# 3.2. Cournot Model

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3.2. Cournot Model. Matilde Machado. 3.2. Cournot Model. Presumptions: All organizations deliver a homogenous item The business sector cost is thusly the aftereffect of the aggregate supply (same cost for all organizations) Firms choose at the same time the amount to create

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3.2. Cournot Model Assumptions: All organizations create a homogenous item The market cost is accordingly the consequence of the aggregate supply (same cost for all organizations) Firms choose all the while the amount to deliver Quantity is the key variable. In the event that OPEC was not a cartel, then oil extraction would be a decent case of Cournot rivalry. Horticultural items? http://www.iser.osaka-u.ac.jp/library/dp/2010/DP0766.pdf ? The balance idea utilized is Nash Equilibrium (Cournot-Nash) 3.2. Cournot Model

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3.2. Cournot Model Graphically: Let's expect the duopoly case (n=2) MC=c Residual request of firm 1: RD 1 (p,q 2 )=D(p)- q 2 . The issue of the firm with remaining interest RD is like the monopolist's. 3.2. Cournot Model

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3.2. Cournot Model Graphically (cont.): P p* D(p) MC RD1(q2) = Residual request q* 1 = R 1 (q 2 ) q 2 MR 3.2. Cournot Model

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3.2. Cournot Model Graphically (cont.): q* 1 (q 2 )=R 1 (q 2 ) is the ideal amount as a component of q 2 Let's take 2 extraordinary cases q 2 : Case I: q 2 =0 RD 1 (p,0)=D(p) entire request  q* 1 (0)=q M Firm 1 ought to create the Monopolist's amount 3.2. Cournot Model

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3.2. Cournot Model D(p) Case 2: q 2 =q c RD 1 (p,q c )=D(p)- q c Residual Demand q c D(p) MR<MC q* 1 =0 q c MR 3.2. Cournot Model

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3.2. Cournot Model Note: If both request and cost capacities are straight, response capacity will be direct also. q1 Reaction capacity of firm 1 q M q* 1 (q2) q c q2 3.2. Cournot Model

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3.2. Cournot Model If firms are symmetric then the harmony is in the 45º line, the response bends are symmetric and q* 1 =q* 2 q1 q c q1=q2 q* 2 (q 1 ) q M q* 1 E q* 1 (q2) 45º q M q c q* 2 q2 3.2. Cournot Model

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3.2. Cournot Model Comparison between Cournot, Monopoly and Perfect Competition q M <q N <q c q1 q c q* 2 (q 1 ) q 1 +q 2 =q N q 1 +q 2 =q c q M q* 1 (q 2 ) q M q 1 +q 2 =q N q c q2 q 1 +q 2 =q M 3.2. Cournot Model

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3.2. Cournot Model Derivation of the Cournot Equilibrium for n=2 P=a-bQ=a-b(q 1 +q 2 ) MC 1 =MC 2 =c For firm 1: Takes the system of firm 2 as given, i.e. takes q 2 as a steady. Take note of the leftover request here Reaction capacity of firm 1: ideal amount firm 1 ought to deliver given q2. On the off chance that q2 changes, q1 changes too . 3.2. Cournot Model

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3.2. Cournot Model We take care of a comparative issue for firm 2 and get an arrangement of 2 conditions and 2 factors. On the off chance that organizations are symmetric, then Solution of the Symmetric harmony 3.2. Cournot Model

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3.2. Cournot Model Solution of the Symmetric harmony 3.2. Cournot Model

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3.2. Cournot Model Comparing with Monopoly and Perfect Competition Where we acquire that: In flawless rivalry costs increment 1-to-1 with expenses. 3.2. Cournot Model

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3.2. Cournot Model In the Case of n  2 firms: If all organizations are symmetric: 3.2. Cournot Model

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3.2. Cournot Model Total amount and the balance cost are: If the quantity of firms in the oligopoly joins to ∞, the Nash-Cournot balance unites to immaculate rivalry. The model is, along these lines, hearty since with n→ ∞ the states of the model concur with those of the ideal rivalry. 3.2. Cournot Model

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3.2. Cournot Model DWL in the Cournot demonstrate = a rea where the ability to pay is higher than MC p N DWL c Q N q c When the quantity of firms unites to unendingness, the DWL focalizes to zero, which is the same as in Perfect Competition. The DWL diminishes speedier than either cost or amount (rate of n 2 ) 3.2. Cournot Model

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3.2. Cournot Model In the Asymmetric duopoly case with consistent minor expenses. The FOC (from where we determine the response capacities): Replace q 2 in the response capacity of firm 1 and illuminate for q 1 3.2. Cournot Model

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3.2. Cournot Model In the Asymmetric duopoly case with steady minimal expenses. Which we supplant back in q 2 : 3.2. Cournot Model

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3.2. Cournot Model From the harmony amounts we may infer that: If c 1 <c 2 (i.e. firm 1 is more effective): In Cournot, the firm with the biggest piece of the overall industry is the most productive 3.2. Cournot Model

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3.2. Cournot Model From the past outcome, the more effective firm is likewise the one with a bigger value Mcost edge: 3.2. Cournot Model

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3.2. Cournot Model Comparative Statics: The yield of a firm ↓ when: ↑ possess costs ↓ expenses of adversary q 2 ↑ c 1 Shifts the response bend of firm 1 to one side R 1 E' E ↑q* 2 and ↓q* 1 R 2 q 1 3.2. Cournot Model

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3.2. Cournot Model Profits are: Increase with opponent's costs Decrease with claim costs Symmetric to firm 2. 3.2. Cournot Model

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3.2. Cournot Model More for the most part… for any request and cost work. There is a negative externality between Cournot firms. Firms don't disguise the impact that an expansion in the amount they create has on alternate firms. That is when ↑q i the firm brings down the cost to each firm in the market (take note of that the great is homogenous). From the perspective of the business (i.e. of max the aggregate benefit) there will be extreme creation . Externality: firms just consider the impact of the value change in their own yield. At that point their yield is higher than what might be ideal from the business' perspective. 3.2. Cournot Model

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3.2. Cournot Model If we characterize the Lerner record of the market just like: the Herfindhal Concentration Index 3.2. Cournot Model

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3.2. Cournot Model The positive connection amongst benefit and the Herfindhal Concentration Index under Cournot: Remember the FOC for each firm in that industry can be composed as: The far reaching benefits are then: The fixation record is up to a consistent a correct measure of industry gainfulness. 3.2. Cournot Model

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3.2. Cournot Model Note: The Cournot model is in many cases censured on the grounds that in actuality firms have a tendency to pick costs not amounts. The response to this feedback is that when the cournot model is changed to fuse two periods, the principal where firms pick limit and the second where firms contend in costs. This two period display gives an indistinguishable result from the basic Cournot demonstrate. 3.2. Cournot Model