pencilpen, bluebook, pink scantron 8 mc questions, like last time important skills. In section 4, we present the numerical simulations to verify our theoretical results. Profit r reaction functions showing the best responses to competitors choices in the case of cartel agreement, the total profit of the two firms is maximal. To recognize the chaotic behavior of the system, we give the bifurcation diagram and lyapunov exponent spectrum. The inverse demand for a homogeneousproduct stackelberg duopoly is p 12,000 4q. We compare an mfirm cournot model with a hierarchical stackelberg model where m firms choose outputs sequentially. The cost structures for the leader and the follower, respectively, are clql 4,000ql and cf qf 6,000qf a. Top 3 models of duopoly with diagram economics discussion. The stackelberg model can be solved to find the subgame perfect nash equilibrium or equilibria spne, i. This paper details the research of the cournotbertrand duopoly model with the application of nonlinear dynamics theory.
The cournot model, which shows that two firms assume each others output and treat this as a fixed amount, and produce in their own firm according to this. Secondmover advantage and price leadership in bertrand duopoly. A red line and a green line represent the best response of firms 1 and 2 for the production of another firm, respectively. The stackleberg model is just a variation of the cournot in which we assume that one firm has the ability to choose his output before the other firm takes his turn. This is because the leader selects its optimal point on the followers best response curve, whereas a cournot competitor simply accepts the point where the two best response curves cross. Wang, yang 1999, 2004 studied technology licensing issues based on bertrand and stackelberg duopoly competition models. Jun 03, 2008 sorry for the confusion the last answer i gave was for the cournot model. Stackelberg duopoly practice problems 1 consider a market with inverse demand given by. Stackelberg duopoly a sequentialmover game with respect to outputs and pro. The stackelberg leader is able to be more aggressive produce a greater share of the market when it has a lower marginal cost. Firms have to select outputs capacity in order to maximize profits. This demonstration illustrates a simple cournot competition in which there are only two firms, and the inverse function is.
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