The essence of the Cournot model is that each duopolist treats the output level of its competitor as fixed and then decides how much to produce. Privacy Policy 9. Similarly, an iso-profit curve for firm 2 is the locus of points of different levels of output of two competitors which yield to firm 2 the same level of profit, as shown in Fig. We can begin by graphing the best response functions. To nd rm 1’s best response to any given output q2 of rm 2, we need to study rm 1’s prot as a function of its output q1 for given values of q2.If q2 = 0 then rm 1’s prot is p1(q1, 0) = q1(a c q1) for q1 a, a quadratic function that Do you think that government regulation restricting their strategy choices is appropriate in cases where society has to pay for risky bets gone bad. Probably not. 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. Each firm has to decide how much to produce, and the two firms take their decisions at the same time. The Cournot equilibrium is a stable one, provided firm l’s reaction curve is that of firm 2. Plagiarism Prevention 5. [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]Â. , then we can find the optimal output level by solving for the stationary point, or solving: [latex]\color{green} \pi_F=Aq_F-Bq\frac{F}{2}-Bq_Fq_N-cq_F[/latex], Taking the partial derivative of this expression with respect to, The marginal revenue looks the same as a monopolist’s MR function but with one additional term,Â, [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}qN[/latex]Â,  [latex]q^*_N=\frac{A-c}{2B}-\frac{1}{2}qF[/latex]Â,  [latex]q^*_F=\frac{A-c}{2B}-\frac{1}{2}q_N[/latex]Â, [latex]q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100[/latex].Â. The total quantity supplied by all firms then determines the market price. Cournot’s adjustment process is somewhat unrealistic. This means the price is lower because the demand curve is downward sloping. In the Cournot model it is the quantity, not price which is adjusted, with one firm altering its output on the assumption that his rival’s output will remain unchanged. • Compared to perfect competition – Firms face downward sloping demand and thus can Let us suppose the two firms are initially producing output levels that differ from the Cournot equilibrium. Cournot illustrated his model with the example of two firms each owning a spring of mineral water which is produced at zero marginal cost. The Cournot model does not say anything about the dynamics of the adjustment process, i.e., whether the firms adjust their output until the Cournot equilibrium is reached. Cournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. Firm 1’s profit- maximising output is thus a decreasing function of how much it thinks firm 2 will produce. Given its forecast, each firm then chooses a profit-maximising output for itself. His duopoly model consists of two firms marketing a homogenous good. In Cournot’s classic duopoly model, the two players set their quantity independently. Although the basic model is rather simple, its provides useful insights into industries with a small number of firms. If prices can easily be changed, Cournot’s model may thus better capture firms’ strategic reasoning. So what is one Fast Gas’s best response to the Speedy Gas’s price? So the market price will depend on the total output of both firms. Through such movements in a the ‘stair step fashion’, we trace out an adjustment process which converges to the Cournot equilibrium point (E). 18.2 Bertrand Model of Oligopoly: Price Setters. Stackelberg’s Duopoly 5. This makes sense when one firm has to make a strategic decision before knowing about the strategy choice of the other firm. Since there are only two players, they would tend to be highly responsive to competitors’ strategies. If you include the cost to society of bailing out high-risk banks when they fail, the second-best outcome is that much worse. We know that in the Cournot model each firm has to forecast the other firm’s output choice. Cournot’s analysis shows that two firms would react to each other’s output changes until they eventually reached a stable output position from which neither would wish to depart. Similarly, we can derive firm 2’s reaction curve as: which gives firm 2’s optimal choice of output for a given expectation about firm 1’s output, q1e. It is treated as the classical solution to the duopoly problem. Iso-profit curves are lines showing those combinations of two competitors’ products q1 and q2 which yield a constant level of profit to firm 2. The Cournot model is a model of oligopoly in which firms produce a homogeneous good, assuming that the competitor’s output is fixed when deciding how much to produce. The Stackelberg model considers quantity setting firms with an identical product that make output decisions simultaneously. 24.2. 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. Report a Violation 11. 3.2. Each reaction curve shows the relationship between a firm’s profit-maximising output and the amount it thinks its competitor will produce. This is why modern economists generalize the presentation of the Cournot model by using the reaction curves approach. We … Account Disable 12. 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 Subgame Perfect Nash Equilibrium is ( [latex]q^*_F[/latex] , [latex]q^*_F[/latex]). Is this an accurate description of modern banking? With these assumptions in place, we can express Federal’s profit function: Substituting the inverse demand curve we arrive at the expression. 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. The Cournot model considers firms that make an identical product and make output decisions simultaneously. then we can find the optimal output level by solving for the stationary point, or solving: Taking the partial derivative of this expression with respect toÂ, Next: Module 19: Monopolistic Competition, Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. If they have the same price, then each will get one half of the demand at that price. In such a situation the Cournot model will generate sub-optimal outcome. 18.3 Stackelberg Model of Oligopoly: First Mover Advantage. In equilibrium, each firm sets output according to its own reaction curve. The reason why there are few firms in this type of model is because the entry and exit are difficult. Let us suppose there are n firms and industry output Q is the joint contribution of all the firms, i.e., Q = q1 + q2 + … qn. [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]. To increase market power and profits, the two players may engage in collusive cooperation. Cournot competition wikipedia. So where is the correspondence of best response functions? A Nash equilibrium is a correspondence of best response functions which is the same as a crossing of the reaction curves. Thus when using the Cournot model, we must, therefore, confine ourselves to the behaviour of firms in equilibrium. [latex]\color{green}\Pi _F=q_F(\frac{A-C}{2}-B\frac{1}{2}q_F)[/latex] then we can find the optimal output level by solving for the stationary point, or solving: [latex]\color{green}\frac{\partial \Pi _F}{\partial q_F}=0[/latex], If [latex]\color{green}\Pi _F=q_F(\frac{A-c}{2}-B\frac{1}{2}q_F)[/latex], [latex]\color{green}\Pi _F=q_F(\frac{A-c}{2})q_F-B\frac{1}{2}q_{F}^{2}[/latex], [latex]\color{green}\frac{\partial \Pi _F}{\partial q_F}=(\frac{A-c}{2})-Bq_F=0[/latex], [latex]\color{green}q_F=\frac{A-c}{2B}[/latex]. 24.1. Let’s consider a specific example. 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. Each duopolist acts as if his rival’s output were fixed. 24.2. The Cournot oligopoly model is the most popular model of imperfect competition. The model may be presented in many ways. The gas they produce is identical but now they decide their output levels sequentially. Both the Cournot model and the Bertrand model assume simultaneous move games. 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. And it is a model of symmetric oligopoly. 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. Cournot’s equilibrium (which indi­cates how much output will each firm produce) is determined by the intersec­tion of the two reaction curves (point E). A fully solved example showing how to find the Nash equilibrium in the Cournot model of oligopoly with two firms. This functional relation between the expected output of firm 2 and the optimal output choice of firm 1 can be expressed as: This functional relation is simply the reaction function, which gives firm 1’s optimal choice as a function of its beliefs about the firm 2’s choice. In this case A = 1,000, B = 2 and c = 400. In truth, during any adjustment process, the central assumption of the model (i.e., each firm can assume that its competitor’s output remains fixed) will not hold. The profit-maximisation problem of firm 1 is then: For any given belief about the output level of firm 2, q2e there will be some optimal choice of output for firm 1, q1. The case in which n = 2 is considered in another example. The original model leaves a few questions unanswered. If firm 1 decides to produce q1 units of output, it expects that the total output produced will be Q = q1 + q2e and industry output will yield a market price of p (Q) = p (q1 + q2e). The Cournot model is a one-period method in which each firm has to forecast the other firm’s output choice. This means that for each level of firm 1’s output (q1), firm 2 will choose the level of output (q2) that put it on the iso-profit curve farthest to the left as illustrated in Fig. A Cournot equilibrium is a Nash equilibrium to the Cournot model. These are the firms’ best response functions; their profit maximizing output levels given the output choice of their rivals. Uploader Agreement. Each firm’s reaction curve tells us how much to produce, given the output of its competitor. So both Federal Oil and National Oil produce 100 thousand gallons of gasoline a week. Cournot’s model of oligopoly is one of the oldest theories of the behaviour of the individual firm and relates to non-collusive oligopoly. 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. 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. Here we assume that each firm has an expectation about the output choices of the other firms. Cournot's duopoly model (with diagram). In the Cournot model, firms choose quantities simultaneously and independently, and industry output determines price through demand. So the equilibrium condition is the same as that of a monopolist, i.e., MR = MC, where MR = p(Q) [1 – 1/|e(Q)|]. Learning Objective 18.3: Describe sequential move games and explain how they are solved. Can policy correct the situation and lead to a mutually beneficial outcome? The basic behavioural assumption of the model is that each duopolist maximises his profit on the assumption that the quantity produced by his rival is invariant with respect to his own quantity decision. Cournot Model Total quantity and the equilibrium price are: 1 N N n c N N n n a c a c Q nq q n b b n a c a n p a bQ a b c c →∞ →∞ − − = = → = + − = − = − = + → Industrial Economics-Matilde Machado 3.2. 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. 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. The original version is quite limited in that it makes the assumption that the duopolists have identical products and identical costs. Actually Cournot illustrated his model with the example of two firms each owning a spring of mineral water, which is produced at zero costs. Now let's imagine non-cooperative case, but now let's imagine not just two choices, but realistically, there's a whole set of choices. What are the firms' outputs in a Nash equilibrium of Cournot's model? If we re-arrange this we can see that this is simply an expression of MR=MC. These twin crises led to the worst recession since the great depression. 24.1. 24.3 (point E). Why do you think that banks were so willing to engage in risky bets in the early 2000nds? An iso-profit curve for firm 1 is the locus of points indicating different levels of output of firm 1 and its rival firm 2, which yield to firm 1 the same level of profit, as shown in Fig. So [latex]q^*_F=\frac{A-c}{3B}=\frac{1,000-400}{(3)(2)}=\frac{600}{6}=100[/latex]. By symmetry we know $latex q^*_N=100$ as well. But at PF = PS = c both stations are playing their best response to each other simultaneously. Image Guidelines 4. It takes this intuition and puts it into the optimizing math we've been doing so far in this class. List of oligopoly models: 1. If equilibrium is supposed to be reached through a sequence of finite adjustments, only one duopolist sets an output to start with; this induces the other to adjust its output which, in turn, induces the first firm to adjust its output once again, and the process goals so on and on. Immediately you can see the strategic component: the price the both receive for their gas is a function of each company’s output. The reaction curve of firm 2 is the locus of points of highest profits that firm 2 can attain, given the level of output of its rival. We can see that Federal’s profits are determined only by their own output once we explicitly consider National’s response. 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. We call the resulting set of output levels Cournot equilibrium. – A duopoly is an oligopoly with only two firms. 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. 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. 1. This approach is based on the concept of iso-profit curves of the competitors, which are a type of indifference curves of the profit-maximising firms. 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. These graphical illustrations of the best response functions are called reaction curves. The original model was presented in a simple way by assuming that two firms (called duopolists) have identical products and identical costs. Bertrand’s Duopoly Model 3. It will charge a lower price than a monopoly but a higher price than a Bertrand oligopoly. The distinctive feature of the different oligopoly models is the way they attempt to capture the interdependence of firms in the market.
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